\ » ISSSQSSSSSSSSSSS CO IE L I II S ^ II Marine Biological Laboratory Library Woods Hole, Mass. t^*^*^=V, UJ I III Presented by Little, Brown and Co. Nov. 1, If"^ I HI 111 SSE 3QSQQSSSSSSSE8 X CD 000 TOEO The Nature of the Natural Sciences JOSEF ALBERS, A Pair of Structural Constellations: A Matter of Changing Viewpoints We plunge forward into the field of fresh experience with the beliefs our ancestors and we have made already; these determine what we notice; what we notice determines what we do; what we do again determines what we experience; so from one thing to another, although the stubborn fact remains that there is a sensible flux, what is true of it seems from first to last to be largely a matter of our own creation. WILLIAM JAMES I still believe in the possibility of producing a model of reality— that is to say, a theory which will fepresent things themselves. '~" *■ ■ ' ALBERT EINSTEIN And the pursuit whose quest is Nature's understanding, has this among its rewards, that as it progresses its truth is testable. Truth is a "value." The quest itself therefore is in a measure its own satisfaction. We receive the lesson that our advance to knowledge is of asymptotic type, even as continually approaching so continually without arrival. The satisfaction shall therefore be eternal. CHARLES S. SHERRINGTON \^ ly f /V II The Nature of the NATURAL SCIENCES LEONARD K. NASH Harvard University BOSTON TORONTO Little, Brown and Company COPYRIGHT © 1963, BY LITTLE, BROWN AND COMPANY (iNC.) ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER, LIBRARY OF CONGRESS CATALOG CARD NO. 63-17432 FIRST PRINTING Published simultaneously /n Canada by Little, Brown 6- Company (Canada) Limited PRINTED IN THE UNITED STATES OF AMERICA ACKNOWLEDGMENTS The author is grateful to the following publishers for permission to use copyrighted material. To find exact information- on the source of any specific quotation, please refer to the detailed bibliography at the end of this book. George Allen & Unwin, Ltd. American Scientist American Sociological Review Basic Books, Inc. G. Bell & Sons, Ltd. British Journal for the Philos- ophy of Science Butterworth & Co., Ltd. Cambridge University Press Columbia University Press Constable and Co., Ltd. J. M. Dent & Sons, Ltd. Daedalus Diogenes Doubleday & Company, Inc. Etc., A Review of General Se- mantics Farrar, Straus & Company, Inc. Free Press of Glencoe Harper & Row, Publishers, In- corporated Harvard University Press William Heinemann, Ltd. Holt, Rinehart and Winston, Inc. Horizon Press, Inc. Hutchinson Publishing Group Library of Living Philosophers Longmans, Green & Co., Limited Lund, Humphries & Co., Ltd. Macmillan & Co., Ltd. (London) Macmillan Company (New York) McGraw-Hill Book Company, Inc. David McKay Company, Inc. W. W. Norton & Company, Inc. Open Court Publishing Com- pany Oxford University Press Pergamon Press Philosophical Library Philosophical Quarterly Sir Isaac Pitman & Sons, Ltd. Princeton University Press Routledge & Kegan Paul, Ltd. W. B. Saunders Company Scientific Monthly Simon & Schuster, Inc. \Jniversity of California Press University of Chicago Press University of Pennsylvania Press John Wiley & Sons, Inc. Yale University Press Preface ? f H^ HAT IS SCIENCE? That question seldom emerges when scientists talk with each other. Most scientists believe they know quite well what science is and, since they all share much the same fundamental presuppositions, their beliefs rarely broach a subject for debate. However, the challenging ex- perience of teaching students who do not intend to become scientists —students willing to doubt fundamental presuppositions to which they feel no commitment— has led me to a critical re-examination of beliefs I once held unquestionable. In this book I have tried to ex- plain the lines of reasoning and the kinds of considerations that have led to what seems to me now a more tenable set of beliefs. Perhaps this analysis will have some value for others (both students and teachers ) who— having adopted the familiar textbook stereotype— are yet not fully satisfied with this orthodox answer to the question: "What is science?" I do not deceive myself that my answer will prove acceptable to everybody, but I do believe that the reader who joins me in exploring the paths here laid out will come at least to a better understanding of the full scope of^that not-so-simple question. He will, I hope, find that I have cleared a way for him through two major difficulties that ordinarily block the road to understanding. First: I have sought everywhere to deal with "real" science, as it has been created and appraised by "real" scientists. The "ideal" sci- ence analyzed in neat philosophic syllogisms may be attractive in its straightforwardness, but it is lamentably "ideal" in that nothing like vii Vlll PREFACE it has ever existed in this world. In order to escape all temptation to treat science at this dangerously extreme level of abstraction, I have throughout made a systematic eflFort to develop general ideas in the context of actual events in the history of science. I say nothing of what science could or should or might be, or of what scientists could or should or might think. I have instead said only what I be- lieve science has been and is, and what scientists have thought and do think. I believe their practice and beliefs distorted only to the extent that I have tried to make explicit views that are often only implicit, and to the extent that I have emphasized the enormous area of agreement at the expense of the small but significant areas in which scientists disagree. Second: I have tried to give a complete and integrated representa- tion of science, with a just apportionment of attention to science as such and to its history, philosophy, internal organization, social ties, and so forth. I have tried to dissect the total problem, so that its "parts" can be seen clearly; but I have tried to reassemble the "parts" in order that they may be seen correctly. In their natural context there are between them crucially important interactions which can- not be grasped when, as ordinarily, "parts" are treated in complete abstraction from one another. The perspective on science thus de- veloped can treat only cursorily some topics that have been treated in depth by others but, if I have succeeded, this perspective should have a breadth and balance not to be found elsewhere— simply be- cause the depiction of real science "in the round" is so very rarely essayed. The reader of this work needs no understanding of higher mathe- matics, nor of the intricacies of quantum mechanics and relativity. Less than half a dozen algebraic equations appear in the whole of the book and, of course, some loss of coverage is thus entailed. How- ever, I conceive that the most fundamental questions relative to the nature of science were broached long before the advent of contem- porary physics, and that these questions can be treated quite ade- quately in simpler contexts. But even if these examples should prove obscure, the technically untrained reader will, I think, still find him- self quite well able to appraise the validity of the basic arguments which— like the conclusions drawn from them— are largely independ- ent of the technical examples I have used to document and illus- trate them. PREFACE IX A word about the organization of this inquiry may come appro- priately at this point. The table of contents will offer the reader some general indications of the lines of argument to be pursued, and will at the same time indicate to him the relations envisaged by the author among the various sub-topics considered. Chapters I, II, and III represent a discursive survey of the whole area to be explored. Here I introduce the categories to be used subsequently in systematic anal- yses of the many problems that emerge from the preliminary survey. If these three opening chapters prove difficult, they need only be skimmed at a first reading: their rationale will become evident after the succeeding chapters have been read. The nature and organization of the remaining nine chapters are dictated by the examination of the anatomy of science that concludes Chapter III. The social milieu of science is the subject in Chapter IV. In Chapter V the reader will find a consideration of the various characteristics of scientific "laws," and, in Chapter VI, a discussion of the nature and use of the empirical pro- cedures deployed by scientists. The core of the book is represented by Chapters VII, VIII, and IX, which explore in detail the principles and theories that are the hallmarks of science. In the three concluding chapters I have treated science as a social institution (in Chapter X), science as an individual achievement ( in Chapter XI ) , and science as a genuine discovery of the "real world" ( in Chapter XII ) . I should, perhaps, comment on the abundant use that has been made of direct quotations. Sometimes they offer particularly happy expressions of the points to be made; sometimes they serve to indi- cate the sources of arguments not otherwise attributed; sometimes they figure as citations of authority in areas of discourse where I my- self can claim no authority; occasionally they may be no more than landmarks in my own education— statements that first resolved prob- lems that had bothered me. Above all, these quotations are used to display faithfully the opinions of men who have themselves made scientific history. I acknowledge with thanks the courtesy of the many publishers, listed on p. v, who have permitted me to quote from works appearing under their imprint. To deal adequately with all parts of the subject I have set myself, one would have to be deeply versed in history, psychology, sociology, and philosophy— not to mention all the individual sciences. Given a keen awareness of my own limitations, I am particularly grateful for the counsel I have received from friends and colleagues. I owe to X PREFACE J. B. Conant, whom I was once fortunate enough to serve as teaching assistant, my first introduction to some of the problems here dis- cussed, as well as many pointers along the lines here developed. With T. S. Kuhn I long enjoyed an active teaching collaboration and, though we seem to have arrived at rather different conclusions, many of my themes were first suggested by hard-fought discussions with him. The entire manuscript has been read by JoeJ Cohen, Robert S. Cohen, Wendy Doniger, Gerald Holton, Thomas S. Kuhn, Ernest Nagel, Peter Urnes, and Eleanor Webster— to each of whom I am in- debted for an extended commentary that has furnished a wealth of valuable suggestions. In matters of detail I have had many helpful criticisms from K. D. Clouser, Susan and Stanley Goldberg, James Haber, F. L. Holmes, Stephanie Pfaff, and Michael Simon. My wife has devoted long hours to helping me with the reading of proofs. The skill and patience of Ronald Q. Lewton, who edited this book, have been a strong support in times of need. The unstinted assistance of the foregoing persons has saved me from many serious errors; any that remain are the indivisible responsibility of the author. Leonard K. Nash V A I Contents Chapter I COMMON SENSE (AND SCIENCE) 3 Common sense and prevision 5 The Organization of Experience 6 FROM STIMULI TO CONSTRUCTS 7 Observing 8 Constructs 10 FROM CONSTRUCTS TO CONCEPTS 12 The normative factors 13 Varieties of concepts 15 The tool function of concepts 17 FROM CONCEPTS TO COLLIGATIVE RELATIONS 18 Denotation 20 A FOURTH STAGE IN THE ORGANIZATION OF EXPERIENCE 22 Similarities in intent, presuppositions, and subject matter . . 25 Some differences: Progressivism and impressiveness 27 Chapter I I SCIENCE (AND COMMON SENSE) 29 SOME "metaphysical PRINCIPLES" OF SCIENCE 29 XI 90^ Xll CONTENTS The real world 29 Determinism 30 Continuity 30 Dissolubility 31 The Subject Matter of Science 31 RECURRENCE AND REPRODUCIBILITY 31 Facts historical and scientific 33 Uniqueness and identity 34 CONCURRENCE 36 REGULARITY 39 DATA AND JUDGMENT 42 The Organization of Experience 43 CONSTRUCTS 43 SCIENTIFIC CONCEPTS 46 The strangeness of scientific concepts 46 Concepts and the anatomization of experience 48 COLLIGATIVE RELATIONS ("lAWS") 49 The law of the lever 50 Denotation 54 The ensemble of colligative relations 55 SCIENTIFIC THEORIES 57 The kinetic theory 58 Remembering, understanding, discovering 60 Theories and nets 61 Chapter TTT THE ANATOMY OF SCIENCE 63 The Evolution of Science 63 The principle of intelligibility 65 SOME DIFFICULTIES 67 The choice of problems 67 Heuristic tools 67 Organization 68 CONTENTS Xm The social setting 69 The idea of progress 70 A FIRST QUALIFICATION: PATENCY, PROGRESS, AND PRAGMATISM 72 A SECOND QUALIFICATION OF THE PRINCIPLE OF INTELLIGIBILITY 73 Autonomous science and sciences 74 A THIRD QUALIFICATION OF THE PRINCIPLE OF INTELLIGIBILITY 76 The appeal to experience 77 A new conception of scientific method 79 The principle of corrigible fallibility 83 The Body Scientific 84 The anticipatory apparatus 86 The heuristic apparatus 87 Chapter I \/ COSMOLOGY AND TECHNOLOGY 90 Problems 90 Motivation 90 Support 91 Cosmology 92 Inclusiveness 92 Science metamorphosed 92 Disagreement 93 Rigidity and revolution 93 THE CLIMATE OF OPINION 95 The linguistic factor " 98 The aesthetic factor 99 The ethical factor 101 The moral factor 102 THE COSMOLOGY OF ORGANIZED SCIENCE 104 Technology 105 Conceptual exchanges 107 V XIV CONTENTS Material exchanges 108 SCIENCE AND TECHNOLOGY 109 Constraint Ill THE REPROBATION OF SCIENCE 113 Chapter y COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 114 THE EFFICIENCY OF COLLIGATIVE RELATIONS 115 The sulfur relation 117 A COLLIGATWE RELATION: BOTH INVENTION AND DISCOVERY . . 118 Boyle's law 119 DENOTATIONS: IF INDIRECT, YET SOLIDLY ESTABLISHED 123 Galileo's law of free fall 125 A relation of Euclidean geometry 127 THE "proof" and ENDURANCE OF COLLIGATIVE RELATIONS .... 127 The relation of metals 129 Colligative Relations not Wholly Independent of Theories .... 130 The Bode-Titus law 132 CONNOTATIONS AS WELL AS DENOTATIONS 133 Moseley's law 133 The Mendelian laws 135 COLLIGATIVE RELATIONS IN OTHER GUISES 137 Chapter \/ I EMPIRICAL TOOLS AND EMPIRICISM 138 INSTRUMENTS 138 The operating protocol 139 Pointer readings 141 THE EXTERNAL STANDARD OF REFERENCE 143 "Things" as standards 145 Techniques as standards 146 CON-EENTS XV Colligative relations as standards 147 PRIMARY AND SECONDARY DENOTATIONS 147 Calibration 148 Extrapolation 149 Observation and Experiment 1^1 EMPIRICISM AND THE INTERNAL DYNAMICS OF SCIENCE 155 The Scientific Method 157 FINDING THE PROBLEM 160 THE DESIGN AND CONDUCT OF EXPERIMENTS 161 The choice of variables 162 The choice of observables 163 DRAWING CONCLUSIONS FROM EXPERIMENTS 165 THE POWER OF STATISTICAL METHODS 166 The limitation of statistical methods 167 THE MYTH OF METHOD 168 Chapter \ \\ THE PRINCIPLES OF SCIENCE 170 The Existence of a Real World 172 The Principle of Intelligibility 172 FOUR METHODOLOGICAL COROLLARIES 172 Parsimony 173 Penury 174 Clarity 176 Analogy 178 CONGRUITY 179 Simplicity sigillum veri 181 The Principle of Continuity ^ 183 CONTINUITY AND EXPLANATION 184 Energy 185 Atomism 187 DISSOLUBILITY AND SUPERPOSITION 189 Superposition not summation 190 Superposition and explanation 193 V XVI CONTENTS The Principle of Determinism, and Causality 194 Causality as heuristic maxim 196 QUANTUM MECHANICS, DETERMINISM, AND CAUSALITY 199 The Principle of Corrigible Fallihilitij 203 LEARNING PRESUPPOSES ERROR 204 THE MUTUAL CONTROL OF FACTS AND THEORIES 206 Substantive Principles 208 Substantive principles as conventions 211 Chapter VJJ J THEORIES AND MODELS 214 Logic and Mathematics 217 Abstract formalism and scientific law 221 INDUCTION 222 The hypothetico-deductive method 224 DEDUCTION 226 Models 230 Model implicit in formalism 232 Formalism implicit in model 233 MODELS AND SEMANTIC RULES 234 First case: Direct denotations and simple models 234 Second case: Indirect denotations and simple models 236 Third case: Indirect denotations and hierarchic models . . . 237 THE "superfluity" OF THE PHYSICAL MODEL 239 The positivists' "theory without superfluity" 242 Heuristic power from "superfluous explanation" 248 The model taken seriously 250 Chapter I V THE EVOLUTION OF SCIENTIFIC THEORIES 254 THE CRUCIAL EXPERIMENT 256 • • CONTENTS XVll Situations of deadlock 257 The ramified chain of reasoning 258 The totahty of what is tested 260 The crucial experiment in practice 263 Three Functional Criteria 264 CORRELATIVE EFFICIENCY 264 The insufficiency of the correlative index 266 EXPLANATORY APPEAL 267 The two criteria of immediate judgment 268 HEURISTIC POWER 269 Natural Selection of Scientific Theories 272 Viability and validity 274 THE LIFE CYCLE OF A SCIENTIFIC THEORY 276 Infancy and youth 277 Maturity 278 Old age 279 The death struggle 282 Scientific Revolutions? 284 The growth of order 286 The correspondence principle 287 NOT FALSIFICATION BUT SUBORDINATION 289 The "problem" of dual description 292 EVOLUTION AND ERROR 294 Chapter V ORGANIZED SCIENCE 297 The Invisible College 298 COMMUNAL ADMINISTRATION, CONSENSUS, CULTURE 300 THE NORMATIVE FITNCTIONS 302 Protection 303 Selection 305 Appreciation 307 THE CO-ORDINATION OF EFFORT 309 XVlll CONTENTS The Super-Personal Intelligence 311 Complementarity of capacities 312 Complementarity of skills 313 Complementarity of temperaments 313 Complementarity (and cancellation?) of commitments ... 314 PERTURBATIONS OF THE MECHANISM OF SELECTION 315 Defective personal commitment 316 Excessive authority 317 Chapter \ I CREATIVE SCIENCE 319 SCIENTIFIC METHOD: SHADOW AND SUBSTANCE 320 The primacy of hypothesis 324 The Attitude of the Investigator 326 DETACHMENT 329 Intelligence 330 Detachment from commitment 331 Accidental Discoveries 333 FOCAL DISCOVERIES 333 THE THRESHOLD OF IMPRESSIONABILITY 335 Knowledge and expectation 339 Intelligence and temperament 340 PERIPHERAL DISCOVERIES 341 The Creative Imagination 343 Education 343 Youth 344 Two fields of view 346 The situation 347 The man 349 THE BIRTH OF INSIGHT 350 CONTENTS XIX Chapter \ I I THE REAL WORLD 356 NAIVE REALISM 358 PHENOMENALISM 361 Illogical cynicism 362 REPRESENTATIONALISM 363 Beyond Inventions— Discoveries! 365 Science and prediction 366 y THEORIES 368 Heuristic power 369 Simplicity 371 PRINCIPLES 374 The cross-fix 376 INTELLIGIBILITY 379 Ultimate unintelligibilities? 380 BIBLIOGRAPHY 385 INDEX OF NAMES 401 The Nature of the Natural Sciences CHAPTER I Common Sense (and Science) ciENCE is a way of looking at the world. There are, of course, other ways. The man of common sense sees the world in his own way. So does the artist, the philoso- pher, the theologian. The view of the scientist, if at all unique, is characterized by its heavy involvement of elements drawn from all the others. Like the man of common sense, the scientist views the world within the co-ordinate system provided by a framework of con- cepts. But, not content with the common-sense view of the world, the scientist uses a diflFerent conceptual framework. He seeks a higher unity, a deeper understanding, unknown to common sense. He de- vises new concepts; with them he seeks and finds novel and pro- found connections between apparently unrelated phenomena, as well as significant differences between phenomena apparently closely re- lated. With the artist, then, he comes to see the world in new per- spectives, with a new pattern of highlights and shadows, involving new associations, new points of emphasis— and often effective neglect of precisely those relations or connections that loom most prom- inently in the view of common sense. William James writes: What we say about reality thus depends on the perspective into which we throw it. . . . ... By our inclusions and omissions we trace the field's extent; by our emphasis we mark its foreground and its background; by our order we read it in this direction or in that. We receive in short the block of marble, but we carve the statue ourselves. 4 COMMON SENSE (aND SCIENCE ) Novelty of viewpoint is a work of imagination. And, to be sure, imagination is valued in both artists and scientists. Proust suggests the artist charms us by teaching us to see another universe; the sci- entist charms us similarly, by showing us a conceptual order in the chaos of perceptual experience. But, through this same concern for rational unity, the scientist is borne on toward the viewpoint of the philosopher. "Philosophy has often been defined," says James, "as the quest or the vision of the world's unity." The theologian may con- ceive this unity very diflPerently, and use very different criteria in judging the extent to which it has been achieved. But he believes as firmly as the philosopher or the scientist in the unity of the world. The biologist W. R. Thompson, the chemist Conant, and the mathematicians Clifford and Bronowski have all written works with titles juxtaposing science and common sense. Science has, indeed, been defined (by T. H. Huxley) as "organized common sense." In the present age of relativistic and quantum physics many, including both scientists and laymen, find outrageous all comparison of science with common sense. To them science seems flatly to contradict common sense wherever it does not wholly ignore it. Yet consider the testimony of an eminent theoretical physicist of our own age: Oppenheimer urges that we . . . distrust all the philosophers who claim that by examining sci- ence they come to results in contradiction with common sense. Science is based on common sense; it cannot contradict it. Though between science and common sense there exist dissimilarities we must not ( and will not ) overlook, the strong similarities between them establish for us a point of departure. Seeking to understand science, we begin by trying to understand the nature of common sense. Thus proceeding, we simply follow the counsel of Einstein, the subtle theoretician whose views have been widely regarded as a com- plete repudiation of common sense. The whole of science is nothing more than a refinement of every- day thinking. It is for this reason that the critical thinking of the physicist cannot possibly be restricted to the examination of the con- cepts of his own specific field. He cannot proceed without consider- ing critically a much more difficult problem, the problem of analyz- ing the nature of everyday thinking. COMMON SENSE (aND SCIENCE ) 5 Common sense and prevision. Why do we speak of common sense? First, because it is possessed and employed in much the same man- ner by the generahty of mankind. The sage has uncommon sense: his less gifted contemporaries have a sense common to all. Second, because it is unexalted, untheoretical; it is down-to-earth, actively concerned with the business of living as distinct from the purposes or values or meaning of living. We judge that a man lacks common sense when he fails to adopt some course of action we feel he should recognize as most likely to yield him the ends he seeks— when he fails to foresee, as he should, the future consequences of present ac- tion. To lack common sense is to lack a previsional capacity. Can anything as mundane as common sense lay claim to such an exalted capacity? On what basis can the future possibly be foreseen? Past experience oflFers the only possible basis. Common sense must so work upon the experience of the past that it is made available for anticipation of the future. The person lacking common sense may fail to detect any recognizable pattern in his past experience, and so lack all basis for extrapolation into the future; or he may fail to recognize the recurrence of situations that have been eflFectively dealt with in terms of some particular pattern. In either case he fails to learn from experience. Capacity for such learning is a cherished faculty of man; common sense represents the exercise of that faculty. We do not recognize common sense in the lower animals. In them "instinct," various tropisms, and conditioned behavior serve to pro- duce activity without— we may suppose— any prevision of the conse- quences of that response. But if the species is to survive, the instinc- tive responses must for the most part be appropriate responses, giv- ing the appearance of a sound foresight. Meyerson says: . . . foresight is indispensable for action. Now action for any organ- ism of the animal kingdom is an absolute necessity. Surromided by hostile nature it must act, it must foresee, if it wishes to live. "All life, all action," says Fouillee, "is a conscious or an unconscious divining. Divine or you will be devoured." In the higher animals the nonreflective responses give way to ac- tivity more closely controlled by what, in the apes, approaches that which passes as common sense in man. A better contrived, more subtly varied response to the situations of everyday life then be- comes possible. Given sound common sense, says Santayana, 6 COMMON SENSE (aND SCIENCE) . . . each moment of experience becomes consequential and pro- phetic of the rest. The calm places in life are filled with power and its spasms with resource. Instinct in the animal has behind it a deep elemental drive— and well it may, for on it depends the survival of the organism and its species. As the control of action by instinct gives way to control by common sense, the latter assumes immense responsibilities, and thus becomes the focus of acute anxieties. In both animal and human subjects, systematic frustration of reasonable expectations produces neurotic disturbances. Such disturbances may be provoked even by exposure to circumstances that seem unreasonably to deny the cher- ished possibility of finding in past experience pointers toward the future. For example, Hebb notes that: Pavlov . . . taught the dog that food would be given following the sight of one object, and not following that of another. No punishment was given if the dog failed to discriminate between them. The objects were made more and more alike until, after several days of failing to discriminate, the dog's behavior changed, suddenly. Instead of com- ing eagerly to the experimental room the dog struggled to avoid it; instead of standing quietly in the apparatus, waiting for the next signal to appear, he struggled and howled. The deep-seated drive so displayed is presumably carried over into the active purposeftilness of the science which, whenever it succeeds in descrying an order in past experience, makes us master of a futvue shorn of its terrors precisely in the degree that it can be fettered by chains of predictions. The Organization of Experience The individual's experience is varied and chaotic: how can he pos- sibly give it a systematic order? The individual's experience is of certain particular situations of the past: how can he possibly ex- trapolate from them to inevitably non-identical situations of the present (and future)? The individual's experience is personal, sub- jective: how can he possibly arrive at the body of common sense shared by all? To facilitate discussion of these, and other, questions, I shall consider the organization of experience as a sequence of "stages"; but I would emphasize at the outset that these are not pro- COMMON SENSE (aND SCIENCE ) 7 posed as stages in the operations of the senses and the brain, but simply as artifices of discussion: i.e., steps in the abstract analysis of what is in practice an irreducibly integral (and ordinarily non- reflective) process in which each "stage" presupposes or is presup- posed by others. FROM STIMULI TO CONSTRUCTS Merely to see an object is no mean feat of organization. The meas- ure of the achievement is indicated by the results of corneal trans- plantation, giving sight to adults blind from birth. Young tells us: The patient on opening his eyes for the first time . . . reports only a spinning mass of lights and colors. He proves to be quite unable to pick out objects by sight, . . . His brain has not been trained in the rules of seeing, does not know which features are significant and useful for naming objects and conducting life. We are not conscious that there are any such rules; we think that we see, as we say, "nat- urally." But we have in fact learned a whole set of rules during child- hood. At least a month passes before the subjects can recognize even a few objects, and ". . . if sufficiently encouraged they may after some years develop a full visual life and be able even to read." Making all due allowance for the greater co-ordinative plasticity of infancy, still we cannot but recognize that "seeing"— no simple passive reception of an unequivocal signal— is a formulative process in which the re- ceiver plays an active role. This conclusion is reinforced by the results of physiologic re- search.* The eye contains some one hundred million separate recep- tors. To "see" a thing must then demand some work of construction from the myriad atomic stimuli. But even to speak of "construction from atomic stimuli" is an oversimplification. Such stimuli are sep- arately unknown to us; they are not facts but hypotheses. Weyl argues that: Consciousness reacts with an entirety that is not merely a mosaic composed of sensations; on the contrary, these so-called sensual data are a subsequent abstraction. The assertion, that they alone are actu- ally given and the rest is derivative, is not a description that care- * I must take cognizance of these results for, as becomes plain in Chapter XII, I wish to maintain a realist position. 8 COMMON SENSE (aND SCIENCE) fully pictures what is given in its full complexity, but rather a realistic theory arising from the realistic conviction that "only sensations can really be given." Nevertheless, one may believe in a subconscious weaving of the whole pattern out of such elements called pure sensa- tions; ... We began by asking how common sense organizes the data of ex- perience. We see now that the term "experience" itself conceals complexities. At the very least, the "experience" with which common sense comes to grips already bears the stamp of a receptor apparatus tliat— as Langer remarks— contributes actively to a rudimentary or- ganization of what is received. A tendency to organize the sensory field into groups and patterns of sense-data, to perceive fomis rather than a flux of light-impressions, seems to be inherent in our receptor apparatus just as much as in the higher nervous centers with which we do arithmetic and logic. But this unconscious appreciation of forais is the primitive root of all ab- straction, which in turn is the keynote of rationality; so it appears that the conditions for rationality lie deep in our pure animal experience —in our power of perceiving, in the elementary functions of our eyes and ears and fingers. Mental life begins with our mere physiological constitution. Provided with physiologically similar sensory equipment, the higher apes seem to see objects somewhat as we do. Judging from their ac- tions, so do far lower animals; for example, like ours, their vision singles out for attention any trace of movement in a complex but otherwise static visual field. Ability to see "moving objects"— objects to be pursued, to be eaten, or objects to flee or to hide from— has an obvious survival value. Perhaps then, by way of natural selection, capacity to see "objects" comes to be a built-in feature of tlie sensory organs of species successful in the struggle for life. Shaping us for this particular kind of perception, our animal history thus underlies the activity of common sense and science alike. Observing. What part of the purely physiological organization of experience takes place in the sensory organ, and what part in the brain, is unclear. Some of this organization, e.g., the figure-ground distinction, seems to be wholly spontaneous and unlearned. But we do know that visual perception involves, in addition to the immedi- ate locale of the sense termini, a rather large part of the brain. Hebb moreo\'er tells us : COMMON SENSE (aND SCIENCE) 9 Electrophysiology of the central nervous system indicates . . . that the brain is continuously active, in all its parts, and an afferent excitation must be superimposed on an already existent excitation. Thus any and all "automatic" organizational activity will merge into further activity, at the fringe of consciousness, in which learning is involved. We "learn" to use our senses— e.g., to keep our eyes in focus, to run them along the contours that define an object. Beyond this literal aspect of learning lies an equally important figurative aspect. In in- fancy we learn not only control of the musculature of the eye but also the forms or patterns of "things" and "situations." To conceive this learning is difficult: it all takes place without conscious volition in a period lost in the haze of early childhood. Ordinarily we become aware of the function of the learned forms only in cases involving new patterns learned in maturity and, more strikingly, in cases (of illusion) in which the taken-for-granted forms prove insufficient or actively misleading. But our "knowing" always affects our "seeing." We learn not only hoiv to see but also what to see; often we simply don't see anything for which our learning has not, in some sense, pre- pared us. The seaman notes small details in the condition of sea and sky that pass unnoticed by the landlubber. Usually the seaman's vision is no sharper, but he observes, as significant, points the land- lubber could but does not see, because to him they are inconse- quential features of the visual field— taken in by the eye but not by the brain. The seaman possesses a "mental image" (Gestalt, neural pattern, or what you will ) in or against which certain details stand out in bold relief. Consider bird-watching. The old hand's claim to make a valid identification on the basis of a fleeting glimpse aston- ishes the novice, but what stuns him is that the old hand seems to see so much more. Of course the old hand sees more: he is not passively seeing but actively looking, looking for significant similarities and differences in the bird before his eyes and one or several images car- ried in his "mind's eye." The ancients supposed that seeing involved a projection of rays from observer to object seen. Today we conceive seeing as the trans- mission or reflection of rays from object to eye. False as a physical mechanism, the ancient view nonetheless symbolizes an important truth. Seeing involves a merging of something from the object, "out- side," with something contributed by the viewer, from inside. Brain 10 COMMON SENSE (aND SCIENCE) and eye collaborate in seeing. What we claim to perceive depends no more on the sensitivity of the eye than on the conceptual inven- tory deposited in the brain. Nowhere is this more apparent than in experiments like those of which Polanyi gives us the following per- ceptive analysis : Ames and his school have shown that when a ball set against a fea- tureless background is inflated, it is seen as if it retained its size and was coming nearer. This illusion seems to be due to the fact that in this case we accommodate our eyes to a closer range, even though in consequence the object gets out of focus. . . . These defects of the quality and position of our retinal images are accepted here by the eye, in the urge to satisfy the more pressing requirement of seeing the object behave in a reasonable way. Since tennis balls are not known to blow themselves up to the size of footballs, a ball which does so must be seen as approaching us, even though in shaping this sensa- tion tlie eye must override standards of correctness which it would otherwise accept as binding. The rule that we follow in shaping the sight of the inflated ball is one that we taught ourselves as babies, when we first experimented with approaching a rattle to our eyes and moving it away again. We had to choose then between seeing the rattle swelling up and shrink- ing alternately, or seeing it change its distance while retaining its size, and we adopted the latter assumption. By this way of seeing things we eventually constructed a universal interpretative frame- work that assumes the ubiquitous existence of objects, retaining their sizes and shapes when seen at different distances and from difi^erent angles, and their color and brightness when seen under varying il- luminations. . . . In a larger perspective, the present experience of seeing the in- flated ball come nearer to our eyes appears merely as the last of a life- long chain of experiences encountered and shaped by us, to each of which we reacted to make sense of it as best we could, and which are now all subsidiarily effective in the shaping and comprehension of our present experience. Constructs. What we may call "bare experience" already confronts us with an inseparable fusion of perceptual and conceptual ele- ments. For us "the given" is perhaps formed frojn sensory stimuli, or percepts; but formed in the pattern of a supposed general class, which is a concept. What enters consciousness Margenau calls a construct. COMMON SENSE (aND SCIENCE ) 11 We perceive a complex of colors, shapes, motions, mingled with fra- grance and perhaps tactile data, all suffused with an awareness of "out there"; the whole experience is summed up in the declaration: This is a flower. . . . The postulation of an external object is the first phase of the cognitive act. Margenau is careful to emphasize that the spontaneous organization yielding this vision of things involves more than integrations: it involves construction, construction in accordance with rules. Objectivity emerges as a result of this pro- cedure; . . . Objectivity? To be sure, we agree on what we "see" not because the sensory stimuli are precisely the same— they cannot be— but be- cause of the normative function of the conceptual patterns in terms of which our constructions are made. The diflFerences in the stimuli —due, for example, to individual diflFerences in sensitivity, and to the necessarily diflFerent perspectives of two simultaneous observers of the same thing— drop out as the construct is formed in a concep- tual pattern used by all observers. The bare possibility of a common sense depends on common acceptance of the same fundamental group of mobilizing forms or patterns. The spontaneous interaction of percepts and concepts is here enormously advantageous. Objectivity? Certainly not! What emerges from construction is at most some degree of impersonality. The constructs involve a large subjective ( conceptual ) component passing undetected because it is common to all. "Pure observation," "naked fact," are no less hypo- thetical than "atomic stimuli." Thus, as Mill emphasizes, the objects of common sense— objects also for science— are far from purely ob- jective. ... in almost every act of our perceiving faculties, observation and inference are intimately blended. What we are said to observe is usually a compound result, of which one-tenth may be observation, and the remaining nine-tenths inference. Thus we constantly infer the presence of massi\'e solid objects ( e.g., tables, chairs, other people) from sensory data presenting neither solidity nor massiveness. Generally such inferences are sound and extremely helpful. But the spontaneous compounding of "one-tenth observation" with "nine-tenths inference" is also potentially hazard- ous—for a reason clearly suggested by a comment of Hebb's: 12 COMMON SENSE (aND SCIENCE) There is plenty of evidence in children's drawings, and in adult errors in perspective drawing, to show that a person looking at an object thinks he sees more of it than he does. What he knows [or thinks he knows] about the object appears in his drawing, as well as what is visible at the moment; and the significant fact is that neither child nor adult can usually say where his drawing departs from what is actually presented to the sense organ. Unable fully to distinguish observation from inference, man has found it all too easy to believe that, for example, the fixity of the earth is obviously a "given fact." FROM CONSTRUCTS TO CONCEPTS Following the organization of "experience," we have passed from the sensory organ to the brain— from the notion of a bare percept to that of a construct already presupposing the organization given by a con- cept. From early childhood we begin to acquire the multitude of con- cepts necessary for the business of living. For example, the child learns to associate the concept "mother," and the word symbolizing it, with a "particular person." But in what way a particular person? Not one who always acts the same: sometimes she does things that please, sometimes things that hurt; sometimes her voice is soft and loving, sometimes harsh and commanding. She does not always look the same. She does not always wear the same dress, or even always wear dresses; her coiflFure, her make-up, her expression all vary. And all these variations in the child's experience of "mother" must be sub- tracted, allowed for, or dismissed as irrelevant in the formation of the concept. An addition is made when he grasps that underlying the "superficial variations ' in the experience of mother there is an un- changing "something." To achieve even so primitive a concept, the child must perform a feat of abstraction and synthesis that Hebb notes is difficult enough to baffle an infant ape. Dr. R. and Mr. T. are regular attendants in a chimpanzee nursery; the infants are attached to both, and eagerly welcome being picked up by either. Now, in full sight of the infants, Dr. R. puts on Mr. T.'s coat. At once he evokes fear reactions identical with those made to a stranger, and just as strong. Meyerson tells us that all science represents the eflFort to discover, or create, identity in experience. That pursuit is already reflected in COMMON SENSE (aND SCIENCE ) 13 the child's formation of concepts. Piaget emphasizes the importance of concepts of "conservation" in the elaboration of the child's vision of the world. Only by way of his growing recognition of invariants, and invariance, does he come at last to find his world intelligible. Lorenz identifies the essence of Gestalt perception as . . . the single function of extricating the essential constant factor by abstracting from the inessential variable sensory data. The differ- entiation of this function attains an amazing development in the serv- ice of shape constancy and it needs only to be driven one little step further to make possible an absolutely new operation miraculously analogous to the formation of abstract, generic concepts. Whether or not one accepts the Gestalt theory of "extrication," of the constant factor, one recognizes how very natural will be the emergence and refinement of functional capacity for this discrimina- tion in creatures evolved under the pressure of natural selection. The immense value of that "one little step further" is amply suggested by Bartlett's analysis of the choice and arrangement of evidence by nor- mal subjects placed in problem-solving situations. He strongly em- phasizes the leading part played ... by the detection of points of agreement. It is well known that points of agreement are inherently less easy to detect than points of difference. Perhaps the most important distinction between the two, from our present viewpoint, is that the detection of differences alone leads nowhere in particular in a positive sense, but the detection of agreement may. Thus, if one instance is observed to differ in some way from another, it may perhaps be said that something already established about the one is not applicable to the other; but if two instances are observed to agree in some way, it may possibly be im- plied that something already established about the one is applicable to the other. It seems fairly certain that, in a cognitive sense, all ad- vance of knowledge comes by using agreements to get a move on, so to speak, and then using differences to keep the move within limits, and to show where a new direction of move becomes necessary. The normative factors. In Lorenz' view, the constant factor in ex- perience is not so much "given to " as "computed by" the organism. In some degree each must create concepts for himself— and this may seem to raise a serious problem. How can we all come, as we do, to a common understanding of the concepts of common sense? Norma- tive influences plainly are at work. 14 COMMON SENSE (aND SCIENCE) We have in common a biological heritage. Moreover, the experi- ences of early childhood, in die context of which each individual be- gins to form his stock of concepts, are far more uniform for all of us than are the experiences of any later period. Then too, the things and situations called to our attention in childhood— and the way they are presented to us— are in large part determined by a comparatively uniform cultural tradition. More specifically our language, by vir- ture of the resources it oflFers and fails to oflFer, must, as Whorf ob- serves, condition the species of concepts we form and the way we use diem. We cut nature up, organize it into concepts, and ascribe significances as we do, largely because we are parties to an agreement to organize it in this way— an agreement that holds throughout our speech com- munity and is codified in the patterns of our language. Polanyi offers a handsome illustration of how language mediates the interplay of percepts and concepts : Think of a medical student attending a course in the X-ray diagnosis of pulmonary diseases. He watches in a darkened room shadowy traces on a flourescent screen placed against a patient's chest, and hears the radiologist commenting to his assistants, in technical lan- guage, on the significant features of these shadows. At first the stu- dent is completely puzzled. For he can see in the X-ray picture of a chest only the shadows of the heart and the ribs, with a few spidery blotches between them. The experts seem to be romancing about fig- ments of their imagination; he can see nothing that they are talking about. Then as he goes on listening for a few weeks, looking care- fully at ever new pictures of difterent cases, a tentative understand- ing will dawn on him; he will gradually forget about the ribs and be- gin to see the lungs. And eventually, if he perseveres intelligently, a rich panorama of significant details will be revealed to him: . . . He has entered a new world. He still sees only a fraction of what the ex- perts can see, but the pictures are definitely making sense now and so do most of the comments made on them. He is about to grasp what he is being taught; it has clicked. Thus, at the very moment when he has learned the language of pulmonaiy radiology, the student will also have learned to understand pulmonary radiograms. The two can only happen together. Both halves of the problem set to us by an un- intelligible text, referring to an unintelligible subject, jointly guide our efforts to solve them, and they are solved eventually together by dis- COMMON SENSE (aND SCIENCE ) 15 covering a conception which comprises a joint understanding of both the words and the things. Whatever the respective weights of the various normative factors —biological, sociological, cultural, linguistic— together they are pow^- erful in promoting common understanding of the concepts of com- mon sense. Such understanding is then entirely compatible with the individual creative intuition I hold requisite in all concept-formation. Varieties of concepts. The concepts of common sense are manifold. Consider examples of three varieties we shall find strongly repre- sented among the concepts of science. First are those which envision as an element of identity an unchanging thing underlying, and pro- ductive of, our changing percepts. Langer writes: A little reflection shows us that, since no experience occurs more than once, so-called "repeated" experiences are really analogous oc- currences, all fitting a form that was abstracted on the first occasion. ... I believe . . . that we promptly and unconsciously abstract a form from each sensory experience, and use this form to conceive the experience as a whole, as a "thing." In common sense such thing-concepts have generally a quite direct relation to the perceptions that evoke them; but the situation is not uncomplicated. Surely the concept "mother" derives comparatively directly from a set of visual, auditory, and tactile stimuli. But no simple fusion of the sensory elements yields the concept "mother"; no particular construct of mother quite corresponds to the concept "mother." Observe also that the simple common-sense concepts al- ready display a spectrum of unobservability continuous with the much extended spectrum we remark in the thing-concepts of science. Even "mother" is only intermittently present in the sensory field, and the very young child may believe that "mother" is annihilated when he sleeps and recreated by his cries on awakening; but he soon ac- quires full belief in the unobserved, and for him unobservable, con- tinuous existence of "mother." Consider now, as a second variety of common-sense concepts, those class-concepts which group together things so much alike in "important" qualities that we can ignore the respects in which they differ. The whole possibility of learning from experience is tied up with the development of a suitably discriminating group of classifi- 16 COMMON SENSE ( AXD SdENXE) catory concepts that teach us how to find in nonidentical things a significant identit)' in t\'pe. Mill writes: We compare phenomena with each other to get the conception, and we then compare those and other phenomena witli the conception. . . . and if it [a particular instance] agrees with that general con- ception, we include it in the class. The conception becomes the type of comparison. There is this rattle— \\ith its own color, shape, weight, and sound. There is this other rattle, with its own distinct set of qualities. And there is the general concept "rattle." A member of the class must be, in some degree, graspable and shakable; and it must gi\e a "rattling sound," though this may vary greatly in \olume and timbre. In forming the class some of the most striking qualities (e.g., color and shape) are adjudged irrele\ant, and e\'en the key qualities are per- mitted to \ar\- within broad limits. The discrimination so expressed represents appreciation of the function of rattles. Function seems eenerallv decisi^•e in our understandino; of clas- sificatory concepts, bodi in common sense and in science. Often— though we all understand a concept in much the same wa\'— we can find no specific criterion or group of criteria that establishes the class. In such cases we deal far less with rigid specifications than with a general pattern. Failure to fit the pattern in some respects is disregarded if a good fit obtains in other respects that most concern us at the moment. Our grasp of meaning is strengthened by our sense of purpose— a point stated in its broadest application by Popper: . . . an>' two things which are from one point of view similar may be dissimilar from another point of view. Generally, similarity, and \\ith it repetition, always presuppose the adoption of a point of view: some simihirities or repetitions will strike us if we are interested in one problem, and others if we are interested in another problem. . . . points of view, or interests, or expectations, are logical!)' prior, as well as temporally (or causalh' or ps>'choIogically) prior, to repetition. Each of a third \'ariety of common-sense concepts highlights some one attribute of a great many things. Though often unlike in all other respects, these things can meaningfully be compared with re- spect to this one "property." Such quality-concepts, abundantly rep- resented in common sense, express recognition that for a gi\'en pur- X^ose a certain quality is of overriding importance. In getting the first COMMON' SENSE (aXD SCIEXCe) 17 line across a gorge the length of the available cordage is the factor of primary concern; secondary attention may be given to weight and strength, but the composition of the line is of no concern whatever. The pilot of a plane laboring in a storm will feel a primary concern for the weight of his cargo; its shape does not interest him, though its value will cause him longer to defer jettisoning gold than sand. Ultimately, quality-concepts are adjectival, as when we speak of a weighty object or a long rope. But, once recognized as useful, they may be transmuted into nouns, like weight and length. Such a "property of matter" is a characterization of something in relation to a context of obser\'ation. If we take the context for granted, as in- variable if not invariant, we may usefully regard the property as an inherent quality of the something observed. Thus, setting out from the conception of "moving bodies," we come ultimately to the study of "motion" as such. Howe\'er, an element of danger always attends such transmutation. Having rendered "loving" into "love," "honor- able" into "honor," "thinking" into "thought" and even "mind," the philosopher may entice us into pursuit of apparently meaningful but utterly empty questions: e.g., what is the nature of that thing called mind? The man of common sense himself often falls victim of this misconception of adjectives as nouns. Even the scientist has not been immune: e.g., the concept of light as an undulatory phenomenon gives rise to the concept of a medium of undulations— the luminifer- ous ether. The tool function of concepts. Concepts are not found as such in nature; they are evoked in the human mind hij nature. Experience cannot warrant concepts "true" or "false," only appropriate or inap- propriate. Concepts prove themselves as tools prove tliemselves. James writes (in italics) that: . . . our fundamental ways of thinking about things are discoveries of exceedingly remote ancestors, which have been able to preserve themselves throughout the experience of all subsequent time. In my instantaneous visual field I register the construct I call "this man." The characteristics of "this man" stand out from the pattern of the concept "man." I then relate my experience of this man today to my experience of that man yesterday and, within limits, predict my experience of this or that man tomorrow. Ability to make such predictions is enormously valuable, and the concepts conveying such 18 COMMON SENSE (aND SCIENCE) predictive capacity preserve themselves through ages of human thinking. The concept "man" relates yesterday's experience of one man to today's experience of a second and to tomorrow's predicted experi- ence of a third. But how? The concept shows me an element of iden- tity in all the men, but by itself offers nothing intrinsically useful for prediction. "Relate" then must have some further meaning. Effective organization and prediction of experience implies not merely con- cepts but relations among concepts. In my mind the concept "man" is associated with a group of other concepts referring to many as- pects of "human behavior." Through such associations the concept *'man" takes on the full measure of its meaningfulness. "Man" may be old or young, strong or weak, tall or short, white, black, red, or yellow— but by and large "man" shows "human behavior." Organized by the concepts of human behavior, my past experience of "man" permits me to guide my dealings with this man noio by means of forecasts of the various results likely to be produced by alternative courses of action. Only by way of the confirmation of many of those forecasts can the appropriateness of my concepts be demonstrated and their denotations become firmly established. Our selection and understanding of concepts is required for, and inversely determined by, the statement of the relations we seek. FROM CONCEPTS TO COLLIGATIVE RELATIONS What I shall call colligative relations so link together certain ele- ments of our past experience that the appearance of such elements in future experience is made subject to prediction. Typical colligative relations are: "The burned child dreads the fire" or "Water seeks its own level" or Boyle's law— "At constant temperature and with con- stant quantity of gas the product of pressure and volume is a con- stant." A scientific law is often a colligative relation, as Jeffreys indicates : The test of a scientific law is its capacity to account for sensations already recorded, and its interest lies largely in its capacity to pre- dict new ones. The adjective colligative is essentially neutral and descriptive. Literally, to colligate is to bind together. Every relation must repre- sent some kind of binding-together, and to this extent the adjective COMMON SENSE (aND SCIENCE) 19 is redundant. Yet it serves to emphasize the several senses in which these relations represent a binding-together. Thus, for example, they represent a binding-together in time: based on the past, they are used in the present for prediction of the future. Also, these relations associate certain concepts with each other, and thereby reaffiliate the se\^eral elements of experience to which they refer. We link "pressure" and "volume," or "water" and "level," or "child who has been burned" and "fire." Most significantly, in colligative relations we find perceptual and conceptual elements bound together in a balance unduly weighted one way or the other when such relations are termed "phenomenologic" or, contrarily, "causal." Phenomenologic means "descriptive of actual phenomena with avoidance of all interpretation, explanation, and evaluation." A colli- gative relation cannot so be described: it represents both much more and much less than a "description of actual phenomena." Though I have observed very few burned children, I make a general statement about all such creatures in all times and places. Here I go far beyond what I have obser\^ed. But also I say much less than I have observed. The concepts figuring in the general statement single out only cer- tain "significant" aspects of a complex total experience, other aspects of which pass unmentioned, as "irrelevant." But irrelevance is not "given"; it involves a judgment, an "evaluation." In Chapters II and V we shall examine in detail the multiple in- terpretations, explanations, and evaluations we must go through to reach a "purely scientific" relation such as Boyle's law. Only the ghost of actual observations survives in the final statement of the law. To describe such a relation as phenomenologic is folly; to describe it as causal, equal folly. We may feel tempted to say that the doubling of the pressure is the cause of the halving of the volume of a confined gas at constant temperature. We might better confine ourselves to: If the pressure on a confined gas at constant temperature is doubled, then its volume will be hah^ed. Determinism is taken for granted, and a causal connection is implied. But the assignment of causes is here an act of supererogation: the acausal "if . . . then . . ." statement alone discharges the predictive function of Boyle's law. The imputation of causes is more apparent but logically no less superfluous in the colligative relations of common sense. Perhaps the burned child's "dread" is the cause of his subsequent avoidance of fire; but such dread is an hypothesis, not an observation. The useful- 20 COMMON SENSE ( AND SCIENCE) ness of the relation has nothing to do with "dread" construed as cause. 7/ a child has suflFered a burn, then he is not thereafter likely to be found in the immediate vicinity of fires. The original burning and the subsequent avoidance of fires are the observational terms to which the relation gives order, and through which it yields pre- dictions. By supplying an understandable link between the two ob- sen^ational terms, the hypothesis of "dread" may serve a mnemonic function— it also permits terse statement of this common-sense maxim. The same two values are conveyed by the word "seeks" in the maxim: "Water seeks its own level." But the function of the colliga- tive relation is entirely independent of the imputation of purpose, as it is of cause. Whatever the form of their verbal statement, colligati^^e relations have value for common sense if reducible to the form: "If A, then B." We predict the future situation B on the basis of past or present observation that situation A obtains. Purposive behavior becomes possible: wishing to bring about situation B we work to realize situa- tion A. Desiring to halve the volume of a gas, I seek to double the pressure on it. The conceptual formulation of the relation renders it both brief and general, terse and pithy, abstract and broadly applica- ble. The relation constitutes communicable knowledge, where the encyclopedic enumeration required for statement of a purely phe- nomenologic relation would be, practically, incommunicable. Denotation."^ We see "things," no two exactly alike, and arrive at concepts of classes of things essentiaUy alike. Observing things in \'arious situations we pass, by a further creative act, to colligative relations the extreme abstractness of which is generally masked by our familiarity with them. However, if such relations are to have the slightest value to a common sense, usable by all, their conceptual terms must meet one essential criterion: The concepts that figure in the colligative relations of common sense (and science) must have associated with them reasonably unequivocal experiential denota- tions. Only by virtue of such denotations can we get back from the abstraction of the conceptual statement to the "hard realities" of pur- posi\'e action to produce a predictable end. The statement that water * Following Webster, I will use denotation to signify "tlie class of individuals or instances falling under a conception or named by a term. . . . The denotation of a word is its actual meaning; its connotation that which it suggests or imphes in addition to its actual meaning." COMMON SENSE (aND SCIENCE ) 21 seeks its own level becomes meaningful and useful only if I can recognize "water" and the behavior known as "seeking its own level." How precise are these denotations? Their precision is the resultant of a complex process in which desire for reliability and desire for generality (and simplicity) pull in opposite directions. Guided by our past experience we may elect to spell out the denotations in such detail that the risk of misunderstanding is minimized. But by that very act we also minimize the concepts' applicability: the things and situations of the present (and future) will never precisely repro- duce those of the past. The whole possibility of achieving a generally useful colligative relation thus hinges on our willingness not to specify too rigidly the denotations of its conceptual terms. What do I take to be the denotation of "water"? Sometimes clear, sometimes turbid; sometimes "hard," sometimes "soft"; limpid or colored; bland, salty, or bitter; warm or cold; odorless or pungent; potable or contaminated; liquid, solid, or gaseous— how equivocal can a specification be? Yet men of common sense ordinarily agree on what is to be classified as "water." As already noted, the existence of a purpose for which the classification is made sharpens discrim- ination: it establishes the crucial functional characteristics for all who share that purpose. In any matter of seeking its own level, "water" need only be a uniformly dense liquid of modest viscosity- nothing else "counts." For thirsty travelers in the Mohave desert a particular solid will be happily accepted as "water"; but for the cap- tain of a Greenland patrol ship a large block of that particular solid is not "water" but "menace." The concept remains broadly applicable because its denotation rests imprecise, sharpened only as required by the "common sense" of those who, for one purpose or another, must deal with "water." In common sense the tension between the desire for precision and the desire for generality is most often resolved in favor of generality. The number of concepts and relations -with which common sense can work ejffectively is, we shall find, severely restricted. Each concept, each relation, must then render maximum service; and a good deal will be sacrificed in the way of reliability to obtain maximum gen- erality. We all share Poincare's feeling that: "It is far better to fore- see even without certainty than not to foresee at all." Moreover, in the aflFairs of everyday life, with which common sense must deal, we constantly meet multiple special contingencies that no colligative 22 COMMON SENSE (aND SCIENCE) relation— even a specialized one— could handle perfectly. We say "The burned child dreads the fire," but some children who have suflFered a burn do not shun fires. Neither humans nor animals always shun the thing or situation of which they have had disagreeable ex- perience. "It all depends"— on how disagreeable the experience, on the balance of estimated possibility of pleasure against estimated risk of pain, on the psychic state and background of the subject, and so forth. Even specifying all these, the predicted behavior would still sometimes fail to occur. Perfect predictability being unobtainable, we forego the clumsy ( and, in the issue, not readily verifiable ) speci- fications in favor of the brief and unadorned general statement— admittedly crude but perhaps statistically valid as a guide to action. Earlier I suggested that colligative relations could be reduced to the form: "If A, then B." I was not altogether correct. The more ac- curate form is: "If A, then probably approximately B." Due to uncer- tainties in the conceptual denotations, we may err even in routine applications of a given maxim; and in atypical situations even the choice of the approximate maxim may become doubtful. The child who has learned a maxim of common sense has not thereby ac- quired the ability to use it successfully. Knowing it only as an ab- straction, he must still acquire a "feel" for the concrete situations in which it can be used. Polanyi argues that: ... in all applications of a formalism to experience there is an in- determinacy involved, which must be resolved by the observer on the ground of unspecifiable criteria. Now we may say further that the process of applying language to things is also necessarily unformal- ized: that it is inarticulate. Denotation, then, is an art, . . . Experience helps here; indeed, it is indispensable. The child fails to discriminate the situation in which he should look before he leaps from that in which he who hesitates is lost. The experienced battle commander shows his competence in just such discrimination. A FOURTH STAGE IN THE ORGANIZATION OF EXPERIENCE Through three mutually interacting stages we have passed from stimuli to constructs, from constructs to concepts, and from concepts to colligative relations. A multitude of such relations represents the achievement of common sense— a major achievement making pos- COMMON SENSE (aND SCIENCE) 23 sible purposive and generally successful behavior in everyday affairs. But simply as an organization of experience this is still an incom- plete achievement. Command of the bewildering multitude of col- ligative relations— apparently intrinsicalhj individual, discrete, frag- mentary—presents a superficially insoluble problem. To master such relations there seems no alternative to brute-force memorization, an expedient wasteful of time and effort and fundamentally limited by the memory's capacity. The problem is further exacerbated in diat we must memorize not only relations but also the limits in range and reliability pertaining to each, and, beyond that, the manifold denotations that im^est its conceptual terms with experiential rele- vance. The child requires years to master the relations of common sense; the apprentice requires years to master the relations of an empirical craft. We observed earlier that concepts ( words ) mean nothing without relations (sentences), but Wittgenstein adds that "understanding a sentence means understanding a language." Why so? Whitehead has the answer: There is not a sentence which adequately states its own meaning. There is always a background of presupposition which defies analysis by reason of its infinitude. In common sense the major part of the background of presupposi- tion is simply the world-view necessarily implicit in any language of common sense which, for example, takes entirely for granted certain "accredited" concepts of things, and the classes and qualities thereof. Gradually acquiring command of that theory, the child learns, and learns to use, the concepts and relations of common sense precisely as he comes to grasp the "nature" of the world of common sense. Similarly, the apprentice comes to be a master carpenter not simply by memorization and the acquisition of physical dexterity, but when he has grasped the "nature" of wood. With this insight he can pass beyond memorization (of the relations describing the working and structural employments of wood) to something approaching com- prehension of how the various relations arise. We find two major genera in the concepts of common sense ( as in those of science). The first and larger group contains the indicative concepts, with relatively clear denotations, which figure prominently 24 COMMON SENSE (aND SCIENCE ) in colligative relations. A second group, of more abstract explicative concepts, sketches the "causes" and other terms by means of which we seek to grasp the relations. In principle only the indicati^'e con- cepts are directly involved in making predictions— necessarily so since, often, explicative concepts (perhaps figuring "unobservables") do not refer to overt, recognizable things and situations. In practice both groups of concepts are (and probably must be) used; the sec- ond helping us to gain command of relations that function in terms of the first. In common sense even loose and imprecise anthropo- morphic concepts can offer a systematization highly effecti\'e as a mnemonic de\dce. Personifying the things of which we would treat, we imest them with desires and tendencies sufficiently like our own tliat— understanding what our action would be— we easily remember theirs. The child "dreads," water "seeks," nature "abhors," etc. We grasp the relation because we seem to grasp the how of its pro- duction. In common sense the fourth stage in the organization of experi- ence never becomes fully explicit: the formation of a world-view is not, after all, the business of common sense. Often little more than a vague metaphor, the common-sense view of the world leaves a great deal to the judgment and experience of the individual, to his "feeling for die situation." Much has still to be memorized because there remains much that, if "explained," is not yet truly rationalized. The comparatively inchoate body of common sense contains myriad relations not merely disconnected but as downright contradictory as are the injunctions "look before you leap" and "he who hesitates is lost." Science seeks to resolve, or suppress, such contradictions by a con- scious effort mutually to adjust and to unite its myriad relations in a fully explicit, comprehensive, rational order. No longer content to possess Boyle's law, we wish to see Boyle's law in rational connec- tion with a number of other colligative relations describing empiri- cal regularities in the behavior of gases. The kinetic theory provides just such a connection. The several relations now reappear as deduc- tions from the few axioms postulated by the theory. In this dramati- cally new fourth stage in the organization of experience we pass on from colligative relations ("laws") to postulational systems ("theo- ries"), and so achieve the order Einstein considers characteristically that of science: COMMON SENSE ( AND SCIENCE) 25 The aim of science is, on the one hand, a comprehension, as com- plete as possible, of the connection between the sense experiences in their totahty, and, on the other hand, the accomphshment of this aim by the use of a minimum of primary concepts and relations. . . . Science concerns the totahty of the primary concepts, i.e., concepts directly connected with sense experiences, and theorems connecting them. In its first stage of development, science does not contain any- thing else. Our everyday thinking is satisfied on the whole with this level. Such a state of affairs cannot, however, satisfy a spirit which is really scientifically minded; because the totality of concepts and relations obtained in this manner is utterly lacking in logical unity. In order to supplement this deficiency, one invents a system poorer in concepts and relations, a system retaining [though usually in dras- tically modified form] the primary concepts and relations of the "first layer" as logically derived concepts and relations. This new "second- ary system" pays for its higher logical unity by having . . . elemen- tary concepts (concepts of the second layer), . . . which are no longer directly connected with complexes of sense experiences [that is, these are concepts that refer to "unobservables"]. Further striving for logical unity brings us to a tertiary system, . . . Similarities in intent, presuppositions, and subject matter. The profound reorientation of its endeavor sharply diflFerentiates science from common sense, but at least three similarities remain significant. A primal biological drive seeks blindly to make past experience the determinant of present action that will succeed. Become self- conscious in common sense, this drive remains active even on those planes of lofty abstraction along which science extends itself as the continuation of common sense. "There is no sharp line between sci- ence and common sense," says Russell, "both involve expectations, but those resulting from science are more accurate." Meyerson urges that "whoever speaks of science speaks of predetermination," and in Sam- bursky's view this much was true even as far back as the Greeks, for he writes that then, as now, the task of science was to systematize the sum total of our empirical knowledge in such a way as to make it possible to fore- cast future events. This perfectly matches our definition of common sense, but an im- portant redistribution of emphasis will soon be noted. Science and common sense share certain "metaphysical presuppo- 26 COMMON SENSE (aND SCIENCE ) sitions." Down-to-earth common sense with metaphysical presup- positions? Of course, for as Morris Cohen observes: . . . the common sense level is not one of primitive metaphysical innocence. The language of common sense is full of animistic, ancient, and scholastic metaphysics; . . . In the infancy of science its presuppositions were perforce close kin to those of common sense. Science was not born in the void. It began somewhere, and with something. It set out from the position of com- mon sense, and initially took for granted much that common sense assumed. The commitment is not irreversible— scientific experimen- tation began with crude workmen's tools, and these developed later into more suitable equipment; scientific thinking began with the modes of thought of common sense, and these too have under- gone elaboration and modification. Even today, however, scientific thought must set out from the position of contemporary common sense. As Hebb suggests, ... all learning tends to utilize and build on any earlier learning, instead of replacing it (Mowrer, 1941), . . . the learning of the mature animal owes its efficiency to the slow and inefficient learning that has gone before, but may also be limited and canalized by it. The science we learn in maturity is necessarily based on, referred to, and conditioned by the common sense we have learned and accepted in childhood. Not all elements of experience are grist for the mills of either science or common sense. Both seek a communicable knowledge use- fully applicable by all. Both then come naturally to limit their sub- ject matter to experience that is regular enough to give some promise of a potentially predictable association of antecedents and conse- quences; reproducible, or at the very least not infrequently recur- rent; and overt, open to and shared in by all human beings. The profound personal experiences that move us most— that we know best —are not then data acceptable to either science or common sense. They can be accepted only insofar as whatever seems irreducibly spontaneous is rejected ( to meet the demand for regularity ) , what- ever is absolutely unique is left out of account ( to meet the demand for recurrence), and whatever is intrinsically "subjective" is omitted ( to meet the demand for overtness ) . Whate\'er the consequences of COMMON SENSE (aND SCIENCE) 27 such limitation in species of subject matter— and important conse- quences have recently been noted by Sherrington and Schrodinger— this is a limitation science shares with common sense. Some differences: progressivisin and impressiveness. In science we feel a wholly novel dynamic progressivism for which, anticipat- ing the results of later discussion, I find at least three major sources. First, in science the fourth stage in the organization of experience provides an optimal deployment of what we already know in the search for what we do not yet know. Second, in the quest for new knowledge the development of refined physical devices often permits systematic experimentation to replace obsers^ation; and a new elab- oration of mental devices is even more significant. The man of com- mon sense disposes of a limited number of concepts, and must rely on these alone; the conceptual arsenal of the scientist is in constant rapid growth. Finding no existing concept appropriate, he is trained and prepared to make new concepts. Not bound by the resources of everyday language, he makes new words to represent his new con- cepts, and even, as required, new (mathematical) languages with structures different from that of everyday language. Third, science progresses simply because it is critical of its failures. Knowing the relations of common sense to be imperfect, we usually permit the survival even of relations that yield frequent unaccountable failures in prediction. Of a colligative relation of science— of a "law of nature" —we expect and demand more. Here an unexplained failure pro- vokes energetic re-examination of the situation that, by revealing antecedent error, can open the way to subsequent progress. Impressiveness is a further trait we find highly characteristic of modern science. We are amply impressed by the many accurate pre- dictions it supplies, but overivhelmingly impressed by the sense of rational order it conveys to us. Like common sense, science must seek order as means to prediction. But in science the search for theo- retical order takes on new urgency, and becomes so compelling that for most scientists prediction— no longer the end to which organiza- tion is the means— is rather the means of appraising progress toward the goal of rational organization. Why should order seem important as an end in itself? Finding ourselves able to organize our experience of the world, we feel ourselves able to understand the world of our experience. Some curious dualisms of meaning testify to the deep- rootedness of this connection. To articulate means both "to join to- 28 COMMON SENSE (aND SCIENCE) gether" and "to speak distinctly"; to comprehend, both "to include or contain" and "to understand"; coherence, "sticking together" and "consistency in reasoning." There is explanation even in common sense. The tumbling of a mountain stream is for me "explained" by the simple colligative rela- tion: water seeks its own level. Accepting the relation, I see the phe- nomenon as a necessary consequence of an existent initial state. In the same way, if in science I accept Boyle's law, I "understand" the change of volume consequent to the change of pressure on a gas. But now, in that fourth stage of organization characteristic of sci- ence, the myriad colligative relations and laws are themselves brought within a framework of explanation. Accepting the postulates of the kinetic theory, I find that they entail Boyle's law, and many others of its kind. The postulates so explain the relations, and the relations explain the phenomena. Rooted as it is in "vulgar common sense," science takes on the shape sketched by Einstein: Science is the attempt to make the chaotic diversity of our sense- experience correspond to a logically uniform system of thought. In this system single experiences must be correlated with the theoretic structure in such a way that the resulting coordination is unique and convincing. LIBRARY MASS. CHAPTER II Science (and Common Sense) PRELIMINARY survey of science will now be made in terms suggested by its comparison with oiiv reference standard, common sense. SOME "METAPHYSICAL PRINCIPLES" OF SCIENCE Science with "metaphysical principles"? But how else can I describe general ideas that go far beyond the warranty of experience and that are, nevertheless, stubbornly maintained even in tiie face of apparently contradictory experience? The real world. Born comments on . . . Man's need to believe in a real external world, independent of him and permanent, and his ability to mistrust his sensations in order to maintain this belief. The extraordinary success of the common sense (and the common- sense language ) that consistently treats physical objects as possessing "real existence" will not a little justify for the man in the street his belief in reality. But, as Born further observes, The simple and unscientific man's belief in reality is fundamentally the same as that of the scientist. The scientist's accreditation of the idea of a real world remains un- shaken even by the rise of quantum mechanics. Bohr holds to be a fundamental revision of our point of view the realization that: 29 30 SCIENCE (and common sense) ... a close connection exists between the failure of our forms of per- ception, which is founded on the impossibility of a strict separation of phenomena and means of obsei-vation, and the general limits of man's capacity to create concepts, which have their roots in our differentia- tion between subject and object. This being conceded, Rosenfeld, not the least doctrinaire among those who count themselves Bohr's disciples, still maintains that: ... as far as quantum mechanics is concerned, I would say that it is impossible to understand it without assuming that there is an external world which is independent of what we think and which is the ulti- mate origin of all our ideas. In that sense I absolutely reject the sug- gestion of present-day positivists about the subjectivity of our state- ments. Determinism. If I accept the possibility of prediction— whether by common-sense relation or scientific law— I assume determinism. If my past experience teaches me that state A is followed by state B, then, observing a present occurrence of state A, I can predict the future production of state B if and only if I assume the same condi- tions are succeeded always, or at least statistically, by the same re- sults. Prediction often proving possible, the assumption is in a meas- ure justified. But even when prediction fails, rather than question the assumption of determinism on which all hope of prediction depends, I question instead the accuracy and completeness of my specification of the conditions necessary to define state A. At once I seek (and often I find ) a relevant variable earlier overlooked. Continuity. The creature endowed with instinct confronts the apparently chaotic disorder of nature with patterns of fixed re- sponses. That species of creature can then survive only if nature em- bodies some general uniformity to which the fixed responses are, at least statistically, appropriate. Instinct presupposes the continuity of nature? However it may be with instinct, if I accept the possibility of prediction I presuppose, over and above the principle of deter- minism, a principle of continuity. Belief that state B will follow re- liably on the attainment of state A means nothing if not coupled with confidence that state A (or a good approximation to it) ivill recur. We must then assume the "external world" continuous in time, in location, and in species. We assume that things behave here and SCIENCE (and common SENSE ) 31 now in much the way that "similar things" behaved there and then, and will again behave in other eras and places. Dissolubility. Believing in the continuity of nature, I do not con- sider it an absolute continuum. Acknowledging myself a part of na- ture, I still consider myself separate from it. More significantly, we all conceive ours a world of distinct, if interacting, "objects" and "phenomena," in particular "situations" largely independent of the rest of the external world. All our labors of prediction assume this kind of dissolubility, assume each case measurably affected by a relatively small number of conditions— each state of a system ade- quately defined by a relatively small number of variables. Prediction would be impossible had we first to specify or determine the state of the entire universe. Confidently seeking colligative relations, com- mon sense presupposes a principle of dissolubility. Seeking laws, so does science. Emboldened by our predictive successes, both in science and in common sense, we make of the ideas of determinism, continuity, and dissolubility general principles that transcend all possibility of em- pirical justification. These "metaphysical" principles, together with a few others more peculiar to science, are examined in detail in Chapter VII. I broach them here because the sharing of these prin- ciples produces in both science and common sense certain shared criteria for the selection of "fit" subject matter. The Subject Matter of Science We expect recurrence in a world to which the principle of continuity applies, regularity in a world to which the principle of determinism applies, agreement of eyewitnesses in reports of an existing "external world." The principles we accept thus determine the selected ele- ments of experience alone acceptable to us as facts. We are prepared to accept as facts only those elements of experience that are actually or potentially reproducible, regidar enough to offer promise of de- terminist order, and concurrently reported by all "normal" observers. RECURRENCE AND REPRODUCIBILITY Guided by the principle of determinism, we expect that, in circum- stances of adequate control, at least approximate reproduction of the conditions must yield at least approximate reproducibility of tlie 32 SCIENCE (and common sense) results. Ordinarily we can achieve such control in the laboratory, or- dinarily our results are reproducible, and ordinarily the laboratory worker demands reproducibility of anything he is prepared to treat as a result. Yet the demand for reproducibility is not an absolute one. Particularly as regards certain observational results, we may waive reproducibility in practice and accept the much weaker criterion of reproducibility in principle. We do not expect to be able to repro- duce the observations reported for the fall of a particular meteorite. Even in the laboratory, studying cosmic rays we do not expect to be able to reproduce in our cloud chamber exactly the "nuclear event" previously photographed by ourselves or others. In both cases what we observe depends too heavily on variables beyond our con- trol: on the nature, the relative velocity, and the angle of incidence of the intruding "particle." The "event" and the observations made of it are then irreproducible. Yet we accept those observations as facts because we conceive such events as recurrent, or reproducible in principle. Judging that we know the relevant conditions, we agree that the circumstances involved are very "special." And we main- tain that— however improbable in practice— the event, and tlie ob- servations made of it, would be reproduced if the special circum- stances were reproduced in some second meteorite or nucleon. Confronting a particular indentation in the sand— an indentation unique and irreproducible in detail— Robinson Crusoe sees it as a significant datum only because he at once affiliates it with the re- current class "footprints in the sand." Much the same common-sense criterion of acceptability of data is active in the sciences. We accept data on irreproducible things and events when we judge that they belong with "objects of this class," "situations of this type," when we feel that other exemplars of such things and situations are known to us. Even when guided by the subtle sense of analogy with which we are so fortunately endowed, such feelings, such judgments, remain humanly fallible. Recognizing that sometimes we go astray in our judgments of recurrent type and class, we seek ever, by establishing experimental control of conditions, to achieve reproducibility in practice. We acknowledge the less secure criterion of recurrence only when we must. Yet often, even in science, we must. The astron- omer accepts data on the unique trajectory of some particular me- teor because meteors following analogous trajectories are recurrent. And he is likely to reject— as "observational error"— data indicating SCIENCE (and common SENSE ) 33 trajectories "too diflFerent" from those already observed. The physi- cist accepts data on a cosmic ray event he cannot reproduce because he feels it classifiable with other "events of the same kind." The palaeontologist accepts as datum a single jawbone or cranium, and seeks to reconstruct the entire animal involved. The fragment is unique, irreproducible, but he finds in it some filiation or likeness in type with other analogous remains. The sense of analogy renders the datum acceptable and the reconstruction possible. Facts historical and scientific. The distinction drawn between the facts of history and the facts of science (and common sense) is far less sharp and significant than is supposed by one general school of thought— here represented by Langer's statement: . . . nor is historical truth judged by the same criteria as the truth of scientific propositions. For to science, as Lord Russell once remarked in an academic seminar, "A miracle would not be important if it hap- pened only once, or even very rarely"; but in history the point is to find out what did happen just once, what were the specific facts about a specific occasion. As we have just seen, scientists do accept irreproducible data, "spe- cific facts about a specific occasion," if they conceive the occasion to be recurrent. Russell and Langer notwithstanding, the acceptabil- ity of historical data seems to be judged by much the same criterion. In the operations of historians and scientists there is a major dif- ference in temporal reference— is this diflFerence in itself decisive? Surely not! Seeking to reconstruct what happened in the past, the historian must and does take as data only presently available written reports, and the presently surviving physical remnants of antiquity; and part of the interest of his work ( as of the scientist's ) lies in its relevance to present or future situations somehow analogous to those of the past. When as scientist I consider my data, I work in part as historian. I, too, refer to events of the past: I consider my own ex- periments not in their present immediacy but in my memory and (more reliably) in my written laboratory records; I consult the pres- ently a\^ailable reports of my predecessors and contemporaries who have investigated analogous phenomena. My data may be experi- mentally reproducible, as the historian's are not; and perhaps this loould be a decisive diflFerence save that often as scientist I accept the weaker criterion of recurrence. 34 SCIENCE (and common sense) Evaluating my data, I usually find them "consistent" internally— perhaps also in comparison with the data of some other observer(s) of the same or similar events. In any large array of data, however, I am likely to find one or a few that fail of consistency, either inter- nally or externally. If, after long eflFort, I am unable to fit them into the class of the others, I create a new class for them— most often I dismiss them as "errors" or "aberrations." The historian, too, selects his data under the guidance of considerations of consistency. And his interest in his data, and his ability to work with them, are both product of his insight that— however apparently unique and irre- producible the events concerned— yet are they recurrent events, i.e., manifestations of "human nature," "economic determinism," "social stratification," "copyists' error," and so forth. In such classificatory judgments the historian guides himself as does the scientist. Either may err, and then the scientist's error may be the more readily rec- tifiable: often he can get a more abundant supply of data on "events of the same kind." But the palaeontologist is a scientist who generally cannot, and Schliemann a historian who could and did. The scientist finds the unique absolutely intractable, and thus re- jects as data any findings he cannot envision as members of a recur- rent class. The historian finds himself unable "to make anything of" events wholly unlike any others known to him; he, too, shuns the unique. With all due respect to Russell, modern historians rarely do treat of miracles. To the extent that they do so they dispel the uniqueness of miracles by attaching them to a class (e.g., instances of divine intervention in the aflFairs of men, suspensions of natural law, suspensions of human reason). But most nontheological his- torians are uneasy in writing of miracles because it is not plain that they are recurrent; because their proper classification is uncertain; because often there is but one historical account, and that of imper- fect internal consistency, or several accounts with mutual consistency not wholly beyond reproach. The scientist's rejection of miracles as data fit for scientific study is founded on similar considerations— and they are the same considerations he would use routinely as, say, meteor-observer. Uniqueness and identity. We seek general knowledge, general order, general predictability. This quest, frustrated in studies of the wholly unique, can prosper only as we find "sameness." We are then clearly well advised to insist that acceptable as subject matter are SCIENCE (and common SENSE ) 35 only those of the myriad data of experience that show, through re- currence, at least some minimum degree of sameness. One notable exception: if attested by concordant results of independent observ- ers, a unique event may be accepted as subject matter when it seems to violate a supposedly inviolate system of classification. It does not destroy the classification, but it shocks us into attentiveness. The blazing-up of a nova, unmistakably in the sphere of the stars, stirred the interest of men who had assumed the absolute changelessness of that sphere. Aside from such rare exceptions, however, the criterion of recurrence— minimal as it is— is one we seek to enforce absolutely. Common sense rejects data rather lightly. Science does so more reluctantly, and only provisionally, for science is precisely the quest for "sameness" where common sense despairs of finding it. Born writes that the reality of the natural philosopher or scientist . . . presupposes that our sense impressions are not a permanent hallucination, but the indications of, or signals from, an external world which exists independently of us. Although these signals change and move in a most bewildering way, we are aware of objects with invariant properties. The set of these invariants of our sense im- pressions is the physical reality which our mind constructs in a per- fectly unconscious way. This chair here looks different with each movement of my head, each twinkle of my eye, yet I perceive it as the same chair. Science is nothing else than the endeavor to construct these invariants where they are not obvious. Weizsacker strikes a harmonic of the same note when he writes : Certainly experimental science would be impossible if nothing could be perceived, but it would be unnecessary if everything could be perceived. Now at last we can see the full scope of the criterion for selection of subject matter that arises from our acceptance of the principle of continuity. The unique is rejected, as intractable; the identical is also rejected, as uninteresting. My writing table was here last week, is here today, and I assume I will find it here tomorrow. I can scarcely call this a prediction: identity is the norm I take for granted. And as a norm identity is without interest. For the Greeks "phe- nomena" v/ere not simply appearances but appearances of change; for us, too, phenomena are divergences from the perfect continuity of identity. Whether we work in science or in common sense, what 36 sciExcE (and common sense) we accept as data will always be precisely those deviations from perfect continuity we find striking enough to excite our interest but not extreme enough to discourage our endeavor to find continuity, even identity. CONCURRENCE I ha\'e spoken of the concurrence of the reports of diflFerent observers of the same event or thing. Plainly I assume— we all assume— that diflFerent observers tcill see and report the same thing. To any "thing" not so reported or reportable we are quite bold enough to deny status as "fact." W'hether as men of common sense or as scientists, we are prepared to deal only with those parts of our experience in which we find a consensus of agreement with our fellows: overt ex- perience, public experience. "Objective facts?" Again no— they de- pend on human sensitivity and human judgment. But— independent of the sensitivity of any one human— they are the impersonal facts best suited to be subject matter of endeavors seeking knowledge of the "real world" common to all. This much was appreciated very early. Schrodinger quotes the "dark" Heraclitus of Ephesus to the eflFect: It is therefore necessary to follow the common. But while reason is common, the majority live as though they had a private insight of their own. Those who speak with a sound mind must hold fast to what is com- mon to all, . . . The waking have one common world, but the sleeping turn aside each into a world of his own. Taking this "in the epistemological sense," Schrodinger himself writes : Heraclitus is well aware that, actually, there is no diflFerence bet^veen the sense perceptions in dreams and in waking. The only criterion of reality is being common to all. This is the basis upon which we con- struct a real world around us. All spheres of consciousness partially overlap— not quite literally, that is impossible, but by means of physi- cal reactions and communications, which we have learned to under- stand in each other. The overlapping part of the spheres of conscious- ness forms the world that is common to all. However clear in principle, the criterion of concurrence involves serious uncertainties in application. For certification of an observa- SCIENCE (and common SENSE ) 37 tion as "fact" we claim to require a general concurrence of "normally constituted observers." How are we to recognize those normal ob- servers? Beyond the obviously enormous variation in mental charac- teristics of men, the investigations of R. Williams and others demon- strate that even as chemical machines men are never identical with one another. Whatever the situation in the "external world," human experience of it must be xariable because the experiencing hun^an reporters diflFer in biochemical constitution. These differences make themselves felt most notably in reports of tastes and odors. They are less noticeable in reports of visual, auditory, and tactile experience. Even here, however, different individuals falling within the ranee of ^'normal" deviations from the average may make significantly differ- ent reports. Thus Polanyi reminds us of . . . the famous case of the Astronomer Royal, Nicholas Maskeleyne, who [in 1796] dismissed his assistant Kinnebrook for persistently re- cording the passage of stars more than half a second later than he, his superior. Maskeleyne did not realize that an equally watchful ob- server may register systematically different times by the method em- ployed by him; it was only Bessel's realization of this possibility which 20 years later resolved the discrepancy and belatedly justified Kinne- brook. Experimental psychology, of which Bessel thus laid the foundation, has since taught us universally to expect such individual variations in perceptive faculties. Normality, then, is a fairly remote abstraction. Were we to insist that "fact" must represent the rigorous agreement of "normal ob- servers" we might find very few facts indeed. How to proceed? To reject a deviant report or reports ex post facto, as due to "abnor- mality" of the reporters, may seem essentially to vitiate the concur- rence criterion. For then it is not the agreement that makes the fact but we who, by forcing the agreement, in part create the fact. Had we means to detect abnormality independent of failure to concur in observation reports, our position would be stronger. For major ab- normality such means are usually available— lunatics are often recog- nizable as such and we may decline to use them as observers. Less striking abnormalities may also be recognized by the exercise of judgment. Proceeding in this way, most potentially deviant reports might be eliminated by rejecting as qualified observers those likely to give such reports. We can now gain the support of the profound normalizing effect 38 SCIENCE (and common sense) of the concepts used by all obsen^ers— an eflFect particularly marked for the tactile and visual data with which both science and common sense prefer to work. Moreover, for many of the purposes of both, perfectly concordant reports are— however attractive abstractly— simply unnecessary. Finally, if we obtain some 99% of reports con- cordant within the range of acceptability we are in practice quite content to reject the 1% of discrepant reports as due to observational error or some hitherto undetected abnormalitv of the observers. But, even after all these dispensations, still the criterion of concurrence is not reduced to a usable form. For we never could, or do, require a convention of all normal men to attest their concurrence in a "fact." Ordinarily we are satisfied to accept the reports of only a few, and commonly of but one, observer—// the observation involved is one we judge simple and unambiguous. Indeed from a single observer we judge particularly competent we will accept even reports of observa- tions not at all simple and unambiguous. Polanyi tells us that: . . . members of the Fifth International Botanical Congress [1931] declared that "the concept of most species must rest on the judgment and experience of the individual taxonomist," . . . Reflecting on this discussion on the definition of a species, S. C. Hai'land recalled how in Fanny s First Flay, by Bernard Shaw, the dramatic critic replies to the question whether the play was a good play, that if the play was by a good author, then it was a good play. "The situation would ap- pear to be somewhat similar," writes Harland, "in regard to what constitutes a species." In principle the criterion of concurrence is enforced absolutely; in practice we leave large scope to individual judgment— which or- dinarily assumes concurrence— and there is yet no indication that, in the vast majority of cases, we have erred in doing so. Common sense seems to make generally sound judgments of the "simple and unam- biguous" observations in which the report of one "normal" observer is simply repeated when additional witnesses are called in. Science does as well— and even better in that often it can so simplify the observations to be made that the possibility of observational error is minimized. At the extreme of simplification, observation is reduced to reading the position of a needle that moves across a graduated scale until it points to "the result." Judgments of brightness made witii the unaided eye are notably variable, and unreliable, as every SCIENCE (and common SENSE ) 39 amateur photographer well knows. But the pointer reading of an exposure meter yields an observation in which practically every- one at once concurs. A second major gain: the judgment of "normal- ity" is enormously simplified. However deviant from the norm the observer may be, if he is not obviously lunatic or blind we feel that his report of pointer position can be trusted. The use of instruments in general, and pointer-reading instruments in particular, enormously facilitates the application in science of the concurrence criterion of "fact" acknowledged by both science and common sense. Such instruments oflFer us important new powers, but not a general panacea. Instruments may be insufficient even to resolve all problems of concurrence: the Maskeleyne-Kinnebrook episode involved an instrumental observation closely akin to pointer reading. And certainly the major problems of taxonomy seem un- likely to be resolved by any conjectural "reduction" to pointer read- ings. Finally, instruments cannot ensure "objectivity." "Pointer read- ing" may offer so unequivocal a subject for observation that it does not overtax the modest endowment of a Cyclopic moron who can distinguish only black and white. But in principle his observation is not one whit more "objective" than an observation in which we deploy our sensory faculties more extensively. With our instruments we more readily attain the "facts" in which all concur. Warranting their impersonality, our concurrence cannot warrant their "objectiv- ity." But have we need for any such warranty? However "objective" or "subjective," all recurrent experience of which we can attain con- current reports is potential subject matter for science. Whether it becomes actual subject matter depends on a third criterion, to which we now turn. REGULARITY In both science and common sense we work upon experience until it has been reduced to an order on which predictions can be founded. Data which seem to fall beyond any hope of such reduction are apt to go neglected, regardless of their intrinsic interest. To such data we may even deny status as fact— as when Bernard writes : . . . if a phenomenon, in an experiment, had such a contradictory ap- pearance that it did not necessarily connect itself with determinate causes, then reason should reject the fact as nonscientific. ... in the presence of such a fact, men of science must never hesitate; they 40 SCIENCE (and common sense) must believe in science [which Bernard here equates with detennin- ism] and doubt their means of investigation. Spawn of our faith in the principle of determinism, the criterion of regularity here comes in play. Nowhere is the need for judgment more apparent than in use of the criterion of regularity. Polanyi remarks that crystallographic analysis . . . defines a polyhedron which is taken to be the theoretical shape of a crystal specimen. It embodies only such aspects of the specimen as are deemed regular and in respect to these it is required to fit the facts of experience; but otherwise, however widely the crystal speci- men deviates from the theory, this will be [fiiTnly ignored and] put down as a shortcoming of the crystal and not of the theory. Theoretic judgments are necessarily involved whenever the scientist brings the criterion of regularity to bear and, since his theories or his interpretations of them may err, his judgments may err. Yet always he must apply the criterion of regularity, always he must make a be- ginning somewhere— with just those data he judges potentially re- ducible to order. The detailed course of a feather falling in air is totally unpredict- able in the view of common sense and, beyond noticing that the feather falls irregularly, common sense does not concern itself with this matter. The scientist judges that the fall of the feather is completely determined in principle, but complexly determined by multiple conditions difficult to evaluate, much more difficult to con- trol. Such falls are recurrent (though not reproducible); at least ap- proximately concurrent descriptions of them can be obtained from diflFerent observers— and wholly unexceptionable descriptions from high-speed stroboscopic photography. But these data seem still so little accessible to reduction to order ( and, given our theoretic views, so little likely to teach us anything new) that they are rejected as subject matter. Consider mirages. Irreproducible in detail, they are yet recurrent. Moreo\'er, we get substantially concurrent reports of them from all those present at a given place at a given time. Beyond noting, per- haps, that mirages are frequent in desert conditions, common sense declines to deal with data on mirages: it sees no prospect whatever of reducing them to determinist order. This lack of orderability, not the possible presence of a "subjective" element, is what makes the SCIENCE (and common SENSE ) 41 mirage data unacceptable. That is made perfectly plain by the treat- ment of such data in science. For at last they do become scientific data— precisely when scientists first conceive the hope of associating these data in a determinist order with others in the general domains of optics and meteorology. This hope being entertained (and since gratified), mirage obser\^ations become data every bit as acceptable as subject matter for science as the stick ("subjectively?") seen bent in water, and phenomena of refraction more generally. What of the more genuinely subjecti\^e experiences of dreams, hallucinations, apocalyptic revelations, and so forth? The criterion of concurrence may seem permanently to rule them out of court: no- body else is or can be a witness of my dream. However— though the dream is not certifiable as fact— my report of a dream is so certifiable, by the concurrence of multiple observers of me. Rejecting ( as "idle superstition") the ancients' interpretations, modern common sense refused to concern itself with reports of dreams amply recurrent and, as reports, certified by the concurrence of witnesses. Reports of dreams may be related to the wearing of a crown, and reports of hallucinations to excessive use of alcohol, but beyond this common sense seems unwilling to go— unwilling because unable: there seems to be no detectable regularity in the reports of dreams, which come sporadically and without recognizably necessary antecedents. Science shows the same unwillingness as long as it shares the same incapacity. But as soon as we conceive a possibility of ordering these reports of subjective experiences they become acceptable subject matter. Thus details in the reports of dreams, formerly rejected as meaningless, become data of scientific interest to Freud and his followers. Consider a perfectly parallel case involving "physical" rather than "mental" experience. About 50% of human observers report the taste of p-ethoxy-phenylthiocarbamide as intensely bitter; the other 50% as tasteless. My experience of the thiocarbamide is every bit as "real" as my experience of a pointer moving across a graduated scale; but there is a fundamental difference in the matter of concurrence. The position of the pointer is certifiable as fact and the taste of the thio- carbamide is not. But the reports of bitterness or tastelessness do meet the criterion of concurrence and are certifiable as fact by the concurrence of multiple observers of the tasters. What will be done about such facts? As long as there is no prospect of involving them in some regular pattern— essentially nothing. But interest flickers into 42 SCIENCE (and common sense) life with the discovery that this capacity for tasting is inherited with the statistical regularity of a dominant Mendelian trait; and would blaze up if this capacity could be related to other, independently determinable, data— e.g., the presence or absence or variable constitu- tion of some particular enzyme. DATA AND JUDGMENT Common sense deals primarily with what is experienced by all man- kind; science encompasses, in addition, what is experienced, in the laboratory, by but a few. This distinction seems unimportant: the special experience of scientists is potentially available to all willing to enter the laboratory. The fundamental distinction between the data acceptable to science and those acceptable to common sense arises from what has repeatedly been stressed: the involvement of judgment in our use of the three criteria for the selection of subject matter shared by common sense and science. An "object in tlie sky" judged to be an alien spaceship is a datum of interest to astronomers; classified as a case of mass hallucination it is, at most, of marginal interest to psychologists. Thus long before our judgments determine hoio we arrange our data, they determine ichat we accept as data. Like the principles of jurisprudence, our criteria for the selection of subject matter offer general guide lines but not detailed rulings. And even while the scientist works as de- tective he must anticipate how, acting later as judge, he will inter- pret the general criteria in specific rulings on tlie admissibility and weight of the various possible items of evidence. A priori his wisdom cannot be appraised: a posteriori his judgment passes subject to re- \aew. If a scientist finds, in some particular selection of data, hitherto undetected elements of continuity and determinism— we acclaim him a man of genius; failing in his quest, his judgment is by us con- demned—we dismiss him as a misguided fool, or a visionary who sought to do what cannot be done. As it begins science judges the acceptability of subject matter much as does common sense. As science develops— as its view of the world becomes more highly elaborated— it makes these judgments differently. It may then come to pay attention even to data common sense would scorn: a pointer reading is, after all, a rather tri\'ial item of experience to which we pay attention only as, given the theoretic views of science, we grasp its significance. Made bold by successes SCIENCE (and common SENSE ) 43 already won, scientists come to seek more widely and tenaciously for continuity and determinism, even where common sense wholly de- spairs of finding them. Particularly as regards regularity, the scien- tist's horizon of expectation is ever expanding. He finds then even in wholly impersonal data a compelling excitement to which the man of common sense is utterly unawakened. For, says Maxwell: It is a universal condition of the enjoyable that the mind must believe in the existence of a [discoverable] law and yet have a mystery to move in. The Organization of Experience Science involves a fourth stage in the organization of experience, of a sort unknown to common sense. But this fourth stage is not a super- structure built on the otherwise unchanged foundation aflForded by the first three. The colligative relations of science diflFer from those of common sense, if only because they involve different concepts. And, deploying different concepts, the scientist often arrives at con- structs different from those of the man in the street. Let us now sub- ject science to the successive steps of analysis earlier carried out on common sense. CONSTRUCTS The scientist is likely to make common-sense constructs of whatever does not immediately concern him as scientist. Conditioned by a massive common heritage, he is predisposed toward the constructs made by the man of common sense whenever they share the same purpose. Presumably the scientist "sees" the table beneath his ap- paratus as just the "support" it ordinarily seems to the common man. The situation changes drastically when the scientist turns to things that command his attention as scientist. When he looks at his manom- eter he does not, like the ordinary man, see a constiaiction of glass, held on steel supports, and containing mercury. Instead he is apt to "see" only one aspect of his manometer, and that so trivial, appar- ently, it might wholly escape the man of common sense. The scientist sees focaUij only the difference in the height of the mercury columns. His grasp of the scientific concept of pressure shapes his construct of the manometer to highlight what is, for him, "die only thing that matters." 44 SCIENCE (and common sense) ^^'here new concepts are used, new constructs are made. Often these scientific constructs may appear superior approximations to "pure observation reports." Sufficiently taxed (e.g., by optical illu- sions), even common sense will seek to reform its constructs— to separate what is "given" from what, plausibly but perhaps ground- lessly, has been inferred. But history has taught the scientist that a great deal of effort may be invested profitably in this separation— in trying to free constructs from their customary freight of uncon- scious inference. This procedure the scientist calls "paying attention to the observables," and as a procedure it has been of crucial impor- tance to such 20th-century developments as quantum mechanics and relativistic mechanics. The scientist's resolve to "pay attention to observables" is too often mistaken for a profound new insight of modern science. That resolve is already detectable in the remote beginnings of science with such as Aristarchus and Copernicus. Galileo writes: ... I cannot find any bounds for my admiration how reason was able in Aristarchus and Copernicus to commit such a rape upon their senses, as in despite thereof, to make herself mistress of their credulity. Of course there was no rape upon the senses: what reason did was simply to undo or redo what reason had formerly done. By reason, using new concepts, Aristarchus and Copernicus managed to recast or reconstruct what had long passed as the naked report of the senses though it contained a large component of "credulity": plausible in- ference with which it had been laden by common-sense reason. "The naked report of the senses," shown in Chapter I to fall be- yond the reach of common sense, is for science, too, an utterly un- attainable ideal. Also, I think, in some degree a sterile ideal. If I re- port pointer readings and nothing more I report nothing of interest to science. Interest develops precisely as the pointer readings are associated with inferences. Consider Poincare's example: I obsei-\'e the deviation of a galvanometer by the aid of a movable minor which projects a luminous image or spot on a divided scale. The crude fact is this: I see the spot displace itself on the scale, and the scientific fact is this: a current passes in the circuit. ... if I ask an ignorant visitor: Is the current passing? he looks at the wire to try to see something pass; but if I put the same question SCIENCE (and common SENSE ) 45 to my assistant who understands my language, he will know I mean: Does the spot move? and he will look at the scale. Observe the perfect parallelism of this and a common-sense situation sketched by Herschel: In Captain Head's amusing and vivid description of his journey across the Pampas of South America occurs an anecdote quite in point. His guide one day suddenly stopped him, and, pointing high into the air, cried out, "A lion!" Surprised at such an exclamation, ac- companied with such an act, he turned up his eyes, and with diffi- culty perceived, at an immeasurable height, a flight of condors soar- ing in circles in a particular spot. Beneath that spot, far out of sight of himself or guide, lay the carcass of a horse, and over that carcass stood (as the guide well knew) the lion, whom the condors were eyeing with envy from their airy height. The signal of the birds was to him what the sight of the lion alone could have been to the traveler, a full assurance of its existence. The scientist's constructs carry no small burden of inference: see- ing a spot of light, he "observes" (and reports) an electric current. The scientific constructs diflFer from those made by common sense in the nature of their inferential freight, perhaps also in the reduced magnitude of their freight of unconscious inference. But of this there is always some. Braithwaite conceives that: The peaks of [theoretic] science may appear to be floating in the clouds, but their foundations are in the hard facts of experience. Popper proposes a related metaphor w^hich, however, finds "softness'^ in Braithwaite's foundations : The empirical basis of objective science has thus nothing "absolute" about it. Science does not rest upon rock-bottom. The bold sti-ucture of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or "given" base; and when we cease our attempts to drive our piles into a deeper layer, it is not be- cause we have reached fiiTn ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being. The towering structure of theoretic science is then stable only as, from time to time, scientists of the calibre of Aristarchus or Coperni- 46 SCIENCE (and common sense) cus or Einstein recognize a need, and an opportunity, to drive new and deeper pilings— to reformulate the constructs. That opportunity presents itself as new scientific concepts are brought into play. SCIENTIFIC CONCEPTS Scientific concepts, like their counterparts in common sense, fall into two distinguishable though not wholly distinct groups. There are, first, the lower-level indicative concepts, having reasonably clear experiential denotations, which give us power to create and use the colligative relations through which we seek to forecast the future. There are, second, the more abstract explicative concepts, often lack- ing such denotations, which give us power to work a further organ- ization of experience by bringing the separate colligative relations into association with each odier. Extended discussion of the second group of scientific concepts I defer to Chapter VIII, where I consider them in the context of the theories they make possible. Serving diflFerent (logical) functions, they diflFer radically from their common-sense counterparts; servang a similar explicative role, they somewhat resemble those counter- parts. Thus, for example, we forever seek to construe what seems strange and puzzling in terms of analogies with what we have come to find familiar and take for granted. In common sense we may con- ceive physical causes on the analogy of the emotions we suppose to be the "cause" of human activity. In science purpose or volition is not acceptable as a physical cause; but the concept of "force," which loomed so large in Newtonian mechanics, is an anthropomorphic cause patterned on a familiar analogue. Meyerson correctly draws the general conclusion that . . . starting from a conception of the world such as our naive per- ception offers, the physicist has never transformed it save by putting into play the very rules according to which this conception was consti- tuted. He has continually substituted the invisible for the visible, but what he has created is of the same order as what he has destroyed. The strangeness of scientific concepts. The concepts of science, whether indicative or explicative, often strike us as "strange." They must seem strange. The common-sense concepts, grasped in child- hood, we find sanctified in the very structure of everyday language. The scientific concepts we acquire much later in life; only with diffi- SCIENCE (and common SENSE ) 47 culty can we come to feel at ease with these late acquisitions, and with the exotic language in which they are expressed. We may then be led to compare scientific concepts unfavorably with the "natural" concepts of common sense. This is nonsense, for, as Einstein obsers^es: Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. When the task is different, the most appropriate conceptual tool may well be different. Thus, for example, if through the indicative concepts of common sense we arrive at predictively powerful colliga- tive relations, those concepts fully discharge the function for which they were devised. But these relations of common sense do not lend themselves to the fourth stage of organization sought in science. And so in science we seek, through indicative concepts expressly designed with this different function in mind, for relations that do so lend themselves. For conceptual evolution common sense and science thus constitute two distinct though overlapping domains, imposing dis- tinct though related demands. The everyday concepts, enormously successful in the domain of common sense, do not thereby establish any claim to fitness for survival in the domain of science. Because the motions of swimming are useful in propelling us through water, it does not follow that we do best to breast-stroke along the beach. Devices of men bent on the quest for a comprehensive rational order in experience, the concepts of science fall subject to natural selection in the world of man's experience. How by "natural selec- tion"? The scientific concept "cell" is a thing-concept that synthesizes, from various perceptual elements, a "something." Like the common- sense concept of "physical object," "cell" refers also to a conspic- uously abstract something: an extraordinary variety of actual forms are all grouped under the rubric of one diagrammatic representation of a typical cell. In both cases the concrete value of the abstract con- cept is abundantly demonstrated, however, as we find that what it joins together can, in thought or in action, be handled effectively as SL something. Passing on to class-concepts, we encounter here the traditional tools of classification so richly represented in the endeav- ors of biologists and geologists. A less hackneyed example, perhaps, is the chemist's concept— "carbon"— which holds fundamentally iden- tical substances as different as charcoal, graphite, and diamond. Such 48 SCIENCE (and common sense) a concept cannot but seem bizarre: it ignores enormous ("super- ficial") diflFerences, and takes as its basis of classification qualities far less obvious than those on which common sense founds its classifica- tions. However bizarre, these concepts of science nevertheless satisfy a final and decisive criterion: with them we find major elements of order that the classificatory concepts of common sense fail to reveal. Says Bronowski: It is not obviously silly to classify flowers by their colors; after all, the bluer flowers do tend to be associated with colder climates and greater heights. There is nothing wrong with the system in advance. It simply does not work as conveniently and as instructively as Lin- naeus's classification by family likenesses. Thus, Mill correctly observes, general classificatory conceptions formed in advance of complete knowledge must always correspond to Bacon's "notiones temere a rebus abstractae": Yet such premature conceptions we must be continually making up, in our progress to something better. . . . That the conception we have obtained is the one we want, can only be known when we have done the work for the sake of which we wanted it; . . . Concepts and the anatomization of experience. Always the search for order is guided by the scientist's feeling for the nature of what Bronowski calls "the reality behind the appearances." This feeling finds clearest expression in his explicative concepts— the "causes" he thinks significant— but these profoundly influence his construction and use of indicati\^e concepts. An immense advance in science may thus have its roots in an alteration of point of view which produces a new or newly modified group of indicative concepts. Inspired by the Pythagorean faith tliat mathematics is the language of the book of Nature, Galileo brought a new "set" to a realm of experience that had defied all earlier efforts at conquest. Studying moving bodies, Galileo proposed to ignore the weight, size, texture, color, and every- thing else that makes each one a distinctive body, and to consider instead only the mathematically describable motion of which all par- take. "\^elocity," "acceleration," and some of Galileo's other key concepts are typical quality-concepts, indicating one aspect with respect to which many otherwise disparate objects may be compared, and so related, with one another. However, the "qualities" with which SCIENCE (and common SENSE ) 49 Galileo worked do not merely relate objects but, in a sense, create order. Consider that, in his experiments, Galileo could not observe "velocity"; he could observe only that a moving body occupies vari- ous spatial positions at various times. The concept of velocity sug- gests a particular co-ordination of these observations. We divide "dis- tances tra\'eled" by "elapsed times." The quotients so extracted from the actual observations are what we call "velocities." The virtue of such indirection becomes manifest if, for example, we encounter a case of uniform motion: underlying all the changes of position with time we find an unchanging "velocity," in the apparent chaos of kine- matic experience we find an element of identity. Suppose we find no such case of uniform motion. We may then seek through still more abstract concepts for the elusive element of identity we hope and expect to find underlying all change. We can turn to the subtle concept of "acceleration." Accelerations we may extract from the elapsed times and the previously calculated veloci- ties. And in cases of free fall Galileo's intuition finds its triumph. Underlying the changing times and positions of falling bodies gen- erally, there is an unchanging acceleration. Thus we have found not merely order but a genuine element of identity where common sense finds none. Common sense fails here because— no prolific constructor of new concepts— it is most unlikely to create quality-concepts re- ferring to no particular observables but to special, superficially mys- terious combinations thereof. Scientific quality-concepts involving such combinations are of course in no way peculiar to kinematics. Thus the concept density teaches us to see— underlying all our experi- ences of weight and volume with a given substance— a "something constant": the quotients of weights divided by volumes. Such dis- coveries, investing us with new predictive powers, we express in colligative relations. COLLIGATIVE RELATIONS ("LAWS") The relations we can find and express depend on the indicative con- cepts we devise and deploy. Science here enjoys a superiority quali- tative as well as quantitative. The abundant stock of scientific con- cepts makes possible specialization of function; precision of denota- tion need not be so deeply compromised by the search for general applicability. In science we thus arrive at colligative relations ap- parently so far superior to those of common sense we regard them as 50 SCIENCE (and common sense) ^aws of nature." These laws are still, however, humanly created and expressed laws, not unmarked by the characteristics of their creators. By no stretch of imagination can such laws be considered mere "eco- nomic descriptions" of obser\^ables, or the like. At first sight we may conceive the possibility of easily arriving at, say, the law of the lever, purely on the basis of observation. Imagine how we might try to do so— assuming ourselves untutored savages who, however preposter- ously, have a modern outlook, a taste for systematic study, and some knowledge of elementary mathematics. The law of the lever. Our casual experience of moving boulders with a wooden beam is an inadequate foundation for discovery of the law of the lever. In the opening scene of this little fantasy we are found sitting in front of our cave, manipulating an assembly of a light, rigid, straight bar (if not a titanium rod, perhaps a fragment of a giraflFe's shinbone), a sharp horizontal support (if not an agate knife-edge, then a suitably chipped rock outcropping), and an as- sortment of objects. Do not ask now ivhy we should concern ourselves with this curious array of things in the first place: we are too busy discovering the law of the lever. We hang two objects, arbitrarily chosen, at arbitrarily chosen posi- tions along the bar. Sliding the bar along the support, F, we discover one curiously unique position between the points of suspension of the two objects. When this position falls directly over F, the bar re- mains at rest in a horizontal plane— after a series of oscillations we agree to ignore as "irrelevant." When this state is attained we say: *'The system is in balance." Without making any other change, we now add a third object to one of those already suspended. We find that the system then is no longer in balance. But balance can be re- stored, we find, by shifting the bar along the support F in the direc- tion that approaches the added object to F. Continuing such trials, we find that, by suitable placement on the support F, we can bring the system into balance even when we have but one object on one side of F and a great many objects, suspended together, on the other side. Already we have passed far beyond "pure observation." Into our report have crept distinctly conceptual elements like side, support, one and many, horizontal, system, etc. Moreover, if we are still rea- sonably close to pure observations, we are also painfully far from having gotten anywhere with them. Clearly we are not going to get SCIENCE (and common SENSE ) 51 anywhere until we structure the percepts with some further concepts. Though the lever's law be a "law of nature," yet we must contrive to grasp it— contrive with tools mental as well as physical. Though simple, the physical equipment is of considerable artificiality; the concepts we need, though also simple, are substantial abstractions. The first of these concepts is "distance." Speaking of the "distance" between F and the point of suspension of an object, we focus atten- tion on what is, for our purposes, the best characterization of the separation of F and object. "Distance" we hold to be independent of the material composition and surface characteristics of the bar along which it is measured. This kind of independence is not a priori ob- vious: if concerned with the distance of a place to which we wish to journey, we do consider the nature of the intervening terrain (swamps, mountains, rivers, etc.). Indeed, this kind of distance may be more meaningfully expressed in the Indian "moons" (a primitive unit of space-time?) than in miles or kilometers. But let us suppose ourselves fortunate enough to conceive "distance" as a "length" meas- ured along the beam with a meter stick (or a straight spear gradu- ated in arbitrary but equal intervals, and carefully preserved under goatskin in an atmosphere of constant humidity within a vault at the back of our cave ) . "Distance" singles out one aspect of a complex experience; the concept "weight" demands an abstraction at least as difficult. Saying "weighty objects" we come to consider one particular aspect of our experience of objects that may be simple or complex, fluid or solid; completely different in geometric form, material composition, and so on. We so initiate a dissociation of the physical object: from "mov- ing bodies" Galileo passes on to "motion"; from "weighty objects" we pass on to "weight." The "weight" of a body we may conceive as corresponding to the muscle pull we exert to lift it. But this corre- spondence is not uncomplicated: we must, for instance, discriminate the effort of lifting from the mere awkwardness of lifting a body of unfelicitous bulk or shape. ( Was the difficulty of this discrimination responsible for what was once the accepted opinion— that a corpse weighs more than the pliant living body it was?) Fortunately our appreciation of weightiness can be sharpened as we recognize one obvious special case of the law of the lever. Suspending objects at equal distances from the support F, suppose we choose two objects that bring the system into balance when so suspended. The two ob- 52 SCIENCE (and common sense) jects so selected— dissimilar perhaps as a sack of millet and a bar of gold— ha\^e a remarkable relation. Interchanging their positions, we find the system still in balance— an unprecedented de\'elopment. More remarkable still, we find that in all situations of our lever sys- tem anything balanced by the millet is alike balanced by the gold. The equal-arm balance thus singles out that quality— characteristic of millet as of gold— we agree to call "weight." We now adopt a cer- tain object (e.g., a stone) as an arbitrary unit of "weight," just as we took a spearshaft as our unit of length. Another object that balances this stone on our equal-arm balance is then also of one-unit weight. An object balanced by two one-unit objects is said to have two units of weight, and so on. Grasping the concepts weight and distance, we can at last state our problem in an abstract sketch of the system: Wi W2 Placing various weights at various distances along the shaft, we now expect soon to arrive at the law that governs the equilibrium of the system, namely: ti;2 di This "discovery" of a "purely phenomenologic" relation is no drama of man's intellectual powers, but a fantasy. Why? We assumed our- sehes untutored savages. The law was first enunciated by no un- tutored savage. Much is, then, hidden in the qualification "untu- tored savages with a modern outlook." We began with the a\'owed intention of discovering the law of the lever, which we already knew, but not even an untutored savage with a modern outlook would have such knowledge. At the very least we assumed awareness of a problem and the desire to solve it, though this problem does not force itself on us in an experience rich in oddments of many more pressing ^'arieties. Even in formulating our problem we have assumed SCIENCE (and common SENSE ) 53 grasp of the concepts of weight and distance, which are not "given" in experience, and we have further supposed their denotations at once estabhshed with contrivance of auxihary experimental tools like the meter stick and the equal-arm balance. A further element of fantasy develops around just such tools. In a real inquiry, directed toward the discovery of a relation not already known, the clean un- complicated beam and fulcrum with which we began would appear not at the beginning but very near the end. We specified as the beam a light, straight, rigid body— e.g., a segment of a giraflFe's shinbone. But this prescription is not "given" us. A priori we might as well have picked the jawbone of an ass, a subject much less suitable for the dis- covery of the law of the lever. Starting with a simple device, and concepts, suitable for the solution of a problem already clearly for- mulated, we began with more than half the battle already won. Perhaps the greatest element of fantasy in my sketch has yet to be noted. I assumed measurements that lead to the law of the lever. These were synthetic measurements; actual measurements do not yield the simple equality of weight and distance ratios indicated in the law. The weights are, after all, not the only weighty objects in the system: the beam itself has weight. Neglecting this we neglect an essential element of the situation. What to do? We cannot simply introduce the highly sophisticated concept of a "center of gravity"; this surely will not have occurred to us before we have even grasped the law of the lever. Perhaps we might think to stipulate use of a very light beam and very heavy weights. But then a dijfferent complica- tion sets in when the beam begins to bend. Ultimately there are three major courses open to us. First: we might complicate our statement of the law of the lever to allow for the weight of the beam, its rigidity, the lengths by which it projects on either side of the fulcrum, etc. Such an expedient is repugnant to science and to common sense alike; we arrive then at an awkwardly complex expression difficult to think about and difficult to use as a predictive device. Second: we might say our results are "good enough" to justify statement of the uncomplicated law of the lever as a rough working rule. This would be the course followed in com- mon sense. Third: we might adopt a course characteristically that of science. We postulate an ideal lever: a straight, rigid, weightless beam— essentially equivalent to a Euclidean straight line— borne fric- tionlessly on an ideal fulcrum. Feeling we understand why our actual 54 SCIENCE (and common sense) results are not perfectly represented by the ideally simple law, we concei\^e an ideal lever to which, we say, the law would perfectly apply. The practical situation remains wholly unaltered: the intel- lectual thrust is wholly diflFerent. The man of common sense matches law and observation by holding that the ideal law of the lever is only approximate— only a rough but useful description of actual observa- tions. The scientist matches law and obsers^ation by holding that the law of the ideal lever is r/gorow5— adding only that actual observa- tions with real levers are only more or less imperfect approximations to what we would observe were there in the real world ideal levers with which to work. This was essentially the procedure adopted by Archimedes. It represents an immense abstraction. Denotation. For all its abstractness, the law of the lever remains a colligative relation: its statement involves only concepts with reason- ably clear denotations. In "weight" we may seem to deal with an adjectival quality-concept, "weighty," dangerously and absurdly mas- queraded as a noun— a "real quality." And "distance" seems an ab- straction equally extreme. But unlike the philosophic "qualities," our concepts do have denotations. "Weight" is something crudely indi- cated by muscular effort and, more precisely, by measurement with an equal-arm balance; "distance" is something given crudely by visual inspection and, more precisely, by measurement with a meter stick. The instruments somewhat sharpen and clarify the conceptLial de- notations, but there remain major problems they do not even begin to solve. This is nowhere clearer than in the matter of our concept of "lever." The ideal lever, to which alone the ideal law applies rigor- ously, exists only in our minds. We might embark on elaborate speci- fications of certain particular "levers" we have found to be adequate approximations to the ideal. Yet we do not; only by foregoing such specifications do we first gain power to make predictions about sys- tems substantially different from those with which we have already worked. Having in mind the ideal lever— knowing what we're looking for— we can discern lever action in systems in which the presence of any Xevex is far from evident. We come thereby to make excellent predictions about the performance of such devices as wheel (or crank) and axle, compound pulleys, and the like. As always, such generality is purchased only at cost to reliability. Experience alone SCIENCE (and common SENSE ) 55 can now teach us to be wary in applying the simple law to systems highly "non-ideal": e.g., with "beams" made of a roll of paper or a stick of chewing gum. We learn that if we have a reasonably light, reasonably rigid, reasonably straight beam with reasonably good bearing surfaces and reasonably heavy weights— then we can make reasonably accurate predictions of its behavior. Most important of all, we must learn to judge what is meant by "reasonably." Just as in common sense, then, denotation remains in science something of an art, the proper practice of which we learn only by experience. The ensemble of colligative relations. Compare the colligative re- lations of science with those of common sense. The "laws" of science are far more subtle, far more consistent with one another, far more sophisticated. We may suppose them also far superior in reliability and generality but— in view of the tension between these two factors —the superiority cannot be absolute. Given the reliability we expect of it, a "law of nature" must be so formulated that it is almost com- pletely inapplicable in the tangled circumstances of everyday life. Here the rough-and-ready common-sense maxim— however less re- liable—is far more generally applicable. Outside his laboratory even the most doctrinaire scientist bases the vast majority of his decisions on common-sense maxim ("horse sense") rather than on scientific law. On the other hand, given the generality we expect of a "law of. nature" we must, as we have seen, accept a looseness in the denota- tion of its conceptual terms resolved only by the exercise of an art. That art being ever necessary— and necessarily ever uncertain— even the "law of nature" must then reduce to the general form of the colligative relation: // A, then probably approximately B. If a "lever"^ is so loaded that ividi ^ t02d2, then probably it will be in balance; or, if we wish a "lever" to balance, then the second weight, W2, must be attached at a distance from the fulcrum approximately equal to Widi/toz. Considering what we demand of a scientific law, consider- ing too the range within which we check its predictions and the pre- cision with which these checks are made, the qualifications ". . . probably . . . approximately . . ." are needed here as urgently as when we write a maxim of common sense. I conceive that the crucial diflFerence between the colligative rela- tions of science and those of common sense is irreducible to dif- ferences in generality or reliability— or subtlety or consistency or 56 SCIENCE (and common sense) sophistication— important though all of these may be. The crucial diflFerence is, I think, simply this: beyond investing us with predic- tive powers, the scientific relation lends itself to that fourth stage of organization sought by science but inaccessible, and quite unknown, to common sense. ^^'ith Poincare, let us imagine our science systematically built up from relations, as a house is with stones. Common sense provides us with a heap of stones; natural history with heaps of stones carefully assorted according to size, shape, texture, etc. But only in the edifice of science do we have a coherent structure in which the individual stones are bound together in an orderly fashion by the mortar of logic and mathematics. We hope to learn to know the stone by recogniz- ing its position in the house, to master the individual relation by seeing it in the larger context of a postulational system in which it appears as logically derivative. So hoping, we demand that scientific laws lend themselves to such seeing, demand that they constitute subjects suited to the thoughts of men seeking a thorough- going ra- tionalization of experience. The superficially absurd abstractions like the ideal lever here come fully into their own. We think of science as based on our experience of the world, and so it is. Yet sometimes we seem to ignore that experience, even to deny it. Rather than pondering our real experience of real lever sys- tems we set ourselves to contemplate fictions— an ideal lever and the ideal law thereof. In so doing we make an immense gain. The raw phenomena are complicated and variable; the ideal law, which only sketches them, offers an ideally simple statement about "ideal" phe- nomena. Considering the colligative relation, we can forget for the time being all the "imperfections" reflected in our actual experience —confused by the only partially determinate effects of a multitude of "secondary factors"— and take as subject a "pure" relation. We be- gin the difficult task of theoretic construction with ideally simple entities and relations— with readily manipulable fictions represented in terse, abstract, often symbolic form. Such entities are the partless points and widthless lines of geometry, the mass-points (and ideal lever) of mechanics, the ideal gas of pneumatics, the ideal solutions of chemistry— all of them represented by ideal laws. Setting out from these, we may be able to arrive at a conception of some very general postulates from which "follow" a multitude of colligative relations. SCIENCE (and common SENSE ) 57 SCIENTIFIC THEORIES Rejoicing in possession of myriad predictively powerful colligative relations, we find diem less dian our heart's desire in two important respects. First is the practical problem of r^m^mben'ng— remember- ing not merely relations but also, for each, the auxiliary material without which the relation has little value: the "stops" defining its general range of applicability, the "feel" for the reliability of its pre- dictions in various parts of that range, the grasp of the many alter- nate denotations attaching to its conceptual terms. This first problem arises presumably from the inadequacy of human memory; a second problem arises surely from the intransigence of human aspiration. We want to grasp the origin of scientific laws. We want to know how or why they are as good as they are, and how or why they are de- fective as they are. Whatever the predictive capacities they give us, these relations leave us unsatisfied until we can "explain" them. There is then the theoretical problem of understanding. Were we able to solve this second problem, we would take a long step toward solution of the first. We easily remember a rational statement involv- ing some hundred-odd words; we find it far more difficult to memo- rize a hundred-odd words in a nonsense sequence. We seek then to see scientific laws as parts of a higher rational order. Were our minds and our intellectual heritage diflFerent, we might find quite difiFerent orders rational. Being what we are, we find su- premely rational the order of a postulational system, that particular order of which Euclidean geometry presents us with a familiar ex- ample. Such a system stipulates a small number of axioms, and cer- tain rules for handling them. From the axioms, following the rules, we then arrive deductively at a vast number of theorems which are for us thereby "explained." Even today only a few physical theories achieve some distant approximation to the strict form of a postula- tional system; and this form is stilh anything but apparent in the representative theories of, say, geology and biology. But scientific theories have invariably the character of postulational systems: al- ways they offer rational correlations in which, from a given set of premises, we deduce an array of theorems we identify with colliga- tive relations. The "deduction" and, even more, the "identification" involve complexities to be examined in Chapter VIII. For the present 58 SCIENCE (and common sense) I seek only, through a simple example, to display the three func- tional roles of scientific theories. The kinetic theory. With a constant quantity of gas at constant temperature the product of pressure and volume is constant. Through the reasonably clear denotations of its conceptual terms, Boyle's law furnishes a good account of one aspect of our experience of gases. But this account is not perfect: between the law and our experience of gases we find appreciable discrepancies. With these we may deal in characteristic fashion— postulating an "ideal gas" to which Boyle's law is to apply rigorously. Actual gases being then only more or less imperfect approximations to the hypothetical ideal, we apply Boyle's law successfully only as we come to associate with it certain limits in range and reliability. Charles', Leduc's, Dalton's, Gay-Lussac's, and Graham's laws are similar to Boyle's in all essential respects. Each, by a skillful choice of concepts, condenses into a terse abstract state- ment an immense descriptive and predictive capacity. Each is to a degree both general and reliable, but each carries limits in both range and reliability, and applies rigorously only to an "ideal" case. Consider now how a rational order is imposed on this entire group of "gas laws." We begin by making some hypothesis about the na- ture of gases. Here, as in many other cases, we posit the existence of unobservables, thereby to reduce to order the observables described by the colligative relations. Creating the kinetic theory, we postulate that a gas is a space thinly populated with minute corpuscles having a kinetic energy proportional to the absolute temperature of the gas. These particles we suppose to move in accordance with Newton's laws of motion, and to be perfectly elastic in their collisions with each other and with the walls of the container. We have now a model of a gas— but a model still somewhat hard to handle. Hence we make two auxiliary assumptions— inessential to a kinetic theory as such— merely to simplify otherwise difficult deductive operations. We postulate that the corpuscles are point-masses of zero volume; and we postu- late that, save in their collisions, no forces whatever are active be- tween them. These assumptions cannot be perfectly sound for any gas we handle in the laboratory— since all such gases condense, at temperatures appreciably above absolute zero, to liquids that have appreciable volumes. With the introduction of the two simplifying assumptions, then, we are no longer speaking of actual gases but of a more tractable ideal gas. SCIENCE (and common SENSE ) 59 Setting out from our postulates, we now arrive fairly straightfor- wardly at deduced theorems we delightedly identify as precisely the relations named for Boyle, Charles, etc. This is an immense correla- tive achievement. Also an immense explanatory achievement: we see how the behavior described by the colligative relations may be pro- duced. Yet our satisfaction is not wholly unbounded. Using a model of an ideal gas we arrive at Boyle's law, which applies rigorously to that ideal gas but not to actual gases. Feeling we understand how the law arises, we are now all the more anxious to understand why it is not rigorously applicable to actual gases. Ordinarily quite reliable, predictions drawn from Boyle's law are apt to be wide of the mark with gases at high pressures and/or low temperatures. For such failures the relation itself offers no rationale: Boyle's law simply fails, by a larger or smaller margin, under con- ditions we must then memorize. But with the kinetic theory in hand we can understand these failures: we have only to grasp how actual gases may differ from our hypothetical ideal gas. Our gas model involved two assumptions that cannot be perfectly sound. Boyle's law fails under precisely those conditions in which the assumptions would he least satisfactory. There is failure ( 1 ) when the gas pres- sure is high and the gas volume small, so that the fraction of the total volume "filled" by the corpuscles becomes significant; and (2) when the gas temperature is low, so that the kinetic energy of the cor- puscles no longer wholly overrides inter corpuscular attractions. In the shortcomings of the assumptions used in its theoretical deriva- tion, we see the origin of the shortcomings of the empirical law. No longer need we simply memorize the conditions in which Boyle's law fails badly; we now understand in advance that under such condi- tions it must fail. A more sophisticated theoretical construction does without the two simplffying assumptions, and yields a new (van der Waals) relation: (P + V2) (^ — ^) ^^ constant. From measurable characteristics of any gas at its critical point, we calculate a correction term ( h ) rep- resenting the volume "filled" by the corpuscles themselves, and an- other term {a) representing the inter corpuscular attractions. When the volume of the gas (V) is large— i.e., at low pressure {p) and/or high temperature— the correction terms involving a and h are negli- gible, and the van der Waals relation then simply reduces to Boyle's 60 sciExcE (and common sense) law: pV = constant. Boyle's law here emerges as a limiting law. However, when the \^olume of the gas is small— i.e., at low tempera- ture and/or high pressure— the correction terms become significant, and the predictions of the van der W'aals relation then difiFer sub- stantially from the comparatively inferior predictions furnished in these conditions by Boyle's law. Remembering, understanding, discovering. Our first theory sug- gests how Boyle's law may arise, and further suggests how it may come to fail where it does fail. Our second theory ofiFers us means to estimate in advance the magnitude of the failure. And Boyle's law here is paradigm of all the familiar gas laws. We can then feel we understand both the successes and the failures of all these laws. The kinetic theory thus proves its eflFecti\'eness as an explanatory device. Always we remember better what we feel we understand, and in any case the need for remembering is now triply reduced. First, we can now derive any of the many gas laws, as it is needed, from a few easily remembered theoretic axioms. E\^en making no derivation, each law now reminds us of others in the group with which we have come to associate it. Second, making the deri\'ations, we find the sim- ple laws obtainable only with the aid of certain auxiliary assump- tions and approximations. Grasping the circumstances in which these are likely to fail, we simultaneously grasp the limits in range and reliability attaching to the simple laws. Third, the task of memory is reduced even as concerns the many alternate denotations attach- ing to the concepts that figure in the derivative relations. We must still learn some primary denotations, but the "equivalence" of any alternate denotation is itself a colligative relation we come to grasp easily as it too finds theoretic accommodation (ordinarily elsewhere than in the kinetic theory ) . Scientific theories thus function superbly as correlative devices. Good theories are more than correlative devices, more even than explanatory devices. Good theories are also heuristic devices— tools that assist us in winning new knowledge. From theoretic postulates we arrive deductively at theorems we identify with known colliga- tive relations; sometimes also at other theorems we identify with colligative relations not previously known. We are then led to look for certain things not before seen, or perhaps even thought of. Thus, for example, the kinetic theory suggested to Maxwell the novel idea that gas viscosity should be independent of gas pressure. Investigat- SCIENCE (and common SENSE ) 61 ing, we find this deduction easily confirmable, as are indeed a good many others of its kind drawn from the kinetic theory. Theories and nets. In the first stage of the organization of experi- ence flocks (in the sense of locks of wool or hair) of hypothetical "atomic stimuli" are formed into immediate, individual constructs— e.g., "objects" that exist stably in an otherwise chaotic welter of stim- uli. In the second stage classes of objects and of the qualities of objects are developed. Concepts are formed; from selected groups of fibers are spun multiple fine threads which, in the third stage, are intertwined to form colligative relations. At this level the maxims of common sense, the rules of the craftsman, and many of the laws of the scientist appear together. Only in science do we push on fur- ther, to a fourth stage, in a fully self-conscious way. We weave the relations together in postulational systems, theories. Says Popper: Theories are nets cast to catch what we call "the world": to ra- tionalize, to explain, and to master it. We endeavor to make the mesh ever finer and finer. He who realizes the existence of such a conceptual fabric, and is capable of lifting it, carries with it all its cords, all the colligative relations it accommodates. This metaphor grossly oversimplifies: each "stage" is not simply produced from, but also helps to produce, those that precede it. Moreover, in describing the functions of scientific theories, the case I have sketched is too "ideal." Qualitatively the elements of gain are correctly represented. Quantitatively the gains may be less impres- sive, because fully to master a scientific theory is a task far more difficult than I have indicated. For example, from the theoretical postulates the manifold colligative relations descend by deductive chains that normally involve, beyond conscious assumptions and ap- proximations we have to learn to use as appropriate, further assump- tions and approximations the experienced scientist makes automati- cally, without full awareness of what he is doing. To master the theory, and so to command the relations it holds in chains, one then requires— beyond premises and rules for their manipulation— a "feel" for the system. Immensely powerful tools, scientific theories are also imperfect tools, handled with full effectiveness only by those who have that subtle art of which Toulmin writes: 62 SCIENCE (and common sense) It is part of the art of the sciences, which has to be picked up in the course of the scientist's training, to recognize the situations in which any particular theory or principle can be appealed to, and when it will cease to hold. Nobody today can master all of science because nobody today lives long enough to master the arts of all scientific theories. But he who has mastered a few major theories does thereby come most literally to comprehend certain entire domains of his experience. CHAPTER III The Anatomy of Science ONsroER science in the metaphor of social organism, swimming in a cultural milieu on which it acts, and by which it is acted upon. What that organism is today, it has become by evolution. Beginning with a brief historical survey, we become aware of certain features of science, today so taken for granted that we recognize their nature and importance only as we look back upon the antique science in which they were absent or had at most a rudimentary development. The Evolution of Science Along the continuum that stretches from common sense to science, only a somewhat arbitrary act suffices to define a "beginning." Arbi- trariness is minimized, however, if we take as criterion of the emer- gence of science the appearance of its characteristic fourth-stage organization. Historically this appearance has somediing of the abruptness of a mutation. Neolithic man had already mastered agriculture and animal hus- bandry; milling, baking, and brewing; tool-making; pottery- and brick-making; etc. Somewhat later the great delta civilizations mas- tered the complex manufacture of bronze, which required a combina- tion of ores mined in places hundreds if not thousands of miles apart. Still later, men mastered the even more complex procedures involved in successful smelting of iron. To carry on anif of these processes is to have mastered whole sets of predictively powerful coUigative rela- 63 64 THE ANATOMY OF SCIEXCE tions of the type: If you take ore of this (describable) sort and treat it in this (describable) manner, then prohahlij you will obtain a metal having approximately these (describable) properties. Such relations go far beyond the content of ordinary common sense, but I cannot base on them a claim that early man was already a scientist. I suppose that observation, unsystematic empiricism, and common- sense reasoning pro\ide an ample foundation for the discovery and use of such relations— the sets of which are the maxims, recipes, formulas, and rules that constitute craft traditions. No craft tradition is properly denominated science. If we deny to carpentry status as "science" we cannot so dignify the colligative rela- tions developed by early man— immense achievements though they were. This position I maintain even when some of the relations are semi-quantitative, or even fully quantitative. The relations of prac- tical metallurgy must already be at least semi-quantitati\'e. The Babylonians go on to de\'elop fully quantitative formulas for predic- tion of eclipses; the Egyptians, some of the theorems of physical geometry. To such relations one is reluctant to deny status as science, but one is hard pressed to see how they can be clearly differentiated from others making only a very dubious claim to such consideration. The involvement of mathematics, after all, is not a distinctive mark of science. Biology has for long been a science, though in it mathe- matics is but slightly brought into play; astrology is often highly mathematical without being at all a science. Hall remarks that: It is possible to derive [astronomical] predictions from purely mathe- matical procedures, as the Babylonians did, without making any hypothesis concerning the mechanism involved. Here precisely is the point. Just that concern for mechanism signal- izes the appearance of what is recognizably science. In man's history this is a late development— coming first, says Schrodinger, not with the Babylonians or Egyptians but with the Ionian Greeks, in the 6th century B.C. The Egyptian surveyor possessed and used a number of relations connecting distances, areas, shapes, and the like. Though often highly sophisticated and precise, these relations are not unreasonably asso- ciated with common sense: they remained discrete, unorganized, each in itself a separate enigma. The situation is changed through the studies of a long series of Greek investigators, culminating with THE ANATOMY OF SCIENCE 65 Euclid. Postulating certain axiomatic relations between certain postulated "entities" (point, line, plane, etc.), Euclid shows that de- duction from the axioms yields the many relations used by the Egyp- tian surveyor, and a number of other such relations not previously recognized. This system thus handsomely discharges the three major functions— correlative, explanatory, and heuristic— characteristic of a scientific theory. Only in its comparative perfection is Euclid's ge- ometry atypical of the Greek achievement. In Greek astronomical theories, for example, we find again a large-scale co-ordination of hitherto separate relations (used in time-keeping, navigation, calen- dar-construction, eclipse-prediction, and the like), again an indication of certain new relations for which to look, and again a most impres- sive sense of explanation. Of this kind of achievement Margenau writes : ... a theory was born; the surface of mere correlation was broken, subsurface explanation had begun. To put it another way: The con- tingency of correlation had given way to logical necessity. Typically gratified in colligative relations like those used by the Egyptian surveyor, what I call the "Egyptian desire" evokes the in- tensely practical common-sense quest for order on which prediction can be founded. The new element that produces science— what I call the "Greek desire"— e\'okcs a search for theoretic explanation of those relations, pursued urgently even when it offers no promise of improving the predictive capacities with which we are already en- dowed by the se\^eral relations. Far overshadowing the impressive though imperfect theoretic explanations the Greeks actually propose, is their first bold conception that such explanation is possible! The principle of intelligibility. The "Greek way" turns on a new principle— distinct from those inherited by science from common sense— asserting the world comprehensible by nian. Superficially innocuous, this view is revolutionary.- Consider one example. Does not the divinity essential in a god render that god and his activi- ties incompletely intelligible to mortal men? For, says Coleridge, "Incomprehensibility is as necessary an attribute of the First Cause as Love, or Power, or Intelligence." Accepting the principle of intelligibility we then recognize that the gods must not figure in the postulates of physical theories. Expecting to find physical phe- nomena intelligible, we seek to see them effects of natural (as distinct 66 THE ANATOMY OF SCIENCE from supernatural) causes— and so arrive at the resolute naturalism characteristic of the best Greek thought. Such naturalism in turn profoundly affects our view of the princi- ple of determinism; for, after all, that principle may be viewed in many unequally "respectable" ways. A malignant demon, or a witch's curse, may reasonably be postulated as the hidden determinant of a death for which no overt determinant can be detected. Hard-headed Greek potters attached grotesque masks to their kilns, to frighten away unseen demons postulated to account for the otherwise inex- plicable failure of certain entire firings. The idea of determinism may even be made into an argument for divination, as shown in the expo- sition of Stoic doctrine quoted by Sambursky: ... in every field of enquiry great length of time employed in con- tinued observation begets an extraordinary fund of [common-sense] knowledge, which . . . makes it clear what efl^eet follows any given cause, and what sign precedes any given event. . . . the universe was so created that certain results would be preceded by certain signs, which are given sometimes by entrails and by birds, sometimes by lightnings, by portents and by stars, sometimes by dreams, and sometimes by utterances of persons in a frenzy. And these signs do not often deceive the persons who observe them properly. If prophe- cies, based on erroneous deductions and interpretation, turn out to be false, the fault is not chargeable to the signs but to the lack of skill in the intei^preters. The failures of divination here receive the treatment we ourselves give to, say, failures of the conservation of mass in the experiments of novice chemists. We take the reliability of the conservation law as a matter of principle; just so one can take divination also as of prin- ciple. Nothing about the principle of determinism as such thus en- forces rejection of divination, and what ive regard as similar supersti- tions. From the Greek postulate of intelligibilit}% however, there can arise rejection of divination: we reject as inadequate a determinist order we cannot understand. The multi-faceted principle of intelligibility, elsewhere treated at length, underlies the entire attempt to construct theoretic explana- tions of colligative relations. Today notable successes already won in such construction encourage confidence in the principle— which we take wholly for granted. But for the Greeks the principle was no more than a daring assumption— and we honor them most for that indomi- THE ANATOMY OF SCIENCE 67 table faith in the capacities of human reason which is an essential precondition for the emergence of science. SOME DIFFICULTIES Though science be here created, something more than the infusion of the principle of intelligibility into common sense is required to make of science a going concern. Impressive though it is, ancient science is science still incomplete, imperfect, incapable of self-perpetuation. The choice of problems. Ancient science sufiFered simply as a pio- neering enterprise, bound to take wrong turns in a still trackless wil- derness. Over and over again it spent itself in attacks on what ive recognize as trivial and/or intractable problems. Amply perceptive— and, in our view, thoroughly wrong— was, for example, Aristotle's feeling that mortal man is best advised to seek scientific understand- ing of equally mortal plants and animals, and notably ill-equipped to understand the apparently immutable rocks. Scientists can learn to choose better problems only as science acquires a history. Thus, given some two millennia of intermittent effort, continued failure to solve certain of the problems broached by ancient science becomes testi- mony that these problems might better be abandoned or, at the very least, subjected to the kind of drastic reformulation the problem of motion received at the hands of Galileo. The technology of the Renaissance world in which science was re- born is relevant in this connection. Practical ballistics, for example, raised in new form, and with new urgency, the classical problem of motion. Retrospectively we see that many such problems derived from technology were "good" problems: i.e., feasible of solution, and with solutions rewarding in insight. Whatever the balance of the his- toric and technologic factors, accession of a worthier set of problems did put modern science on the roads to advances denied its ancient progenitor. Heuristic tools. Ancient science picked the "wrong" problems and, again typical of a pioneering venture, had inadequate tools with which to treat them. Lacking experimental tools, it lacked even more acutely intellectual tools. If Empedocles identifies the two major forces of the physical world with Love and Hate, or if Aristotle (among others) constructs a system in which teleology is the prime motive power, who can find this surprising? What else could be ex- pected of men who had a penetrating insight into human motivation 68 THE ANATOMY OF SCIENCE but no clear concept of a simple machine? Who will conceive a clock- work universe before a clock is invented? Again a more fully developed technology helps to get things mov- ing. Beyond providing an abundance of materials and de\aces, serv- iceable to science as experimental tools, the mature technology of the post-Renaissance period opened the way to new conceptual tools. On a new wealth of industrial experience was founded a new and (in the issue) powerful group of mechanistic concepts and analogies, as alternati\'e to the limited and limiting group of animistic concepts and analogies used in ancient science. Through history, once again, earlier errors become recognizable, and so avoidable. Nothing sig- nified a priori the inappropriateness of the alchemists' conception that chemical change is most significantly characterized by the changes in color accompanying it. More than a millennium of patient but fruitless endeavor does convey some impression of such in- appropriateness, and so encourages a search for new and better concepts. Organization. The preservation of scientific history requires some organization. For this will suffice organizations external to science —Islamic library or Christian monastery. But history itself teaches us how much more fundamental is the need for organization within science. In the ancient world there existed no generally accepted scientific tradition, practically no stable scientific institutions (the Alexandrian Museum is a notable but late exception), and very few persons working as scientists at any one time. DijEerent workers, largely self-educated, disagreed about the fundamental tenets of the science then cultivated by each in his own way. Men asked wholly dijBFerent questions, and found for them wholly diflFerent answers. The work of each had then little relevance and often, because of termino- logical uncertainties, little meaning for the others. Ancient scientists were by necessity, if not by inclination, thoroughgoing individualists. Ancient science faltered, failed, because it lacked cohesiveness. From its rebirth modern science could draw on organizational pos- sibilities unknown to the ancients. In stable academic institutions like the University of Padua a tradition might be maintained in a library, and interpreted by able teachers to students who, in their turn, would become teachers of their successors. All the universities rested on one common foundation in scholasticism. From Oxford and Cambridge to Paris and Padua we find important diflFerences in detail, but al- THE ANATOMY OF SCIENCE 69 ways a common point of departure in a terminology and a set of premises shared by all. No matter how far the scientist might voyage in thought, he remained in touch with contemporaries who, mov- ing perhaps in other directions, shared always the same base of operations. Quite aside from the universities, men informed by the same tradi- tion and sharing the same enthusiasm might band together, as in the Accademia del Cimento and the Royal Society. Such local organiza- tion was supplemented by a rapid transmission of intelligence along channels earlier developed for mercantile, ecclesiastic, and political purposes, a transmission also newly and dramatically broadened by the invention of printing. Within the 150-year period embracing the publication of the works of Copernicus and Newton— and the birth of modern science— an association of scientists as pervasive as it was loose, and as powerful as it was intangible, invested science with a cohesiveness as crucially important as it was then novel, and today commonplace. The extravagant dissipation of eflFort so marked in ancient science is, as Herschel notes, already replaced by something of that co-ordination of efiFort we take for granted: . . . the sparks of information from time to time struck out, instead of glimmering for a moment, and dying away in oblivion, began to accumulate into a genial glow, and the flame was at length kindled which was speedily to acquire the strength and rapid spread of a conflagration. The social setting. Today science so thrives, in a culture we take wholly for granted, that some among us are led to the absurdity of supposing science independent of its social setting. Historical per- spective rectifies that judgment: even the general organization of so- ciety can aflFect science. Ancient society was, for the most part, highly stratified. Possibly such stratification impairs communication between scholar and craftsman; probably it will suggest to the former that higher truths must be sought through contemplation, not through vulgar manipulative techniques. Often there may be also a crucial disparagement of the basic principle of intelligibility: in a highly stratified society supernaturaiism, convenient superstitions, may have a weighty social role. But any serious concern for the social expedi- ency of supernaturaiism cannot but endanger grasp of the principle of intelligibility. Ultimately, for whatever reason, all hold is lost on 70 THE ANATOMY OF SCIENCE that principle. (The Dark Ages are, in this respect, not inappropri- ately so termed. ) Accepting a cosmology in which the world is base, and in itself of no importance, a man will in any case feel far more concern to purify his soul than to acquire the "vain knowledge" of which he supposes himself incapable. Science could then be reborn only as, in fact, it was— in a world that had acquired a deep new in- terest in man, in human life, and in the terrestrial habitat of man; that had acquired, too, a deep new faith in human capacity for knowl- edge. Langer obsers^es that long before science could produce cul- tural change it had in part to be produced by such change: ... it was far less the information men acquired that undid their religious beliefs than the change of heart which prompted such re- search. The desire to construct a world-picture out of facts super- seded the older ambition to weave a fabric of "values," . . . The principle of intelligibility so reborn is of course in perfect harmony with the spirit of the Renaissance: not simply measure, man is to be also measurer of all things. Moreover "man" is not some fa- bled sage of antiquity, but modern man. The newfound confidence of man in himself was buttressed by the recovery of ancient learning. The ancients, so long supposed to have attained perfection of possible knowledge, were then found to have di£Fered sharply among them- selves. This previously unsuspected disagreement seemed amply to sanction the disagreement of modern man with previously accepted ancient doctrine. Such sanction was crucially important to many, and not least to Copernicus. One need then no longer be content to patch the Ptolemaic system to ixiaintain a predictive device and to "save the phenomena." Kepler's laws are born of the effort not simply to describe and predict but to understand the mechanics of the heav- ens. With new faith in the possibility of new progress in human un- derstanding, science takes a new turn. The idea of progress. The idea of progress that we take so much for granted is a very considerable novelty. A few in antiquity con- ceived at least the limited idea of a continuously progressive science. Discussing a newly discovered mathematical theorem on the volumes of regular solids, Archimedes (quoted by Sambursky) says: I am persuaded that it will be of no litde sei-vice to mathematics; for I apprehend that some, either of my contemporaries or of my suc- cessors, will, by means of the method when once established, be THE ANATOMY OF SCIENCE 71 able to discover other theorems in addition, which have not yet occurred to me. Also quoted by Sambursky is Seneca, writing on cometary theories : The day will come when time and the researches of long generations will bring to light what is now concealed. A single generation is not enough for the solution of such great problems. . . . Let us be con- tent with what we have discovered so far. Those who come after us will also add their share to truth. These statements, so true to the spirit of modern science, express what was in the ancient world a comparatively rare insight: the gen- eral idea of progress was not yet established— by most, not even con- ceived. No trace of that idea can be found in Aristotle's opinion that, rather than damage the prestige of all law, it were better to leave un- changed an admittedly bad law. There are indeed all too many an- cient spokesmen for the medieval view of succession not as evolution but devolution; a long inexorable corruption and decay— from antique perfection of world, man, and knowledge— to final and soon-to-be accomplished dissolution. In the ancient and medieval periods the world is then something to be endured, not a place in which improvement is to be expected or even sought. Haggard writes : The medieval Christians saw in childbirth the result of a carnal sin to be expiated in pain as defined in Genesis 111:16. . . . During me- dieval times the mortality for both the child and the mother rose to a point never reached before. This rise of mortality was in part the consequence of indifference to the suffering of women. It was due also to the cultural backwardness of the civilization and the low value placed on life. It was aggravated by the increasing difficulty attending childbirth. These were the "ages of faith," a period characterized as much by the filth of the people as by the fervor and asceticism of their religion; consequently nothing was done to overcome the enor- mous mortality of the mother and of the child at birth. It was typical of the age that attempts were made to fonn intrauterine baptismal tubes, by which the child, locked by some ill chance in its mother's womb, could be baptized and its soul saved before the mother and the child were left to die together. Highly overcharged this account doubtless is. Yet the ingenuity that devised intrauterine baptismal tubes might not have been wholly 72 THE ANATOMY OF SCIENCE incompetent in the design of obstetrical forceps. \Miy was this in- genuity not so deployed? Clearly because man had not yet grasped that something can he done, should he done, for the betterment of human life. Bacon is not quite the first to argue that by learning to understand the world we gain power to change it; but the general idea of prog- ress does not emerge in recognizable form much before 1600. A cos- mologic idea, it has a technologic root. When little if anything else in the world seemed even compatible with the idea, technology ac- ti\'ely encouraged it. A crude pre-scientific technology, still almost wholly dependent on cut-and-try empiricism and individual inven- tiveness, had brought forth notable improvements in mining and metallurgy, the horse collar, wind- and water-mills, medicinal distil- lates—genuine wonders! However evoked, the idea of progress is absolutely vital to science, and no society lacking the idea ( as did the great civilizations of the East) has ever supported a flourishing science. The idea is vital be- cause without it the principle of intelligibility is— if not wholly discredited— seriously misunderstood. The most fundamental weak- nesses of ancient science did indeed de\^elop from overextension of the primary source of its strength: that same principle of intelligi- bility. On its rebirth in the modern world, the principle comes to be associated with three essential qualifications. A FIRST QUALIFICATION: PATENCY, PROGRESS, AND PRAGMATISM Physical theories "explain" colligative relations in terms of theoretic postulates themselves unexplained. Taking the principle of intelligi- bility in too extreme a form, I shall seek to close this final gap in understanding; and I may think to have found, in Euclidean geome- try, the way of doing so. Euclid's postulates do not themselves seem to require any explanation, and I may so be led to stipulate that all postulates of all physical theories must be similarly "self-evident." If I do so stipulate I restrict, and perhaps even deny, the possibility of progress. Self-evidency is, after all, no more than conformity with the opinions of a day. Progress is then possible only when I feel free to entertain postulates that are not self-evident. These, if they lead to an attractive theory, may tomorrow be appraised— in terms of al- tered presuppositions and prejudices— as new self-evidencies. THE ANATOMY OF SCIENCE 73 Lacking grasp of the idea of progress, the Greeks (with such nota- ble exceptions as Aristarchus) showed comparatively little willing- ness to consider theoretical postulates that could not be made to seem self-evident. Such willingness represents a comparatively recent cast of mind. It emerges very gradually—it really struggles forth— in the 16th and 17th centuries. The multiple motions of the earth postulated by Copernicus are no self-evidencies, but Copernicus still feels bound to justify them by placing a strong emphasis on the self-evidency of other parts of his system: e.g., the perfect circular motions of celes- tial bodies, troubled by no such shabby evasion as the equant; the appropriately central position of the sun, the majestic giver of heat and light to our world. Almost a century later Descartes still thinks to construct a theoretic system by selecting as postulates only those to him both clear and indubitable, but in this Descartes' is an atti- tude more ancient than modern. What was to become the modern attitude is most vividly expressed in Newton's system. Here the postulates (e.g., of a universal gravitational attraction propagated through space) were defended on no appeal to this or that self- evidency. They were defended quite forthrightly on a newly funda- mental plane: they work. Thus we are taught a more modest inter- pretation of the principle of intelligibility. We learn to content our- selves with explanations in terms of theoretical postulates not neces- sarily self-evident, and so gain power to work with a far greater range of possibilities than before. Believing in scientific progress, we are confident that— if never "self-evident"— our postulates will some day be explained, though then only in terms of still more fundamental postulates themselves tmexplained. A SECOND QUALIFICATION OF THE PRINCIPLE OF INTELLIGIBILITY The principle of intelligibility may lead men to the inordinately optimistic expectation that all aspects of experience— physical, bio- logical, aesthetic, mystical— can be promptly rationalized within one immense system. Thus Aristotle seeks to build a final system, in ap- parently complete confidence that the fullest understanding achiev- able by man can at one stroke be won. Thus Epicurus' atomism is for him not only a comprehensive physical theory but also a cosmology and an ethic. Not all of the ancients pursued such grandiose aims: in such specialized works as the geometry of Euclid, the statics of 74 THE ANATOMY OF SCIENCE Archimedes, the pneumatics of Hero, and the astronomy of a Ptolemy we find what are for us the most important advances made by ancient science. But as long as a great system like Aristotle's is not obviously bankrupt, it is by far the most impressive; and so diverts eflFort from the apparently more pedestrian endeavors ice see as having been better ad\'ised. Almost two millennia after Aristotle his system is reconstructed by Aquinas with no reduction in scope of correlation. Even well after the beginning of the modern era Descartes supposes that he himself can build (or, later, could have built) a complete and final system. But in this same period, and even earlier, a newly modest conception of the principle of intelligibility was slowly gaining ground. Only as it did gain ground does modern science become possible. Copernicus must brush aside the gigantic system of Aquinas to create a new system for astronomy only. To make a gain in local correlation, he is prepared to pay the price of an enormous loss of general correlation, produced when astronomy is thus separated from physics, metaphysics, and the like. Galileo also pays that price when he studies kinematics as a separate subject— distinct from others with which it had been allied by Aristotle. The study of the atmosphere, and of pneumatics in general, becomes similarly an area in which local correlation is sought, and won, as a prize for which one paid by relinquishing the general correlation afforded by the Aristotelian conception of horror vacui. Men learn to content themselves with local correlations of data, and to regard a general system as the remote goal of a long and difficult journey. The Newtonian synthesis clinches this approach by showing that, from tight local correlations, one can, ultimately, journey on to a system of great comprehensive- ness. Autonomous science and sciences. Grasping the principle of in- telligibility, science emerges as a fully self-conscious endeavor to find rational order in experience. This is a science clearly affiliated with philosophy. Greek science was indeed closely (and disastrously?) associated with Greek philosophy. Even on its first appearance in the modern world, science is still "natural philosophy." Yet if the noun implies participation in the concerns of philosophy, the adjecti\'e al- ready reflects a partial separation which, in time, is widened. "Natu- ral philosophy" gives way to "science." If, as Bacon supposed, science THE ANATOMY OF SCIENCE 75 is the "handmaiden of theology," she has yet a hfe of her own. This new autonomy is of prime importance. Science feels free to reject as subject matter much that concerns theology and philosophy: for this and other reasons the problems of science often can be solved as many of those of theology and philosophy cannot. Moreover, many then "extraneous" considerations cease to trouble the aflFairs of an autonomous science. Investigators who differ profoundly in their metaphysical convictions can still collaborate in science. In defense of the germ theory Pasteur, devout Roman Catholic, makes common cause with Tyndall, an atheist in the eyes of most of his contempo- raries. The separation of an autonomous science is followed by the sepa- ration of semi-autonomous sciences, and then of specialties within these. Scientific advance assumes a new pattern. At a number of dis- tinct growing tips purely local correlations are projected outward. Larger correlations come later, as the separate shoots are linked through the same branch, and tlie several branches come (perhaps) to depend from the same trunk. Impatient to advance, we set aside this pattern only at detriment to advance. The ancient scientist aspired to a general system embracing much if not all of his experience. He had then some fear of making radical separations of that experience: separated "parts" might not again fit together in a whole. But, reading what seems to be the lesson of scientific history, ice venture quite drastic separations of elements of our experience. We become bold enough even to subdivide a unitary "phenomenon" for consideration in different disciplines. We observe the flight of a pigeon. Physics ( aerodynamics ) tells us something of how the beating of wings sustains motion in air, physics ( kinematics ) affords us a very simple description of the motion of the bird when it is shot, and physics ( energetics ) makes us aware that further prob- lems remain to be solved. We may turn then to chemistry and bio- chemistry to learn something of the mechanisms of power produc- tion in birds. To biology we leave the problem of how a bird of this particular sort has come to be; to psychology the problem of why the bird elects to fly when and as he does. We deploy the concept of dissolubility more aggressively as we gain confidence in its natural complement. Accepting a principle of superposition, we take it for granted that parts loill ultimately fit together in a whole. With faith 76 THE ANATOMY OF SCIENCE in such progress, we look to make small gains, in expectation of greater. And we do gain where, hoping to win everything with one dramatic insight, the Greeks won little. A THIRD QUALIFICATION OF THE PRINCIPLE OF INTELLIGIBILITY The Greeks made observations, even experiments, but most often experiments meagre in number and observations needlessly crude. Profound stimulus, the principle of intelligibility can be also snare. Overconfidence in the supreme power of human intelligence breeds a dangerously arrogant rationalism. When diey already "know" the answer men make crvide observations, if they make any. Even when they do not already have an answer, rationalists will suppose they require only a few observations to suggest the axiomatic propositions that yield, by rigorous deduction, definitive theoretical answers to all questions that can be asked. More than a millennium after Greek science died, Descartes still considered diat a few experiments should suffice to reveal the system of the universe— experiments being neces- sary only to establish which of a few comparably self-evident alter- nate propositions the Creator had decided to actualize. To conceive necessary only a few observations, or experiments, is far from the worst conclusion rationalists can reach. For how may one best seek the transcendent reality of diat Platonic world of pure ideas, access to which demands all a contemplative reason can sup- ply? How better than by turning one's back on the manifold distrac- tions of the gross material world of the senses, where the pure ideas can at most manifest themselves only as distorted projections in a crude pattern of shadows? "They who wish to approach astronomy correctly will," says Plato, "tLirn their backs upon the heavens." On such a firm denial of the relevance of sensory experience can be founded nothing approximating science as we know it. Modern science begins with a newly modest empirical emphasis for which Francis Bacon is spokesman: There are and can be only two ways of searching into and discover- ing truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immoveable, proceeds to judgement and to the dis- covery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual THE ANATOMY OF SCIENCE 77 and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried. Is this second "way" so diflFerent from that recommended by Aris- totle? The natural path of investigation starts from what is more readily knowable and more evident to us [presumably the observable par- ticulars], and proceeds to what is more self-evident and intrinsically more intelligible [the first principles, or Bacon's "most general axioms"]. Bacon's criticism seems aimed less at Aristotle's maxim than at its interpretation by Aristotle's followers. Taking their departure from a very small body of roughly observed "particulars," many in the Aristotelian tradition expected to arrive promptly ("flying") at first principles. The premature hardening of these can then develop into the first "way" criticized by Bacon: if some particulars incidentally obsers^ed seem out of keeping with the general principles, these par- ticulars are simply dismissed— perhaps as illusions, trivia, errors, or imperfections of an intrinsically corrupt world. The appeal to experience. The warm regard for observational par- ticulars that Bacon preaches is far from a complete novelty of modern science. That regard informs the ancient and vital tradition of Hip- pocratic medicine. Long before the modern period the multiplication of epicycles in the Ptolemaic system testifies to continued efforts to take account of observational particulars. But with the beginning of the modern era the attitude Bacon commends assumes a new weight —perhaps, as Collingwood suggests, through the development of a new cosmologic conception of nature. In the early phase [of Renaissance cosmology], the world of nature, which is now called natura natiirata, is still conceived as a living or- ganism, whose immanent energies and forces are vital and psychical in character. ... as time went on . . . the idea of nature as an organism was replaced by the idea of nature as a machine. . . . But even the earlier view differed sharply from the Greek theory of the world as an organism, owing to its insistence on the conception of immanence. Formal and efficient causes were regarded as being in the world of nature instead of being (as they were for Aristotle) outside nature. This immanence lent a new dignity to the natural world itself. ... it led people ... to look at natural phenomena 78 THE ANATOMY OF SCIENCE with a respectful, attentive, and observant eye; that is to say, it led to a habit of detailed and accurate observation, based on the postulate that everything in nature, however minute and apparently accidental, is permeated by rationality and therefore significant and valuable. \Miatever its source, a new attitude is already clearly working in the founders of modern science. Consider Tycho Brahe. Dissatisfied with the Copernican system, Tycho conceives that a definitive astro- nomical system can be founded only on highly accurate observational data. And he spends his life, as perhaps no man before him had spent his, de^^eloping superior observational instruments and compiling an enormous array of meticulous observations. So to spend one's life is to see the world of experience as— far more than a mass of misleading imperfection— the most essential foundation for the construction of the conceptual world. Tycho was more than a little mad; but the same regard for the details of experience rules also the very different madness of the inheritor of Tycho's data. Johannes Kepler was a Pythagorean mystic —a classic seeker after the harmony of the spheres— and yet not quite of the classic mould. The labor of years finally permitted Kepler to fit Tycho's observations of Mars to an orbit which w^as at no point more than 8' of arc out of agreement with obser\'ation. This trivial discrepancy— recognizable as a discrepancy only because of the enor- mous improvements in observational techniques made by Tycho— any mystic before Kepler would have dismissed w^ithout a second thought. An ideal orbit coming this close must be sound; tlie "insig- nificant" deviations indicate no more than inadequacies in the data and/or the crudeness of the world to which the data refer. How dif- ferent was Kepler's attitude! Divine Mercy has given us in Tycho an observer so faithful that he could not possibly have made this error of eight minutes. We must thank God and take advantage of this situation; we must discover where our assumptions have gone wrong. Kepler came so to a step wholly unprecedented: rejecting orbits com- pounded from circles, he sought a less "ideal" orbit that would bet- ter fit the data. What was to become the new scientific attitude did not of course spring full-blown with Tycho and Kepler. Only slowdy does the ap- peal to brute experience come to be established as the commonplace THE ANATOMY OF SCIENCE 79 it is today. It could become established only as confidence in pure rationalism was sapped. But so it was. To some others, as to Bacon, the purely rational endea\^or of scholasticism seemed to stand for stagnation, particularly in view of the notable advances made in technology by aggressive empiricism. And if the new empirical em- phasis seems antirational, then so much the worse for rationalism; if empiricism promises progress, empiricism will be the choice of men intoxicated by the thought of progress. A new conception of scientific method. Descartes, builder of a classic "system," envisions science as primarily an enterprise of ra- tionalism. Bacon envisions something closer to natural history than to science when he puts primary emphasis on empiricism. Neither fully grasped the form modern science has assumed. Today the bal- ance of abstract theory and concrete fact makes them essentially co- equal: both are indispensable, either may be in error, each controls the other, and both are equally worthy of earnest attention and stren- uous effort. Unlike his contemporaries Bacon and Descartes, Galileo proposes no formal method. But Galileo helps to set the style of mod- ern science by presenting in his work an illuminating expression of what Hall remarks to be a method at once duly theoretical and duly experimental. In the Dialogues and Discourses the foundations of scientific knowl- edge are shown to reside in phenomena and axioms conjointly. By its attention to actual phenomena Galilean science was made real and experiential; by its use of the capacity of the mind to apprehend axio- matic truths its logic was made analogous to that of mathematics. Galileo set off down an indistinct track traveled by a very few among the ancients, but among tliem he whom Galileo most ad- mired: Archimedes. With the aid of such concepts as the ideal lever, Archimedes had shown how, by abstraction, one could pass from the confusions of actual phenomena to "purified" phenomena in an ideal universe of mathematical discourse. With the aid of such concepts as "free fall," in an ideal realm without air resistance, Galileo sought to follow Archimedes into that same mathematical universe. Though then supported by a mathematics far more powerful than any known to Archimedes, the abstraction to mathematizable systems ive take wholly for granted still remained in the age of Galileo the extremely difficult feat sketched by Butterfield: 80 THE ANATOMY OF SCIENCE . . . even when men ^^'ere coming extraordinarily near to what we should call the truth about local motion, they did not clinch the matter— the thing did not come out clear and clean— until tliey had realized and had made completely conscious to themselves the fact that they were in reality transposing the question into a different realm— they were discussing not real bodies as we actually obsei"ve them in the real world, but geometrical bodies moving in a world without resistance and without gravity— moving in that boundless emptiness of Euclidean space which Aristotle had regarded as un- thinkable. And now arises the crucial question— posed, and answered, by Hall as follows : When abstraction has played its part, when attention has been given to the really existing physical properties of bodies, when the mathematization of the phenomena has been fully explored and a theoretical science begins to take shape, how is the investigator to determine whether his image or model of things in the abstracted uni- verse represents faithfully things as they are according to experience? Galileo's answer to this problem, prepared for him by earlier logicians, was the appeal to experiment. If theoretical examination suggests that in specified conditions the event B will follow the event A, then the reasoning can be tested by creating those conditions, and making the observation. By analysis of a collection of \'aried obsers^ations and experiments, Bacon supposed, the scientist strips away successive veils of decep- tive appearance to arrive, at last, at a hard core of secure knowledge. Stripping away, one by one, the concentric coats of an onion, we so arrive at last at its center. This metaphor itself suggests the inade- quacy of the Baconian conce^Dtion: working entirely from the outside, detachment of the onion's smooth and tenacious shells is very diffi- cult. We succeed precisely when, penetrating with knife or finger- nail, we secure the purchase with which we detach the coat by break- ing outward, toward the surface. The successful technique in the metaphor suggests the quadripartite scientific method pioneered by Galileo ( and Archimedes ) : ( 1 ) Resolving to study "falling bodies," the scientist finds that he can hold simultaneously in view very few unrelated elements of ex- perience. Quite early in his enterprise he must then devise a body of THE ANATOMY OF SCIENCE 81 (appropriate, he hopes) concepts— e.g., velocity and acceleration— which invest certain selected (significant, he hopes) elements with relatedness. A considerable abstraction is already expressed in the selection, and a much greater one is now to be made. (2) With bundles of data bound by his concepts, he withdraws from the complex world of experience toward an "ideal" conceptual realm. Refusing to accept the limits common sense sets itself, the scientist deals quite elaborately with refined abstractions akin to those of the philosopher. He seeks to penetrate behind the appearances: he hypothesizes existent in nature certain simple entities and relations {e.g., "free fall"). In terms of these he asks certain new questions, perhaps comes to grips with the core of his problem. Always he seeks for ever greater abstraction, thinking thereby to penetrate ever more deeply— to the essence of an ever wider body of phenomena. (3) How can he gain confidence that his abstract conceptions do hold any such essence? Unlike the ancients, he rejects the expedient appeal to self-evidence. He tries instead to break back out to ob- servables: drawing deductions from his abstract postulates, he ven- tures to predict what, under certain circumstances, should be found in actual experience. Thus always in the end the scientist returns from the world of abstractions, however remote, to the world of ex- perience the man of common sense never fully leaves— and the philos- opher never fully regains. (4) The scientist need not return all the way to the raw experience of observation, but only as far as experience provided by laboratory systems purposefully designed to highlight the eflFects of the factors to which the abstract concepts direct attention. With Galileo we come then at last to the classic experiments on the inclined plane. The theoretic predictions being borne out, the theoretic construction may be sound. But were inexplicable predictive failures to be found, these— not to be brushed aside as marks of the nonideality of an intrinsically imperfect world— are to be recognized as calling the ab- stract constructions in question. Considering our experience, we create in our thoughts a world of ideal abstractions. Whatever its beauty, this world is nonetheless an artifice of thought. Ultimately the business of science is to talk not of this world but of the "real" world, with all its imperfections and complexities. Experience thus becomes the touchstone by which we prove (in the sense of test) our abstract conceptions. 82 THE ANATOMY OF SCIENCE A further small dash of Baconian empiricism is required to give Galileo's procedure a fully modern flavor. Thus Galileo himself is still too much the Platonist to accept Kepler's elliptic orbits in place of the "perfect" circular orbits that did not meet the obser\'ations quite as well. He is still too little inclined to pay attention to minute details of experience in a world clearly falling short of classic per- fection; this is evident even in his account of the results of the cele- brated experiments on the inclined plane. These results he reports as agreeing with each other, and with theoretical predictions, to a de- gree wholly unattainable with his crude equipment. Intending no dishonesty, Galileo clearly reports not the actual results, but rather what he confidently expected ivoidd have been the results if only things had been more perfectly arranged— ideal results to which he judged the actual results a sufficient approximation. Galileo is not alone in such reporting, of course. Perier does much the same in reporting the results of the Puy de Dome experiment, and Pascal reports many "experiments " patently not experiments done but demonstrations confidently conceived. In such instances we never know what are actual experimental results, what are ideal- ized results of actual experiments, and what are only hypothetical results of hypothetical experiments. From this intolerable situation science escapes only through the emphasis made by such as Boyle on the absolute need to distinguish clearly between what is observed and what should be, might be, or could be observed. Such emphasis we find in Bovle's somewhat acerb commentarv on Pascal's "results," as well as in Boyle's own incredibly tedious reports of his own re- sults—down to the last trivial but possibly remotely relevant detail. Faithful Baconian that he was, Boyle is far too empirically minded. But in Newton's Opticks we find at last a very nearly optimal balance of theory and experiment, brilliantly struck by an Englishman who, influenced but not obsessed by the Baconian tradition, adopts the Galilean approach. We arrive here at that experimental science de- scribed by Weizsacker: Only the triad of thinking, acting, and perceiving makes the experi- ment possible. . . . It is not even sufficient that, in addition to perception, one of the two active dispositions is added to perception: only thinking or only acting. In the first case, the result is philosophy; the second, handi- craft. . . . Galileo ... is probably the first to embody that unity THE ANATOMY OF SCIENCE 83 which is no longer either philosophy or handicraft because it encom- passes both; each of his manipulations is guided by thought, each of his thoughts by experimental evidence. The Egyptian and the Greek inquiries come thus to complement and strengthen each other, and from their crossing emerges a modern science invested with true hybrid \'igor. The principle of corrigible fallibility. However we conceive sci- ence, we cannot begin our work without some facts and some ideas provisionally accepted as unchallengeable. But the ideas may be quite wrong; the facts ill-observed or laden with "credulity" (see p. 44). Obsessed by such fears we don't do science! From such ob- session scientists are freed by their acceptance of what I call the principle of corrigible fallibility. It is a principle of action. Beginning with the best available facts and ideas, we proceed vigorously in the faith that any errors in them will be revealed by the interaction of facts and ideas— by the interaction of rational and empirical elements in neither of which individually we have, or can have, absolute con- fidence. We amend our hypotheses in the light of our experiments; but we also reject (as "errors"), "correct," and explain away some of our data when they conflict with "indubitable principles." In such unquestioning acceptance of principles to which all experience is made to conform {e.g., the conservation laws) science may seem at one with divination, or magic. Yet science progresses as magic does not, and not simply because science had the good fortune to hit on the "right" principles at the outset. It did not! But it learned better principles. Bacon envisioned a "gradual and unbroken ascent" to the most powerful axioms, or first principles. The subsequent history of sci- ence demonstrates, however, that even a gradual ascent is not un- broken, that no principle remains forever beyond the challenge of experience. It is then far from facetious to describe the history of science as a tale of great and beautiful theories slain by ugly little facts— or, in Bronowski's phrasing: Science is a great many things, . . . but in the end they all return to this: science is the acceptance of what works and the rejection of what does not. That needs more courage than we might think. It needs more courage than we have ever found when we have faced our worldly problems. 84 TEIE ANATOMY OF SCIENCE Perhaps this is mere vulgar pragmatism. But it is the attitude that has made scientific thought so rapidly progressive while human thought in other domains has been hobbled by inability to reject ideas tliat, however refined and attractive, too plainly don't work. The Body Scientific In the fable, the blind men's accounts amply suggest that the unseen "elephant" has difiPerentiated parts. Just so, the extreme variability of modern accounts of the invisible abstraction "science" should pre- pare us to find complexity in what we ordinarily regard as an integral enterprise. The artisan, the statesman, and the proverbial man in the street almost invariably define science as something pertaining to technology. The theologian, the philosopher, and any other non- scientific scholar are most likely to define science in terms of cos- mology: world-pictures of the mechanical universe, the evolving universe, the statistical universe, and so on. Asking scientists for the meaning of "science" we find that most do at least agree on what science is not. Almost all scientists draw a sharp distinction between science properly-so-called ("pure science") and the applications of science in technology; most will also distinguish science properly-so- called from the world-pictures of cosmology. Thus, for example, Weizsacker urges on us the need to distinguish between two meanings of classical physics: as a world view and as a methodological instrument. Scientists ai*e members of human society, and science is conducted within a general cultural atmosphere. Not science, but only a wholly fictional abstraction, lives in a social vacuum. How then is one to treat of "real" science without embarking on a general sociology? We can hope adequately to treat science as a separate entity if only we can first grasp the nature and effects of its various linkages with its social milieu. These interactions, all proceeding through the me- diating enterprises of cosmology and technology, I examine in Chap- ter IV. Undertaking an anatomization of "science," I begin by distinguish- ing it from two other enterprises intimately enough allied to be confused with it, and it with them. The more detailed structure re- vealed, as the anatomization is now pressed forward, will be found THE ANATOMY OF SCIENCE 85 to impose an organization on the remainder of the inquiry to which this book has been directed. SCIENCE COSMOLOGY TECHNOLOGY Even after we distinguish science from technology and cosmology, there remain diflFerences of opinion on what we mean by "science." Conant notes two apparently contradictory opinions, qualified by him as the "static" and the "dynamic." In the static view we associate science with the fabric of scientific knowledge, as when Dingle writes : Science is an achievement and not a method of achieving. On the other hand, from considerations of probability theory Brown infers "... a tendency to diminution of scientific knowledge in the absence of further experimentation or confirmation"; and so adopts the dynamic view: Left to itself, the world of science slowly diminishes as each result classed as scientific has to be reclassed as anecdotal or historical. . . . Science is a continuous living process; it is made up of activities rather than records; and if the activities cease it dies. Consider that "work," "learning," and "research" have all dual usages, as verbs and nouns. "Science" is explicitly only a noun, but implicitly it shares a significant dualism of meaning with "learning," etc.— and even with its supposed opposite, "art." Art may be the activity of artists, but also the pictures, sculptures, etc. so produced. Holding a "dynamic" view of art, one can maintain that art is dead if no pictures are being produced. But holding that pictures are last- ing achievements even when no more such pictures are being painted —adopting a "static" view— one speaks of Aurignacean cave painting as art. Recognizing the implicit dualism of "science," we obviate the apparent contradiction of dynamic and static views. I do not complicate the diagram to indicate the dual meanings of technology and cosmology, but my representation fails seriously by 86 TEIE ANATOMY OF SCIENCE Scientific activity SCIENCE Scientific accomplishment COSMOLOGY TECHNOLOGY not distinguishing two distinctly diflFerent kinds of scientific activ- ity. The activity of individuals— immensely diverse and apparently anarchic— is the highly personal expression of individual creativity. Such activity ( examined at some length in Chapter XI ) is stabilized, co-ordinated, and fostered by die activity of organized science. Science is to its core a social enterprise; neglecting this, we neglect elements that determine at a most fundamental level the nature and capacity of science. Most obviously, science deals only with experi- ence at least potentially common to all whereas, say, art treats of experience that is highly individual. In the aphorism— L'arf, cest moi; la science, cest nous—\he dichotomy is drawn oversharply. But the poet has properly recognized the decisive role in science of col- lective activity, collective judgment, perhaps even collective wis- dom. The nature and functions of organized science I consider in Chapter X. Even yet the anatomization is incomplete. Weizsacker speaks of classical physics as a "methodological instrument." Clearly appertain- ing to the activity of science, a methodological instrument is not it- self activity but, rather, one product of antecedent activity. We attain a more revealing picture when, just as we distinguished two kinds of scientific activity, we distinguish also two kinds of scientific accomplishment: see the diagram on the facing page. The anticipatory apparatus. Temporarily ignoring some complex overlaps, we may say that in the main the anticipatory apparatvis is the locus of a gargantuan assembly of colligative relations, or laws, investing us with powers of prediction. Here the Egyptian desire finds its consummation; and the conception of science as "accumula- tive knowledge," its most conspicuous \^indication. Always our pre- THE ANATOMY OF SCIENCE 87 Organized science Creative science SCIENCE Anticipatory apparatus Heuristic apparatus dictive capacities grow, always we find increase in the number of relations, and of the relations between relations sketched in theories heie functioning as correlative devices. Dingle urges that: ... if, as we must surely do, we wish to characterize science by the element in it that persists and grows, and not by that which con- tinually changes, we must recognize . . . the progressive discovery of relations between the various constituents of our experience, . . . Amid all the changes of theories and pictures and conceptions, the re- lations remain and steadily accumulate. Franklin found that lightning was a manifestation of the electric ether revealed in laboratory ex- periments. The electric ether has disappeared, and other theories of electricity have in turn succeeded it and disappeared also, but the rela- tion between lightning and laboratory sparks remains. Maxwell es- tablished a relation between light and electromagnetic oscillations. His ether also has gone, but the relation stays. All pennanent ad- vances in science are discoveries of relations betv\^een phenomena, and the factor in science that shows a steady uninterrupted growth is the extent of the field of related observations. This effective immortality of scientific relations, together with some other of their characteristics, I examine in Chapter V. The heuristic apparatus. The heuristic apparatus is the repository of tools for the winning of new knowledge. Though of great diversity, these tools fall naturally in two major groups. I imagine the heuristic apparatus bifurcated into two lobes. A conceptual lobe represents the tools of thought. An empirical lobe represents the tools of action —the instruments and devices, techniques and procedures, materials and specimens with and on which the scientist makes his observa- 88 THE ANATOMY OF SCIENCE tions. The use and usefulness of these empirical devices I consider in Chapter Vl. An imentory of the contents of the conceptual lobe is difficult. Prominent here is a considerable group of methodological and sub- stantive principles, examined in Chapter VII. Here too appear col- ligative relations in a variety of other guises, as well as a great array of concepts furnishing terms for the expression of theories and rela- tions. Here also is found a heterogeneous stock ( 1 ) for the framing of analogies and the construction of models, and an enormous stock (2) of formal relations furnished by logic and mathematics. Modern science arose after, and profited from, the development of mathematical tools the Greeks wholly lacked: e.g., the concepts of zero, probability, and functional relationship. The profits are enor- mous because advances in mathematics oflFer more than convenient new symbols and devices for the expression of colligative relations. They provide also immensely powerful new machinery for the con- struction of postulational systems. As alternative to the restricted possibilities of deduction in the syllogistic and Euclidean modes, we acquire a variety of others the importance of which first becomes manifest in the magnificent achievement of the Newtonian synthesis. Much accelerated by growth of the formal stock ( 2 ) , due to prog- ress in logic and mathematics, the advance of science is probably even more profoundly accelerated by growth of the analogic stock ( 1 ) . Once science achieves a competent development, and becomes capable of generating its own analogic stock, its further progress may thus be rendered auto-accelerative. That is, with more ample ana- logic stock scientific advance becomes more rapid, and more rapidly generates new analogic stock, as a result of which . . . and on and on. We find this eflPect even in die formation of laws. Ohm, for exam- ple, arrives at his well known law by treating the "flow" of electricity as analogous to the "flow" of heat previously treated by Fourier. Success thus feeds on success, as is even more apparent when we turn from laws to theories. The astronomers' conception of the solar system furnishes the analogy on which Bohr founds his conception of the nuclear atom with circumambient electrons; and that theory of the atom, completed in quantum mechanics, furnishes in its turn the analogy by which we conceive a "shell structure" of the nucleus. However we appraise their relative importance, both the formal stock and the analogic stock clearly belong to the heuristic apparatus. THE ANATOMY OF SCIENCE 89 In Chapter VIII I examine how theories are constructed by the as- sociation of logical or mathematical formalisms with models or anal- ogies. Shall I then place theories also in the heuristic apparatus? As devices correlating scientific laws they belong in part to the anticipa- tory apparatus; as explanatory devices, designed to meet the Greek desire for understanding, they belong in part to the area of cosmol- ogy. Their status there I discuss in Chapter XII. But sharp separation of the correlative, explanatory, and heuristic functions of scientific theories is quite artificial. I find their heuristic function irreducibly dependent on their correlative and explanatory functions. Resolving to treat theories as heuristic devices, I can then feel confident they will be treated in all their aspects. One further consideration strength- ens this resolve: an extended analysis of the complex criteria involved in the selection of scientific theories— set forth in Chapter IX— leads to the conclusion that heuristic power is the decisive criterion of selection. Science, I argued, begins as an extension of common sense. The anatomy of science must then be present, if only in rudimentary form, in the anatomy of common sense. So it is. Common sense does comprise an anticipatory apparatus: a manifold of colligative rela- tions. Common sense does relate to practical concerns like those of technology, and accepts uncritically (in its language) a cosmology. Like science, common sense develops through the work of creative individuals. The organization perpetuating common sense consists of all who speak the language of common sense; the organization perpetuating science involves all who speak the language of science. Where then are localized the differences that so sharply differentiate science from common sense? In the hueristic apparatus. In common sense the heuristic apparatus has so little formal development that ordinarily we do not even recognize it as a heuristic apparatus. The differentiation of science from common sense begins when a few new concepts {e.g., intelligibility) appear in the heuristic apparatus of common sense. Ultimately these additions make themselves felt throughout the anatomical configuration, and nowhere more strongly than in a heuristic apparatus itself become enormously hypertro- phied. Possession of a highly elaborated organ for the winning of new knowledge then invests science with a dynamism unknown to common sense. CHAPTER IV Cosmology and Technology OSMOLOGY and technology me- diate the Hnkages of science with its social milieu. By way of some of the most obvious and direct of these linkages, scientific activity ac- quires a supply of problems, motivation, and logistic support. Problems. Out of cosmology develop broad questions about the nature of the world and of man, parts of which have concerned scien- tists in all ages. These are Greek "Why?" questions, considerably re- formulated when they become the concern of science. Much more limited Egyptian "How?" problems are broached by technology— and, more specifically, by its failures and inadequacies. These prob- lems—of immense importance in the historical development of science —are also drastically reformulated as they become the concern of science. They are generalized, set in a much broader context, and most often treated with no immediate regard for technology as such. Practical difficulties in navigation, calendar-construction, and astro- logical forecasting initiate die development of scientific astronomy. A new science of pneumatics takes its departure from an unexpected limit of 34 feet on the capacity of lift pumps; a new science of ther- modynamics, from an unexpected limit on the efficiency attainable with steam engines. Examined by Pasteur, certain problems of the fermentation industry lead to the foundation of a new science of bacteriology; in our own day troublesome "noise" in wireless trans- mission broaches a problem that ends only in the creation of the new science of radio astronomy. Motivation. Believing in the possibility of enriching human life 90 COSMOLOGY AND TECHNOLOGY 91 and alleviating its hardships, some men have sought and valued scientific knowledge read as technologic power. From Bacon to such as Bernal in our own day, these men have pursued science with technologic intent. By other men, from Kepler and Newton to such as Sherrington and Polanyi, science has been pursued and valued for its cosmologic significance. Science may then be conceived as the search for beautiful mathematical harmonies implicit in the cosmos and discoverable by man, or as the foundation of "natural religion." Today men may pursue scientific knowledge "for its own sake," but of course the \'aluation then set on "pure" learning is itself a cosmo- logic judgment. Support. Like other humans, scientists need food and shelter; they need, in addition, the physical equipment their work demands. Until such time as science affords them financial support, men lacking in- dependent means cannot easily function as scientists, and few of them will even study science. Probably the distribution of ecologic niches for scientists affects the direction of scientific endeavor; cer- tainly the extent of the availability of such niches strongly affects the scale of scientific endeavor. Edelstein finds ancient science fatally weakened by lack of social support, but right up to 1800 there are very few posts for scientists, and very few who make their livings as scientists. Significantly enough, the word "scientist" is of coinage only slightly more than a century old; only then did the existence of a substantial professional group raise the need for a group designation. When the nonscientist supports science most often his interest is not in science as such, but only in science as contributor to the cos- mology or technology in which he does take an active interest. Sup- port given out of concern for technology appears quite early: the Ptolemys had quite practical reasons for supporting the Alexandrian Museum. On the other hand, such support dwindled to nothing dur- ing the Dark Ages in which man's attention turned from this world to another. As the modern era opened, experimental science gained a foothold in the universities as the affiliate of already established technologic and cosmologic concerns; i.e., as a subject studied by students of medicine and divinity, respectively. In this period Bacon preaches support of science both as the handmaiden of theology and as the great root of technologic advance. Bacon's estimate of the potential capacity of science to produce such advance far exceeded its actual capacity then, and for some two centuries thereafter. The 92 COSMOLOGY AND TECHNOLOGY situation today is entirely diflFerent and— if the funds given science with intent to benefit technology continue as abundant as they have become in the last twenty years— some early and drastic reorganiza- tion of the whole pattern of scientific endeavor seems well nigh inevitable. Cosmology The microcosmic life cycle of the liver fluke is, in the hands of a Sherrington, a subject as fit for cosmologic thought as the macrocos- mic evolution of the spiral nebulae. More than inquiry into the wholeness of the universe, cosmology is the search for answers, and the answers given, to questions concerning the "real nature" of the world and of man, and even concerning the "reason" or "value" of the world and of man. Each scientist entertains a cosmology he does not, and perhaps cannot, wholly distinguish from his science. That im- portant distinction is, however, often possible for the onlooker alert to four traits that characterize cosmology. Inclusiveness. No concern of science, the "meaning" of human ex- istence cannot but concern cosmology. Purporting itself a world view, cosmology (a "branch of metaphysics," according to Webster) must take in much that science rejects as unfit for its consideration. Science metamorphosed. Quite differently incorporated in different cosmologies, science is there always metamorphosed in a fashion highly distinctive of cosmology. The concept "atom" (or "energy"), a useful tool of scientific thought, becomes then the "real stuff of which the universe is made." What have been found in science "sug- gestive" analogies, "permissible" principles, "sufficient" theories, "eflB- cient" laws, and "appropriate" concepts are by the cosmologist all seen as "truths." A law known highly reliable is confidently assumed exact; known to be of great generality, it is confidently assumed uni- versally applicable. As Bridgman notes, so much is true even in "purely scientific" cosmogony: To me the most striking thing about cosmogony is the perfectly hair- raising extrapolations which it is necessary to make. We have to ex- tend to times of the order of lO^"^ years and distances of the order of 10^ light years laws which have been checked in a range of not more than 3 X 10- years, and certainly in distances not greater than the dis- tance which the solar system has traveled in that time, or about COSMOLOGY AND TECHNOLOGY 93 4 X 10 ~ 2 ligtit years. It seems to me that one cannot take such extrap- olations seriously unless one subscribes to a metaphysics that claims that laws of the necessary mathematical precision really control the actual physical universe. Disagreement. In our cosmologies we do not agree. On the merits of a purely scientific idea more than 25 years old practically all scien- tists are in substantial agreement; cosmologic issues now millennia old are often still the subject of acrimonious debate. Consider: hu- mans, with their limited knowledge, can build a world-\'iew only by relying very heavily on analogies. But analogies are less "given" than "felt": where I sense fundamental analogy you may find only trivial similarity, or even significant opposition. Consider further: prior to the "hair-raising extrapolations," our choice of what we will extrapo- late determines for each of us the nature of his cosmology, and con- versely. Some cosmologists, adopting an "organismic" view, choose to stress the continued failure to reduce all phenomena to mathe- matical expression. Others prefer to stress the great successes already won in the construction of mathematical laws and theories— successes the cosmologic connotation of which was read by the eminent scien- tist Jeans as: "God is a mathematician." The statistical form of cer- tain scientific laws and theories is emphasized by some. The conno- tation of an abstruse mathematical theory may then be read as : "The uncertainty principle restores Free Will." An alternate connotation, read with equal legitimacy but having a very different cosmologic flavor, is: "At bottom everything is ruled by blind chance." Other cosmologists may choose to emphasize the non-statistical form of certain relations: the integral laws (of least action, etc.) are taken by Planck and others to indicate a certain causal purposiveness in nature. But this conclusion can be combatted, as it is by Born, with the argument that: The minimum principles are not due to nature's parsimony but to human economy of thinking, as Mach said; the integral of action con- denses a set of differential equations into one simple expression. Rigidity and revolution. Because of its inclusiveness, my cosmol- ogy involves what are to me matters of deep personal concern. I am committed to my personal cosmology, and the hardening of my re- solve to meet the perennial challenge of other cosmologies is mir- 94 COSMOLOGY AND TECHNOLOGY rored in a hardening of my ideas. As ideas become dius finalized as dogmas, even creeds, diere yawns between cosmology and science the Jamesian chasm— "between categories fulminated before nature be- gan, and categories gradually forming themselves in nature's pres- ence." Founded on the principle of corrigible fallibility— denying to itself any claim to knowledge of "first principles"— science remains ever plastic, even to drastic change. In cosmology the possibility of change is commonly unrecognized, even denied: hard but brittle, a cosmology crumbles under the impact of new ideas, the effect of which is then plainly revolutionary. Are there not "scientific revolutions"? Even a revolution in cos- mology must have some secondary impact in science: the attitudes engendered by my personal cosmology influence the orientation of my efforts as scientist. But the discussion of "scientific revolutions" (in Chapter IX) leads to the conclusion that their most conspicuous trait is their i/n-revolutionary quality in science. Even without bene- fit of that discussion, one easily recognizes that in our actual usage the term "scientific revolution" designates solely certain episodes that were revolutions in cosmology. The works of Copernicus, New- ton, Darwin, and perhaps Freud are commonly regarded as scientific revolutions. But the works of Lavoisier, Dalton, and Maxwell are rarely so regarded, though inferior neither in novelty nor in scientific importance. \Miy? In the first group of works each has ^'ery large cosmologic connotations; we attach no such connotations to the works in the second group. As a scientific doctrine Copernicus' theory was no worse than ludicrous. Its immediate cosmologic impact was sufficient to rouse die wrath of Luther; its delayed impact was violently explosi\'e. And obser\'e that while Galileo was "only" severely rebuked for espous- ing the Copernican theory as science, Bruno was (in 1600) burnt at the stake for heresies nourished by its rich cosmologic implications, e.g., the infinitude of the universe and the plurality of inhabited worlds. Here, in cosmology and not in science, occurs the true Co- pernican revolution. As die directly contrasting case consider La- voisier who, overthrowing the phlogiston theory, may be held to have worked a revolution. Indeed, chemical thought is by him changed as drastically as astronomical thought by Copernicus. However, while Copernicus is generally acknowledged to have worked a revo- lution in human thought, the very most we say for Lavoisier is that COSMOLOGY AND TECHNOLOGY 95 he worked a chemical revolution. Copernicus' work forced a re- appraisal of die nature of the cosmos and of man's place in it; La- voisier's work forced nothing of the sort. With the name of Newton we associate a genuine revolution in cosmology. For example, the Newtonian conception of "natural law" leads through Locke and others to the outlook of the Age of Enlight- enment. The elegance of the mechanism of the cosmos Newton him- self regarded as absolute proof of the existence of God; but elabora- tion of the "world-machine" led inexorably to Laplace's conviction that, in celestial mechanics, the hypothesis of God is a superfluity. Consider now: in science Dalton's atomic theory did for chemistry, and Maxwell's electromagnetic theory for physical optics, very much what Newton did for physical dynamics. But Dalton's work or Max- well's work is never called "scientific revolution"! Even the violent overthrow of the long-entrenched caloric theory by the kinetic theory (in which action Maxwell also distinguished himself) fails to win estate as "scientific revolution." Naturally! The effect in sci- ence of a theoretical advance is almost irrelevant to any claim on that title, the sine qua non for award of which is the production of a major upheaval in cosmology. This is precisely what was produced by the work of Darwin. Darwin destroyed no established scientific theory: indeed the idea of evolution (though not evolution by natural selec- tion) had been "in the air" for more than half a century. Surely it is obvious that the genuine revolution in which Darwin figures ( and in which, significantly enough, Huxley figures even larger) is a revolu- tion in cosmology. And the discrimination expressed when we speak of a Darwinian or Newtonian ( or Freudian ) revolution— but never of a Daltonian or Maxwellian revolution— itself defines for us the do- main of cosmology: it is the locus of primary impact of what we call "scientific revolutions." THE CLIMATE OF OPINION Contemplating the very irregular appearance of genius, scientific and otherwise, Kroeber hypothesizes that of many seeds of potential gen- ius, produced sparsely but relatively uniformly in all places and times, only those few flower that are reared in the cultural environ- ments of certain particular places and times. Consider, as an example, the astonishing galaxy of scientists who grew up in or near Budapest around the turn of the present century. Hungary had not earlier, and 96 COSMOLOGY AND TECHNOLOGY has not since, produced so large and illustrious a group as Hevesy, Polanyi, Szent-Gyorgi, Szilard, Teller, Von Bekesy, Von Karman, Von Neumann, Wigner, and many others. Perhaps the situation is as Duhem depicts it: Contemplation of a set of experimental laws does not, therefore, suf- fice to suggest to the physicist what hypotheses he should choose in order to give a theoretical representation of these laws; it is also nec- essaiy that the thoughts habitual with those among whom he lives and the tendencies impressed on his own mind by his previous studies come and guide him, and restrict the excessively great latitude left to his choice by the rules of logic. How many parts of physics retain to this day a merely empirical form until circumstances prepare the genius of a physicist to conceive the hypothesis which will organize them into a theory! However this may be, even quite local variations in the cultural environment may have spectacular eflFects. Consider what happened at the University of Padua. Here flourished a literally radical culture. Going back (by way of Averroes rather than Aquinas) to the tap- root of scholastic thought, to Aristotle, it embraced also a Galenic element of respect for observation and experiment. The University had a strong secular orientation, buttressed by the dominion of the strongest anticlerical state then extant (Venice), and oflFered a free- dom of thought unparalleled in any learned institution of the time. What a profusion of scientific genius is found among men whose outlook this University had moulded: Cusanus, Copernicus, Fabri- cius, Vesalius, Harvey, Galileo— all these and others, making up a substantial proportion of that small company which made modern science, had drunk the heady wine of Padua. We found in Chapters I and II that perceived "naked fact" is, if not quite mythical, at least substantially hypothetical. We find now that, in confrontation of "naked fact," scientific ideas are born of human minds suflFused with extrascientific, metaphysical presupposi- tions. Eddington indeed remarks that "because a man works in a laboratory it does not follow that he is not an incorrigible metaphysi- cian." Consider for example how much the design and conduct of contemporary laboratory practice owes to a not-always-accredited cosmologic con\dction that for every macroscopic physical effect ob- served there should be a discoverable "natural" cause. And, outside the laboratory, Eddington was himself a living demonstration of the COSMOLOGY AND TECHNOLOGY 97 enormous role that personal metaphysics may play in "purely scien- tific" matters when deeper theoretical judgments are involved. This eflFect is obvious even in the routine deployment made of the principle of continuity. In company with common sense, science long accepted ideas of fabulous things and events occurring "strangely" in remote places and times. Until Kepler, Galileo, Descartes, and New- ton, few indeed were those who dared to extend to the celestial realm the laws known to obtain in terrestrial contexts. Conversely, 19th-century physicists did not hesitate to extend relations, ham- mered out in the macroscopic world of experience, to the hypotheti- cal microcosmic world underlying it. Today the timidity of the earlier attitudes and the confidence of the later both appear excessive, but of course both depend (like those "hair-raising extrapolations" of which Bridgman speaks) on essentially metaphysical presupposi- tions. The cosmology of the individual scientist— uncritically formulated, unarticulated, and active at a level well below full consciousness- must, as Crombie observes, make itself felt throughout his science. . . . there has never been natural science with no preconception at all of theoretical objectives of a philosophical kind. . . The procedures of science are methods of answering questions about phenomena; . . . But the form the questions take, the direc- • tion and extent to which they are pressed in the search for an ex- planation, will inevitably be strongly influenced by the investigator's philosophy or conception of nature, his metaphysical presuppositions or "regulative beliefs," for it is these that will determine his concep- tion of the real subject of his inquiry, of the direction in which the truth hidden in the appearances will be found. Beyond "promising" problems and "responsible" techniques, even what are "acceptable" solutions will so be defined. A science giving purposive explanations in answering "Why" questions yields to a science giving causal explanations in answering "How" questions; and this may, in its turn, yield ground to a science furnishing only functional relations, permitting answers to "What-When-Where" questions. All these sciences reflect cosmologic opinions, and are themselves mirrored in such opinions. Commenting on the great pioneers of science, Polanyi remarks that "even their outlook will remain predominantly determined by the 98 COSMOLOGY AND TECHNOLOGY time and place of their origin." And, as regards scientists generally, surely an affirmative answer must be given to Weizsacker's query: Should we not say that the historical situation of human consciousness belongs to the a priori of physics? To us ancient atomism appears to have offered an extremely promis- ing alternative to the animistic conceptions widely accepted in antiq- uity. But atomism never "caught on"; it was, as Sambursky observes, fatally incompatible with the whole cosmology of the age. Today we aim at projecting the mathematical and physical laws of the physical universe into man, with the object of explaining the phe- nomena of life by physics and mathematics; whereas the Greeks sought to extrapolate man into the expanse of the cosmos and re- garded the cosmos as a living organism. Their biological metaphors, such as the breathing of the cosmos, are not simply allegorical: they really mean that the cosmos has its own rhythm of life, that its laws are basically organic and that therefore it is conscious of the musical harmony of the spheres. The conception of the world as a living body was present in all periods of Greek science. Any deviating tendency, such as the atomic theory, did not take firm root in the science of the Ancient World. The linguistic factor. Almost a century ago, long before Sapir and Whorf reached their more extreme conclusions, Stallo already fovmd it obvious . . . that the thoughts of men at any particular period are limited and controlled by the forms of their expression, viz., by language (using this term in its most comprehensive sense); that the language spoken and "thought in" by a given generation is to a certain extent a record of the intellectual activity of preceding generations, and thus embodies and serves to perpetuate its errors as well as its truths; that this is the fact hinted at, if not accurately expressed, in the old ob- servation according to which every distinct form or system of speech involves a distinct metaphysical theory; . . . From that metaphysics we do not fully escape even as we acquire scientific and mathematical languages. Always in thought, if not also in statement, we supplement those languages with parts of every- day speech. Into science then stretches the aura of the covert cosmol- ogy enshrined in common-sense language: the existence of "things"; COSMOLOGY AND TECHNOLOGY 99 the dichotomies of subject and object, mind and body, wa\ e and particle, etc. Reflection of the logical sense of those who made it, a language cannot but condition the reasoning of those who use it, whether in science or elsewhere. A language conditions the way in which ques- tions are put and the way in which answers are formulated; to some extent it determines even what questions can be put and the kinds of answers that can be given. As questions put to nature, even our experiments will not then escape conditioning by the cosmology of our language and, as Whorf strongly emphasizes, the same irreduc- ible element of subjectivity will color what we like to think of as nature's answer. . . . the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds— and this means largely by the linguistic systems in our minds. ... no individual is free to describe nature with absolute imparti- ality but is constrained to certain modes of interpretation even while he thinks himself most free. . . . users of markedly different grammars are pointed by their grammars toward different types of observations and different evalua- tions of externally similar acts of observation, . . . The aesthetic factor. "Taste" for classic simplicity or baroque com- plexity—or taste perhaps gratified in great and multiplex ends pro- duced by few and fundamentally simple mechanisms— such taste shapes cosmology and, thence, enters into the making of "scientific taste." Dingle cites an amusing example of the aesthetic factor, sig- nificant though it was pronounced in the 13th century, well before the rise of modern science. Contemplating the extremely cumber- some Ptolemaic system, the devout and learned Alphonso of Castile was moved to remark that, had he been present at the Creation, he could have given the Creator some good advice. The same feeling of repugnance for the Ptolemaic system enters into the complex of motivations that stirred Copernicus to the creation of his system; and aesthetic appeal almost alone sustains Copernican astronomy through the difficult first half-century of its life. Consider that the Copernican system could be, and was, held to "explain" the familiar only in terms of the preposterous. The changes in the heavens are "explained" by a triple motion of the earth of 100 COSMOLOGY AND TECHNOLOGY which we must suppose ourseh^es entirely unaware. The absence of stellar parallax is "explained" by the postulate— not merely arbitrary but acti\'ely repulsive— that the nearest stars are fantastically distant. Necessarily impugning scholastic interpretations of motion, the Co- pernican system could itself account for the continuance of celestial motions only by the suggestion of a special "naturalness" to motion in perfect circles. Inadequate at best, this "explanation" collapses widi Kepler's demonstration that the planets do not pursue accu- rately circular courses. Why then did anybody credit the Copernican theory? Because of course to a few that theory oflFered a breath- taking vision of mathematical harmony. Polanyi well observes that we have here no simple rejection of the anthropocentricity implicit in a geocentric system but, rather, a preference for a diflFerent aes- thetic anthropocentricity maintaining that nature is the embodiment of mathematical regularities harmonious in the ears of men. A further element of aesthetic appeal sustained Copernicus' system in the face of the far sterner challenge posed by the Tychonic system for the next three-quarters of a century. Far more readily reconciled with scholastic mechanics, but mathematically the exact equivalent of the Copernican theory, Tycho's system remained clearly superior even as a correlative device until the work of Newton. The earth is stationary, and neither the "evidence of the senses" nor the absence of detectable parallax need then be explained away with additional postulates. We say that the Tychonic system is wrong, and rejoice that some men rejected it from the outset. On what basis could they possibly do so? As far as I can make out, the root of their rejection of the Tychonic system lay in its failure to assign the central position to that great luminary, the sun. To a Neoplatonic the sun "belonged" in the center, and he could cling to the Copernican theory simply out of regard for this element of aesthetic appeal wholly lacking in its competitor. Aesthetic considerations remain powerful in science. Everlastingly compelling, considerations of symmetry (physical and/or mathe- matical) are no less so in the present era of quantum mechanics. In- deed, but a few years ago the concern for symmetry evoked from de Broglie a distinct echo of Copernicus' opinion that, to be acceptable, a theory must appear "sufficiently pleasing to the mind." . . . some physicists have even come to doubt the existence of a real symmetry between light and matter concerning the duality of their COSMOLOGY AND TECHNOLOGY 101 nature. On this point we are of an exactly opposite opinion: the sym- metry bet\veen matter and hght, which sei-ved as the basis of the de- velopment of wave mechanics, is so satisfying to the mind and to us seems so much to be the profound reason for the success of these new theories, that, in our opinion, we must not abandon it at any price. In scientific creation the activity of the aesthetic factor is often patent —if not in de Broglie's own work, for example, then surely in those considerations of "mathematical perfection and beauty" that, says Born, guided "Maxwell's decisive step" in the framing of his elec- tromagnetic theory. In scientific judgment the activity of the aesthetic factor remains evident as long as we characterize the theories we accept as "beautiful," "elegant," and "refined," and those we reject as "clumsy." There is some justice even in the extreme view of du Noiiy, who writes : Whenever there is no objective confirmation, our attitude toward cer- tain theories depends, in the last resort, on aesthetic considerations, disturbing as this may seem. The ethical factor. A science need only be "true"; a cosmology we hope to find "good." In any society the powers that be ( church, state, school, press, vox populi, etc.) will hold certain cosmologic views *'good" and others "bad"— in that they impugn sound religious doc- trine, good citizenship, the healthy outlook, etc. Thus, for example, to Plato the naturalistic view appeared a danger to the state: The theories of our modern men of enlightenment must be held to account for the mischief they cause. Now the effect of their composi- tions is this: when you and I produce our evidence of the existence of gods and allege this very point— the deity or divinity of sun and moon, planets and earth— the converts of these sages will reply that they are but earth and stones, incapable of minding human conduct, however plausibly we have coated them over with a varnish of sugared elo- quence. To prevent the "mischief," Plato urged that teaching of the naturalis- tic doctrine be proscribed, and its teachers imprisoned. Apparently action of this sort never became a major factor in the life of ancient science. But as science assumes a larger role in cosmologic construc- tion, the pressure "authority" brings to bear on the shaping of cosmol- ogy will be felt increasingly in science also. The flames that consume Bruno threaten to spread to Galileo: the attempt to suppress Coper- nican cosmologies becomes in time an attack on their essential foun- 102 COSMOLOGY AND TECHNOLOGY dation, Copernican astronomy. Some two and one-half centuries later, horror of the cosmologic overtones of an ethically blind natural selec- tion produces the furious attack on Darwin's biology. In our own day the ethical factor prompted the So\iet regime to suppress one genetic theory ( and to extirpate its supporters ) in favor of another that was felt to be more readily compatible with the demands imposed by the state philosophy. The scientist is not simply the passive victim of external pressures. Ethical considerations enter into the construction of his own cosmol- ogy—and thence into his science. To be sure, he is taught to do his science without regard to such considerations, but this is a counsel of perfection. \A^ill a mechanism of natural selection first commend itself to a scientist who believes that natural phenomena express the development of some mighty ethical purpose? Was the judgment of Russian geneticists wholly unaffected by their acknowledgement of the official philosophy of the state? Einstein's passionate refusal to accept as final the statistical description, furnished by modern quan- tum mechanics, cries an anguished protest against the conception of nature governed by "a god who plays at dice." We smile condescend- ingly at Einstein's attempt to inject into scientific discussion what is transparently an ethical argument. Can we afford the condescension? Is not acceptance of amorality itself an ethical decision? When the quantum physicist most vigorously denies all cosmologic commit- ments and pretensions, has he not already given tacit assent to the Lucretian cosmology— with its blind, purposeless, random tumbling of particles in the void? The moral factor. Only rather arbitrarily distinguished from the ethical factor, some moral elements in the climate of opinion act powerfully on science. Consider for example the effect of Calvinist emphasis not on God's love but on God's ivill: the doctrine of pre- destination is perhaps necessarily associated with a cosmologic con- ception of immutable late. A faith in the lawfulness of the universe is surely essential to science, and Needham well inquires: Was the state of mind in which an egg-laying cock could be prose- cuted at law necessary in a culture which should later have the prop- erty of producing a Kepler? One cannot progress, or even think of progressing, in scientific under- standing if he considers nature ruled by one or more capricious or COSMOLOGY AND TECHNOLOGY 103 even actively malevolent deities. Modern science takes its departure from a quite diflFerent moral conviction— kin perhaps to Einstein's faith that: Raffiriiert ist der Hen Gott, aber boshaft ist er nicht. The Lord God is subtle, but malicious he is not. Beyond belief that man can understand nature, there is the further feeling that man may be obligated to seek such understanding. His mind, the gift of God, is most fittingly employed in searching the world that God created for what Bacon calls that spark of knowledge of God which may be had by the light of nature and the consideration of created things; and thus can be fairly held to be divine in respect to its object and natural in respect of its source of information. This conception of natural religion becomes a powerful stimulus to science— particularly in England right through the period of Priestley —and perhaps even today it has not fully spent itself, for Oppen- heimer notes that: . . . Einstein has seen in his theories of relativity only a further con- firmation of Spinoza's view that it is man's highest function to know and to understand the objective world and its laws. Here surely we gain some sense of what Snow describes as "a moral component right in the grain of science itself." Powerfully influenced by accepted religious doctrine, the scien- tifically relevant moral tone of a society depends also on other factors. Of four predominantly Roman Catholic countries— Italy, France, Spain, and Ireland— the first two have developed important indige- nous scientific movements, while the last two have not, though each of these was at one time a substantial center of learning. Observe however that, unlike Spain and Ireland, France and Italy have sus- tained important movements of religious dissent. May a decisive factor be the extent to which dissent is accepted as a moral right? If not also elsewhere, in science capacity for dissent (from existing "self-evidencies") and the possibility of progress are firmly linked. If Roman Catholicism does not encourage capacity for dissent from established doctrine, can this explain the results of the Notre Dame 104 COSMOLOGY AND TECHNOLOGY studies showing the disproportionately small number of American Roman Catholics among important American scientists?* Capacity for doubt and dissent may, on the other hand, abound in one who —as member of an "out-group" (perhaps a religious minority)— is forced to regard existing orthodoxies from the outside, and so more sceptically than the orthodox for whom orthodoxy is final. The pre- dominance of dissenters in early English science, and the dispropor- tionately large number of Jews in the ranks of major scientific inno- vators, perhaps finds here some explanation. Not all out-groups pro- duce a multitude of great scientists. Insufficient in itself, scepticism must be complemented by a moral faith that, in the dissenting and Jewish traditions, judges scholarship a matter of "value." THE COSMOLOGY OF ORGANIZED SCIENCE Cosmology is not a highly organized enterprise: each scientist is his own cosmologist, and to each his own individual cosmology is, over- whelmingly, the most appealing. Multiple factors originating in his local community enter into the cosmology of each, and thence into his science. How then can science have unity? By virtue of its own existence as a social entity! Organized science creates and maintains its own cultural milieu, its own ideological atmosphere, in which the scientist dwells so long as he studies science and works as scientist. Organized science has its own language ("scientific language"), its own aesthetics ("simplicity"), its own ethics ("truth is the supreme good"), its own morality ("the search for truth is the supreme moral obligation"). To these add a set of principles, accepted by practically all scientists of a given generation, which determine the whole tex- ture of scientific thought. Summing over all, one finds a respectable approximation to a corporate cosmology. Nowhere stated as such, this cosmology forms part of the scientific tradition with which the individual scientist becomes familiar during his education, and in his later dealings with his colleagues. Encour- aged by this tradition to disregard die various influences originating in the social milieu of his native community, the scientist can never wholly disregard them— but their eflFect is greatly attenuated or di- luted by the cosmology of organized science. Despite the variations in * On this very large subject see R. K. Merton, Social Theory and Social Struc- ture (Free Press of Glencoe, 1957), chapter 18, "Puritanism, Pietism, and Science." COSMOLOGY AND TECHNOLOGY 105 individual cosmology, a substratum of identity in the cosmologies of all scientists makes possible the unity of scientific endeavor. Consider also the indirect eflFect of science on itself: everywhere science modifies, and makes more uniform, the scientifically relevant climate of opinion. Our aesthetic sensibilities are deeply conditioned by the simple majesty of certain scientific theories incorporated in cosmology. Poincare exclaims : One may dream a harmonious world, but how far the real world will leave it behind! The greatest artists that ever lived, the Greeks, made their heavens; how shabby it is beside the tiTie heavens, ours! Our ethical sensibilities are not unaflFected by the concept of an evo- lution controlled by blind natural selection produced in the struggle for existence. Not even our moral judgments are left wholly un- changed, for as Butterfield observes: . . . the so-called "scientific revolution," popularly associated with the sixteenth and seventeenth centuries, . . . outshines everything since the rise of Christianity and reduces the Renaissance and Refor- mation to the rank of mere episodes, mere internal displacements, within the system of medieval Christendom. Since it changed the char- acter of man's habitual mental operations even in the conduct of the nonmaterial sciences, while transforming the whole diagram of the physical universe and the very texture of human life itself, it looms so large as the real origin both of the modern world and of the modern mentality that our customary periodisation of European history has become an anachronism and an encumbrance. Technology Like science itself, technology comprises both activity ( of engineers, technologists, practicing physicians, etc.) and the fruits of the ac- tivity (factories, goods, and services). Living as we do in a world of scientific technology, we find it almost incredible that until quite recently technology should have led the way— with science following, rather ineflFectually, in its train. But consider the situation in, say, prescientific iron metallurgy. The metallurgist knew that, to make iron, one must heat its ore with charcoal under certain conditions. In the group of colligative relations defining this and other operations of his craft, the metallurgist held prescriptions for success which science was for long wholly unable to improve. 106 COSMOLOGY AND TECHNOLOGY As chemistry opened out at the beginning of the 18th century, the metallurgists' processes were still a challenge to chemists, whose studies ultimately put them in position to ofiFer the working metallur- gist a rationalization of his practice: ore is made metal as phlogiston passes into the ore from the charcoal. But this rationalization sug- gests no improvement in metallurgical practice, and had little if any ejffect on that practice. Toward the end of the century Lavoisier created his new oxygen theory, oflFering a new rationalization: ore is made metal as oxygen is taken out of the ore by the charcoal. But again the working metallurgist is no better off for the explanation. The impact of La\'oisier's inno\^ation in chemistry is not felt in the metallurgical industry until long after Lavoisier's death. Today the situation is dramatically different, in metallurgy and elsewhere. Binkley seeks to pinpoint the time at which science first became a major factor in technology: Comment on the Great Exhibition [London, 1851] usually linked mechanical arts and science, but not in the sense that science was the leader and art the follower. Whewell, the historian of science, . . . took it for granted that the natural and "proper sequence" was for creative activity in the arts to go first, and science to follow after with its speculations— exactly the process that was taking place in the development of the doctrine of theiTnodynamics from the steam en- gine. In 1867, when Paris held its second World Exhibition, the place of science in its relations to industry was noticeably changing. By that time the aniline dyes had arrived as the products of organic chemistry, and a number of electric dynamos were on exhibit. When Michel Chevalier, the free-trade economist, wrote his introduction to the jury reports of the Exhibition, he attributed increase in productive power to the advance of science. . . . the difference between Whewell's at- titude in 1851 and Chevalier's in 1867 can be taken as marking the point at which science established before the public a claim to the leadership in the industrial arts. . . . Probably the transition is not quite so abrupt as Binkley suggests. Even a century earlier than this science had already contributed actively to technology— improved navigational aids, a preparation of sulfuric acid (fundamentally the alchemists') operable on an indus- trial scale, and so on. From the middle of the 18th to the middle of the 19th century the applied arts derive from science an ever increas- ing number of small but crucially important contributions, e.g., chlo- COSMOLOGY AND TECHNOLOGY 107 rine as a bleaching agent, and the miner's safety lamp. However, Binkley is quite right in maintaining that only about a century ago did the acti\^ely creative role of science in technology become ap- parent—with the establishment of electrical and chemical industries that owed their creation wholly to the antecedent existence of sci- ence. From the thus completed interaction between them develops a genuinely symbiotic relation of science and technology. Conceptual exchanges. The "gas laws," relations worked out en- tirely in science, render important services to technologists concerned with the design of compressors, superchargers, internal combustion engines, steam and gas turbines, and the like. In place of the many separate relations, the engineer may prefer to use the correlative de- vice constituted by the kinetic theory: he works then with a few more general equations in which all the individual laws are implicit. In either case, by routine use of the anticipatory apparatus, he avoids wasteful cut-and-try endeavors; he more swiftly attains his goals by processes having, in Conant's phrase, a "low degree of empiricism." For all its progressiveness, technology tends to maintain itself within a fixed frame of reference, by which ultimately it can be con- fined. A spectacular liberation may then occur under the impact of new ideas generated in science. Consider rapid communication as the problem it was in 1800. Treating it purely technologically, one might seek to achieve brighter beacons ( or larger mirrors ) on higher hills, smoother post roads traversed by horses bred for speed and stamina, the use of homing pigeons similarly bred, and so on. Were one well traveled, he might even think of trying larger drums or blacker smoke. Exploitation of such possibilities does indeed lead to technologic advance, which is however inevitably canalized and limited by a narrow conception of what are possible means of com- munication. In 1800 no technologist ignorant of science could apprehend the reformulation of the problem of communication that was to be produced from the bizarre studies— of the attraction of bits of chaflF to rubbed amber or glass, or of the twitching of the leg of a dead frog —which fascinated a few contemporary scholars. Yet, well within half a century, these studies eventuated in scientific ideas that formed the basis for the development by Morse and Bell of the telegraph and the telephone, respectively. These were revolutionary ap- proaches to the problem of communication. The same cycle is subse- 108 COSMOLOGY AND TECHNOLOGY quently repeated. Great advances in telegraphy and telephony, con- ceivable in 1850, were achieved as (with the aid of a few scientists like Lord Kehdn ) technology set out to explore to their ends the ruts newly formed in the problem of communication. W'hat could not be foreseen in 1850 was that Faraday's physical concept of "field" would shortly lead to Maxwell's subtle electromagnetic theory, and that in turn to certain experiments by Hertz. A few years after the turn of the century Marconi's wireless signals would span the Atlantic. But without the antecedent Faraday, Maxwell, and Hertz there would be no Marconi. Science breaks for technology trails not merely new but previously inconceivable. Technology makes reciprocal conceptual contributions to science. Today science has its own dynamism, generating internally a large proportion of the problems, the excitement, the new colligative rela- tions, and the analogic stock for which it once drew heavily on ex- ternal sources like technology. Even today, however, technology re- mains an important contributor of all, and not least important for its supply of analogic stock. Earlier in this century the functioning of the brain was conceived with the aid of the analogy furnished by the telephone exchange. More recently cybernetics finds what appears a more appropriate analogy, in electric networks with many negative- feedback loops. "Feedback" is itself a concept of technologic origin- first exemplified in the Watt engine-governor and, more recently and abundantly, in electric circuitry. Material exchanges. Obvious, and obviously important, these ma- terial exchanges will be no more than indicated. By supplying the requisite elaborate glassware, the glass factory at Rouen played an essential role in Pascal's enlightening variations of Torricelli's ex- periment. The balances that served Lavoisier and Stas were fabri- cated by the makers of balances for government mints. As the tools of science become ever more complex, science becomes ever more dependent on the technological resources it can tap. Influencing the ways scientists attack their problems, this dependence may determine even what problems can be attacked. A reciprocal flow of materials, tools, and techniques passes from science to technology. Nowhere available outside the scientific labo- ratory, the rare and expensive substance aniline is found by Perkin to yield a valuable dye, mauve. To obtain mauve Perkin institutes a wholly novel large-scale production, from coal tar, of aniline— which COSMOLOGY AND TECHNOLOGY 109 becomes in consequence a cheap and abundant starting material for chemical inquiries previously impossible. In such exchanges the sym- biosis of science and technology finds its clearest expression. Hertz's short-range transmitters and receivers are, through technologic de- velopment, transmuted into efficient radio equipment. This, in the hands of scientists, leads to further explorations in which the possi- bility of radar detection is first manifested. A further technologic development yields practical radar devices, the newly available com- ponents of which open to exploration new areas of fundamental sci- entific research, e.g., microwave spectroscopy. SCIENCE AND TECHNOLOGY Their intimate symbiotic relation makes difficult a satisfactory dis- tinction of science from technology. Define science as what scientists do? But men like Perkin, Caro, Kelvin, and Pasteur have shuttled back and forth between what is clearly science and what is no less clearly technology. Define science rather in terms of results that com- bine novelty with generality? A much better possibility, I think. Only novelty that has some generality is scientifically interesting novelty, and Poincare remarks : . . . scientists believe there is a hierarchy of facts . . . the most interesting facts are those which may serve many times; these are the facts which have a chance of coming up again. What then is a good experiment? It is that which informs us of something besides an isolated fact; it is that which enables us to fore- see, that is, that which enables us to generalize. Consider an example. While seeking means to reduce or eliminate internal blackening in the incandescent lamp, Edison stumbled on what we call the Edison eflFect. This remained an isolated curiosity for some years, but ultimately was caught up in the web of the theory of the electron elaborated by J. J. Thomson. Thus identified with the emission of thermo-electrons, the Edison eflFect becomes a crucial factor in such further advances as the Fleming valve and the de Forest triode— early harbingers of a flood of electronic devices of immense importance to both technology and science. The Edison eflFect is science: the discovery of a new and general phenomenon. Edison's far more celebrated invention of the incandescent lamp is not science. Exploiting well known general relations— e.g., a current heats a resistor, a body strongly heated becomes incandescent, no 110 COSMOLOGY AND TECHNOLOGY combustion takes place in a vacuum, etc.— Edison drew from his own systematic empiricism the discovery of a suitable filament, and from bis great ingenuity the means of putting together a practical device. His product is a genuine novelty, a new "fact" if you will, but not a fact of interest to science. Here is the root of the disdain with which scientists not infrequently regard inventions (and inventors). For example, Bell's invention of the telephone draws from Maxwell this comment: When at last this little instrument appeared, consisting, as it does, of parts every one of which is familiar to us, and capable of being put together by an amateur, the disappointment arising from its humble appearance was only partially relieved on finding that it was really able to talk. Undeniably a new and important "fact," the telephone is scorned by Maxwell because the general elements on which it depends are not novel, and the element of novelty that it represents is not general- izable. Precisely the same dipartite inadequacy disqualifies the in- vention of the incandescent lamp as science. With the results in hand, the distinction of what is science from what is technology may be feasible; but a distinction drawn after the event does not fully satisfy us. Can we identify in advance those inquiries likely to yield results of interest and value to science? At one time the intent with which work was instituted oflFered some basis for prognosis. The effort to de\'elop a practically \'aluable product or process could then be classed as "technology"— unlikely to produce results that duly combine both novelty and generality. Attention to the site of the activity often rendered prognosis even more secure: from a university laboratory one expected "science"; from an industrial laboratory, "technology." Today both criteria have become seriously inadequate. As to site, a few industrial laboratories now have an appreciable output of "science" at its best: the diffrac- tion of electrons, a new class of semi-conductors, and a new foundation for communication theory are all discoveries emanating from the Bell Laboratories, for example. On the other hand, some academic labo- ratories now have as their chief product work that is, at best, "tech- nology." As to intent, in research on cell metabolism the scientist ( and his financial backers ) can never be wholly insensible of the in- A estigation's possible bearing on the problem of cancer. In such areas COSMOLOGY AND TECHNOLOGY 111 there can no more be a perfectly "pure" science than, as Picasso re- marks, there can be a perfectly abstract art: There is no abstract art. You must always start with something. After- wards you can remove all traces of reality. There's no danger then anyway, because the idea of the object will have left an indelible mark. It is what started the artist off, excited his ideas, and stirred up his emotions. Constraint. Perhaps the least unreliable forecast of the scientific importance of any gi\'en inquiry turns less on the nature of the inves- tigafioM than on the talent of the investigafor; he who has already discovered much is not unlikely to discover more. But forced to wear blinders, even the gifted scientist sees less. Priestley's comment on his own career applies also to many other distinguished scientific careers : In looking for one thing I have generally found another, and some- times a thing of much more value than that which I was in quest of. Other things being equal, more will be discovered when the inves- tigator retains power to pursue promising tangential leads opening up during his investigation. A Rayleigh, prosecuting a self-assigned investigation, is free to follow his research wherever it leads him. Turning aside from his initial study, he traces a curious anomaly back to its root, and so discovers a new element, argon. But a Hille- brand, working toward a specified goal in a government laboratory, could not stop to examine a similar anomaly which pointed to a similar discovery: the terrestrial occurrence of the element helium. In a retrospective reflection, Hillebrand wrote that . . . the chemical investigation had consumed a vast amount of time, and I felt strong scruples about taking more from regular routine work. For this and other reasons he failed to look into the suggestion made by one of us in a doubtfully serious spirit, that a new element might be in question. The successes won by Rayleighs and lost by Hillebrands suggest to Conant that the presence or absence of constraint is a distinction far more important than that now doubtfully drawn betv/een pure and applied science. One might attempt to distinguish as applied 112 COSMOLOGY AND TECHNOLOGY science the endeavor to prepare a nitrogen mustard with superior properties as a chemotherapeutic agent and as pure science some general study of cell metabolism. The second project is perhaps more likely to yield results of interest to science, but either may do so and neither may do so. The first project is more likely to proceed under constraint, but in both cases constraint to a rigid program set down at the outset sharply reduces the chances that scientifically important results will be obtained. Trotter properly emphasizes that: Great discoveries will . . . continue to be unexpected and the ad- vance of science occur on an irregular front in which the salients mark the places where amongst the facts the going is good. Even re- search deliberately directed against short-range targets is apt to be held up contrary to all reasonable expectation or to score its successes through unintentional deflections. i Emphasis on science immediately applicable to the problems of technology necessarily diverts support, and men, from the kind of science that— following to their unexpected ends lines of research having little or no apparent relevance to current technologic prob- lems and practice— leads ultimately to complete reconstruction of the technologic horizon. The utterly unprecedented dynamism today displayed by science and technology is founded on the fully devel- oped symbiotic interaction between them. This interaction ensures that any loss to science will be a loss felt also by technology, and the dynamism ensures only that the loss will be felt sooner rather than later. An understandable concern for national security may suggest the desirability of secrecy imposed to protect the scientific discovery made the year before last, or constraint imposed to secure the fullest possible exploitation of last year's technologic triumph. But in the present dynamic situation these policies are completely self-defeating if as a result science does not this year arrive at the basis of what will become next year's technology. Even the "purest" scientist is not unmindful of the possibility of such advances. If, as science develops under its own internal dynamics, he can grasp the possibility of some previously impossible resolution of an urgent technologic need or problem— then there await him fame and money; beyond such "sordid gain," perhaps the satisfaction of the benefactor of his com- munity; and always the prospect that, through technologic exploita- tion of his science, his materials and tools will be returned to him a COSMOLOGY AND TECHNOLOGY 113 hundredfold improved and multiplied. There is then some automatic co-ordination of scientific endeavor and technologic needs, co-ordina- tion achieved without any of the losses entailed when constraint be- comes a general policy for science. THE REPROBATION OF SCIENCE For better or worse, the automobile affects social mores; radio, tele- vision, and the cinema condition aesthetic taste. Acting through technology, science changes the whole pattern of our culture. Our central-city civilization can first arise only with the development of artificial fertilizers that vastly increase the yield of agriculture, public health measures typically reflected in municipal water sys- tems, and so forth. Today we are most acutely aware of some rather different technologic exploitations of science. Contemplating the nu- clear weapon and its intercontinental carrier, we may well feel stirred to moral rejection of the science that has made them possible. Science vastly multiplies and diversifies the range of possibilities humanly attainable, among which we choose those we will make realities. But unless we reject as morally evil the ultimate scientific commitment to the quest for knowledge— and some of course do- moral condemnation of science is nonsense. The scientist makes an ethical judgment, and assumes a moral responsibility, when he elects to take part in the technologic exploitation of science for destructive purposes. "Social demand" may applaud but cannot itself justify such a decision— any more than it can the decision of the smith who turns iron into swords rather than plowshares. But scientific knowledge is ethically as neutral as iron: "evil" only when forged as a sword, "good" when beaten into a plowshare. Conceivably there is some knowledge that can lead only to "evil"; certainly there is no knowl- edge that can lead only to "good." The discovery of some marvelous vaccine against a lethal plague would seem solely "good"; but it opens up also wholly new possibilities for "evil"— an aggressor will wage germ warfare only if he possesses means to protect his own population. Science a curse, its exploitation bringing death and dis- aster? It may be so. But life is commonly esteemed the supreme blessing; and the vast majority of us would not now be alive save for advances in agriculture and hygiene that are also exploitations of science. Ambivalence attaches to the works of science simply because their technologic exploitations rest in the hands of men. CHAPTER V Colligative Relations and g\C47n^ Scieivtific Laws f ^ BRARY MASS. OME colligative relations plainly arise from everyday experience ( e.g., "Two things cannot occupy the same place at the same time"); others are uniquely the products of science (e.g., Boyle's law). Some are qualitative ("Metals resemble each other in their physical properties" ) ; some are statistical ( Men- del's genetic ratios); some yield precise quantitative predictions ( Moseley's law ) . Some are exact to the limit of our capacity to check them experimentally (the law of the lever); most meet the test of experience only approximately (Kepler's first and second laws of planetary motion ) . They range continuously from what appear to be no more than definitions ("Sulfur is a yellow crystalline solid . . ."); to almost purely mathematical theorems ("In the space of our ex- perience the sum of the angles of a triangle is 180°"); to what may appear no more than conventions (Galileo's law of free fall). Some are obviously of restricted applicability ( the Bode-Titus law ) ; others ( the equivalence of gravitational and inertial masses ) seem to be of extreme generality. Relations multifarious as these presumably fall in separable sub- groups. However, the present purpose is to show that— their over- whelming di\ ersity notwithstanding— all share enough in common amply to justify grouping them together, as colligative relations. 114 COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 115 THE EFFICIENCY OF COLLIGATIVE RELATIONS In Chapter II we observed that from a typical colhgative relation like the law of the lever we obtain predictions that may prove only approximately correct. Consider now how I will proceed when I seek to draw from the law of the lever predictions exact to the limit of my capacity to check them experimentally. Obviously I do well to begin by checking the graduation of my meter stick and the calibration of my weights; but I can hardly expect reliably to predict the behavior of a system incompletely defined in any "significant" sense. I must then carry through an extensive study, beginning perhaps with ex- amination of the external conditions. Ideally the experiment should be made in a room or enclosure free from drafts (which might dis- turb the condition of balance), held at a uniform constant tempera- ture ( to avoid any uneven expansions or contractions of the beam ) , constant humidity ( to avoid the adsorption or desorption of water on or from the beam or the weights ) , and constant pressure ( to a\'oid variable buoyancy effects on beam and weights that have finite vol- umes). Lacking these ideal conditions, I can still proceed, by calcula- tion from measurements of the external conditions, provided that I have amassed much information about the components of the sys- tem: their volumes, surface areas and characteristics, coefficients of thermal expansion, and so on. About the actual system I will in any case need very precise infor- mation. Are all the bearing surfaces essentially frictionless, coplanar, parallel to each other, and perpendicular to the beam? If not, further measurements and calculations must supply appropriate corrections for the deviations. What is the coefficient defining the rigidity of the beam, what does it weigh, and where is its center of gravity? This last I cannot calculate from the geometry of the beam without mak- ing the potentially fallible assumption that it is perfectly homoge- neous. Presumably I will prefer to make a preliminary trial to de- termine the position of the fulcrum when the unloaded beam is in balance; but this, rather painfully, necessitates that I assume at least some part of the law of the lever in deriving the predictions by which I hope to establish its exactitude. Completing all these preliminary studies, I can make predictions I would be vastly surprised to find detectably in error. Nevertheless the possibility of at least minor error always exists and occasionally 116 COLLIGATR-E RELATIONS AND SCIENTIFIC LAWS materializes: some of the preliminary measurements may have been faulty, some of the many variables I thought it safe to ignore may actually have affected the outcome of the test, etc. I can still argue that the law of the lever is absolute, exact, and "true" as applied to the hypothetical ideal lever: by definition that retreat position is al- ways secure. But as a colligative relation usefully applicable to actual lever systems the law is clearly contingent ( since prediction depends on potentially fallible antecedent determinations of conditions ) , ap- proximate (since all the possibly relevant conditions cannot be con- trolled or determined), and at most efficient (to the extent that it represents an optimal reconciliation of our conflicting desires for ease and generality of application and for reliability ) . That our desires conflict is nowhere clearer than in the last ex- ample. As ordinarily conceived, the law of the lever is a relation of great generality. But, seeking to draw from it predictions of maxi- mum reliability, we had sharply to slirink its applicability. In effect, we limited it to systems approximating an analytical balance under the closely controlled conditions of the laboratory— to systems ap- proximating in their extreme artificiality the extreme abstraction of tlie ideal lever. Meyerson writes : Doubtless, if nature were not ordered, if it did not present us with similar objects, capable of furnishing generalized concepts, we could not formulate laws . . . In fact, we only attain laws by violating nature, by isolating more or less artificially a phenomenon from the whole, by checking those influences which would have falsified the observation. Thus the law cannot directly express reality. The phenomenon as it is envisaged by it, the "pure" phenomenon, is rarely observed without our interven- tion, and even with this it remains imperfect, disturbed by accessory phenomena. The artificiality of the special lever system with which we worked reflects our attempt to isolate it from the rest of the universe, to in- sulate it from the manifold accessory factors operative in the raw phenomenon but omitted in the statement of a law that refers ex- plicitly only to certain weights and distances. Ordinarily sufficient (though not perfect) isolation, insulation, can be achieved: that is the message of the principle of dissolubility. And ordinarily we arrive at acceptable predictions without taking account of more than a very few complicating factors. We do not, cannot ordinarily, even con- COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 117 template undertaking the extravagant series of studies essential for exact prediction. Demanding such studies, the law of the lever would lose all its value: with but a fraction of the effort required for pre- diction we could simply set up the lever system and observe what happens. Thus, as Duhem remarks, A mathematical deduction . . . may therefore be useful or otiose, according to whether or not it permits us to derive a practically definite prediction of the result of an experiment whose conditions are practically given. Predictions drawn with difficulty from the more complicated van der Waals relation are usually more reliable than those drawn from Boyle's law. But ordinarily we elect to use Boyle's law— from which we easily derive a host of predictions usually quite well enough borne out in practice. Paraphrasing Einstein, may I not insist that insofar as a colligative relation is generally applicable it is not exact, and insofar as it is exact it is not generally applicable? What we seek in a colligative re- lation is efficiency— a reasonable balance of reliability, generality, and convenience— and efficiency is all that is attested by the successful functioning of a colligative relation as such. To be sure, in their cos- mologic speculations, scientists have sometimes claimed discovery of the true laws by which nature is governed. That cosmologic dogma is, however, no present concern of ours— as becomes clear when we consider, for example, the equivalence of inertial and gravitational masses. We may hold it universally and absolutely "true" because we accept as final the relativistic theory in which this equivalence is a deduction entailed by postulates ive accept. But tlien surely we are not treating it simply as a colligative relation. Alternatively, we might hold the equivalence "true" because it has been confirmed to the limit of our experimental measurements. Here we introduce the covert assumption that a law so confirmed must be mathematically exact, and so unite the colligative relation with a superfluous meta- physical assumption. As a colligative relation the "law" is no more than efficient. The generality of this important conclusion is perhaps best illustrated by showing its applicability to a colligative relation apparently wholly different in form from any so far examined. The sulfur relation. Sulfur is a yellow crystalline solid with density 2.07, melting at 119.0°C and boiling at 444.6°C, a good insulator, 118 COLLIGATR'E RELATIONS AND SCIENTIFIC LAWS soluble in carbon disulfide, burning in oxygen to give a gas . . . and so on. Is this any more than a definition of what we mean by "sulfur"? Meyerson teaches us to see that the definition yields the following per- fectly genuine colligative relation: If a substance displays many of the following properties . . . , then probably it will display all the others. Such a relation oflFers multiple predictions of which many have been confirmed repeatedly. Can any such prediction ever fail? Yes! The definition notwithstanding, every chemist well knows that the sulfur of experience may be quite diflFerent from the ideal sulfur of the definition. "Real" sulfur may be not yellow but white; not hard and crystalline but rubbery or amorphous; melting not at 119.0°C but at some other temperature dependent on its previous history, purity, and isotopic composition— and so on. What to do? Restrict application of the relation to some standard sulfur prepared by a specified procedure? Certainly not! Just as we guard the generality of such concepts as "water" and "lever," we in- sist on keeping "sulfur," and its defining relations, conveniently ap- plicable to the myriad specimens of real sulfur— each with its own impurities and its own history. Seeking efficiency, we make the char- acteristic compromise, as is perhaps most evident when we ask: How "many" properties must we check before identifying a substance as sulfur and predicting its other properties? Obviously, the more properties we check the less likely we are to make false identifica- tions and false predictions. Ordinarily, howev^er, we are content to check only one or a few properties— perhaps even none beyond the label on the container. A COLLIGATIVE RELATIOxN: BOTH INVENTION AND DISCOVERY We invent the concepts weight and distance; we invent the ideal lev^er to which the law of the lever applies by definition. But the law acquires value only through a simultaneous discovery: there are in nature distinguishable systems predictably conformable to the law. Similarly, the concept sulfur is an invention, scientifically meaningful only because we often encounter recognizable specimens sufficiently approximating "ideal" sulfur that useful predictions can be drawn from the sulfur relation. These complementary elements of inven- tion and disco\^ery are evident even in the more abstract scientific concepts. Some writers dispute whether Thomson invented or dis- covered the electron. This futile issue is easily resolved: the electron COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 119 is both invention and discovery. Purely as a concept it is an inven- tion; but its scientific value becomes established only with the dis- covery in our experience of certain items readily interpretable in terms of this concept. Boyle s law. In this new context let us examine in greater detail the complex passage, from observational data to scientific law, that was only sketched when the law of the lever was discussed in Chapter II. Imagine that we invent sl J-tube apparatus, like Boyle's own, with a pocket of air trapped by mercury in the closed short limb. We observe \ / 'B y— -L At left: A small volume of air, trapped in the closed arm of the J-tube, is compressed into a smaller volume when more mercury is added. The total pressure acting on the confined gas is m.ade up of the hydro- static pressure, p.i, plus the atmospheric pressure, pa, acting on the mercury surface in the open arm of the J-tube. At right: A barometer permits the determination of the atmospheric pressure which, acting on the surface of the mercury in the dish, holds the mercury in the evacuated tube at a height that reflects the magni- tude uf the atmospheric pressure, Pr. 120 COLLIGATWE RELATIOXS AND SCIENTIFIC LAWS that, as more mercury is poured into the open end of the longer Hmb, the mercury levels ascend in both tubes. Paying no attention to the complicated (and irreproducible ) oscillations of the mercury columns, we note their positions only after they have become quies- cent. This is our choice, but to it corresponds something that is our discovery: the final positions of the mercury columns are reproducible and apparently independent of the antecedent oscillations. That the two columns ascend together tells us essentially nothing. Indeed, we must not be bothered with the increasing length of the mercury column in the short limb: we note instead the decreasing length of the column of air therein. This length we concei\^e a meas- ure of the "volume" of the entrapped air. And, similarly, we must not measure the length of the mercury column in the long limb but rather the difference in the heights of the columns in the two tubes. To this difference we add the height of the mercury column, meas- ured from the mercury level in the reservoir, in an entirely separate device— a Torricellian barometer. This complex procedure is directed by the subtle concept "pressure." Thus we translate certain ob- serv^ables into conceptual terms we invent, and this is no simple mat- ter. Having made his experiments, Boyle did not himself arrive at the law that bears his name; his friend Townley had to point out to him that the product of pressures and volumes is very nearly a con- stant. And here, after all the many inventions, we reach a discovery —though not yet a discovery of Boyle's law as such. Experiment furnishes a finite series of points on, say, a plot of pV versus p; but Boyle's law represents a line on that plot. Relying on the principle of continuity, we link up the points with a smooth line- assuming nonexistent any discontinuities that may happen to fall be- tween even close-spaced points. We close the gaps by a veritable generalization: we interpolate, on the strength of Newton's faith, and ours, that Natura non saltus facit. And, from the line thus in part in- vented, we read off any of an infinitely large set of values interpolated, with a confidence not much inferior to that we have in the compara- tively small set of values measured. But still we have not attained to Boyle's law which, on our plot, is the equation of a straight line. Lamentably enough, no straight line does pass through all the ex- perimental points. With a gas space more constant in bore, a meter stick more care- fully graduated, and so forth, the divergence of the points from a COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 121 straight line may be reduced, but not eliminated. We look then for sources of "experimental error." Perfectly typically, we find them in variables originally passed over as "irrelevant." We find the points very much less scattered when we control the temperature with a thermostat. A brief wait ("to establish equilibrium") before each reading sometimes helps; otherwise the gas may remain slightly over- heated by the compression consequent to rapid addition of the mercury. We find further that the gas sample must im^olve no equilibrium mixture (lest the number of gaseous particles change with the pressure), that it must be reasonably far from its critical point and also reasonably dry (lest at high pressure part of the sample be "lost" though condensation), that the two arms of the J-tube must be reasonably equal in diameter (lest there be "capil- larity effects" ) , and on and on. We find that the more we take such precautions the more we re- duce the scatter of the experimental points. But always, in any large set of measurements, we will have to dismiss (perhaps as "reading errors") one or a few points that fall far from the line. And always, as Poincare observes, the bulk of the points will still show residual scattering away from the line we actually draw. . . . the curve that we shall trace will pass between the observed points and near these points; it will not pass through these points themselves. Thus one does not restrict himself to generalizing the experiments, but corrects them; and the physicist who should try to abstain from these corrections and really be content with the bare experiment, would be forced to enunciate some very strange laws. If the points form an approximately rectilinear array, we draw the straight line, defined perhaps by the method of least squares, that goes nearest to but not through all of them. Not to take as "best" the curve that is the smoothest reasonable approximation to the experi- mental points— that restraint our scientific taste, long molded by a conception of gradualism, would find "strange" indeed. The slightly uneven line actually defined by the points is, we feel, uneven only because of small but always finite experimental errors. By an act of faith we then pass to the limit: we say that if there were no such errors there would be no deviation from exact linearity. We then write the mathematical equation: pV = constant; but this expression refers rigorously only to the outcome of experiments we have not 122 COLLIGATH'E RELATIONS AND SCIENTIFIC LAWS done and cannot do. Human invention plays here no inconsiderable role. We are still far from Boyle's law as it is commonly concei\'ed. We ha\'e made a few experiments, at a particular time and place, with a particular apparatiis containing a particular gas. We aspire to far greater generality. We extend Boyle's law to measurements made by very different means, e.g., with pressures imposed by a solid piston. To the concepts pressure and volume we thus attach additional de- notations we deem "equivalent." We assign the denotations; but also ice discover, applying them to experiments, that in each case the product pV is gratifyingly constant. Now, with a few additional trials, and further invocation of the principle of continuity, we gen- eralize the law to apply in all places, at all times, and under all con- ditions of constant temperature. Drawing still further on the princi- ple of continuity, we suppose that in nature there are not simply things but things of a species: on the basis of a few more trials we generalize our results to all "gases"— including N^arieties yet unknown —and so arrive at last at Boyle's law in all its lustrous majesty. The luster is of course somewhat tarnished by the subsequent discovery that Boyle's law applies exactly only to an "ideal gas" we must our- sehes invent. Here is a recapitulation of the steps by which we reached Boyle's law: 1. Creation of certain conceptual and experimental tools 2. Experiments of which "relevant" elements are reported in concep- tual terms and "irrele\'ancies" are dismissed 3. Reintroduction of variables originally concei\'ed "irrelevant," as restrictions on applicability of law 4. Rejection of deviant points, and scattering of points, as "experi- mental error" 5. Generalization of points to line: statement of law as a mathemati- cal relation 6. Generalization to other systems, and to entirely different kinds of systems 7. Generalization of law in place, time, and circumstances 8. Generalization of law for all "gases" 9. Gonception of ideal gas to which law applies rigorously by defi- nition COLLIGATR^ RELATIONS AND SCIENTIFIC LAWS 123 Rarely would one find in practice any such systematic sequence of explici!: steps. Ordinarily these analyses are conducted unreflectingly, with implicit assumptions. But, however they are made, all these steps must be taken before Boyle's law can be pronounced. We may then wish to reconsider the major discontinuity, in the sequence fact-law-theory, that is commonly alleged to fall between law ("a description") and theory ("an explanation"). Belief in any such dis- continuity founders when, reviewing the progression leading up to Boyle's law, one recognizes the extreme difficulty (if not utter im- possibility) of detecting where observation ends and theoretical manipulation begins— where discovered fact gives way to im^ented abstraction. And we may indeed say of scientific laws generally what Royce has said of scientific theories— that they are . . . neither unbiased reports of the actual constitution of an external reality, nor yet arbitrary constructions of fancy. . . . They are con- structions molded, but not predetermined in their details, by ex- perience. We report facts; we let the facts speak; but we, as we in- vestigate, in the popular phrase, "talk back" to the facts. We inteipret as well as report. DENOTATIONS: IF INDIRECT, YET SOLIDLY ESTABLISHED For its functions as a predictive device, a colligative relation must, we saw earlier, involve only concepts having reasonably clean-cut denotations. Let us now assure ourselves that the situation remains unaltered even when the concepts are notably abstract, and their denotations are established only indirectly, with the aid of an elaborate computation apparently irreducibly "theoretical." Consider, as a representative example, a combined form of Kepler's first and second laws: a planet traverses an elliptic orbit, with the sun at one focus, at such a rate that the radial line sweeps out equal areas in equal times. We readily understand that a "planet" is a presumptive "body" seen as a point of light that moves, more or less irregularly, against the background of the "fixed stars." But now what are we to take as the denotations of "sun-focused elliptic orbits," etc.? A more pedestrian case will point the way. Grasping the appropriate conceptual denotations, we all combine certain observable terms in certain ways whenever we measure a "pressure." Just so with "sun-focused elliptic orbits." On the basis of various astronomical obser^^ations, we plot on paper an orbit for the 124 COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS earth. Everybody who attaches the same denotation to the concept of Keplerian orbit— that is, everybody who in this sense speaks the same language— will arrive at the same orbit. As with pressure, the orbit is computed in an agreed-upon way from observations on which all agree, too. Continuing in the same fashion, by a deter- minate set of mathematical manipulations we pass from observations of the positions of the planet in the sky to an orbit for it plotted on paper— much as we proceed from observations of a J-tube to a plot of pV versus p. And now to prediction! Given Boyle's law and the plot of pV versus p we readily derive predictions of what we should ( and ordinarily do) observe under specified conditions. Just so, given Kep- ler's laws and the plotted orbits, the inverse of the procedure by which past observations were rendered as "points" on paper yields us predictions of where in the sky a given planet will be observable at specified times in the future. These predictions are generally found quite respectably ( though not perfectly ) sound. Functioning as a typical colligative relation, the Keplerian laws seem to differ from the other relations so far considered only in the magnitude of the paper-and-pencil operation which intervenes be- tween observations made and observations predicted. But this mag- nitude may be no more than an incidental reflection of the state of scientific development. Thus years ago the derivation of densities ( from observed weights and volumes ) , speeds ( from observed times and distances ) , and pressures ( from the observed heights of mercury columns ) demanded paper-and-pencil operations today wholly elim- inated by the use of such devices as the hydrometer, speedometer, and Bourdon gage. From such devices we can read "density," "speed," and "pressure" directly, and can more directly predict what will so be read. V/ith primitive instrumentation an elaborate compu- tational operation may be required; with more elaborate instrumen- tation, on the other hand, little or no such operation may be needed even to use Kepler's laws. Provided the specifications of the paper- and-pencil operation are clearly understood and generally acknowl- edged—as they are in the case of Kepler's laws— the conceptual deno- tations remain firmly established in the one case as in the other. And by such anchoring colligative relations are secured from what might otherwise prove an irresistible drift into the status of conventions. Each and every colligative relation, sooner or later, is challenged by some datum or data at variance with it. Lest science dissolve into COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 125 chaos we must, Ste. -Claire Deville enjoins, rally to defend the threat- ened relation: Every time an exceptional fact has been discovered the first task, even the first duty, practically imposed on the man of science has been to make every effort to cause the fact to come under the common rule by means of an explanation which sometimes requires more work and reflection than the discovery itself. For the preservation of the rule we have abundant resources, as is shown in Chapter IX. Even if all these fail, we can almost always find an escape hatch in the assumption that the system in question is "nonideal." Thus, for example, we suppose that Kepler's laws fail of perfect accuracy because the motion of any given planet is "per- turbed" by its interaction with other planets. And blithely we hy- pothesize ideal systems in which no such complications exist, and to which the ideal law applies perfectly. How then can we ever bring ourselves to recognize as genuine the failure ( s ) of a colligative rela- tion in which we have confidence? If the colligative relation is made true, regardless of what the data indicate, is it not simply a conven- tion? Consider a relation that, at least superficially, well lends itself to such interpretation. Galileo's law of free fall. We express this law mathematically as: 5 ^ i gt'^. Here g is a proportionality constant that measurably de- pends only on the locale of the experiment, and t is the "elapsed time" during which a "freely falling body," starting from rest, traverses the "vertical distance" s. The denotations of s, g, and t seem adequately clear; but on many occasions the law may seem to fail, and fail badly. A sheet of paper or a feather do not fall in accordance with the law. A dead pigeon or a steel ball bearing, falling a short distance in air, conform to the law; but a live pigeon in air, or a steel ball bearing in oil, do not. Stipulate that a "freely falling body" can only be one falling in a vacuum, unopposed by viscous resistance? So doing we at once eliminate the discrepant cases just noted, but not all discrepant cases: even in vacuum charged objects moving in electromagnetic fields may not behave as "freely falling bodies." How then do we treat the law? Quite simply. We assert that it is invariably valid in the absence of "extraneous forces." When the re- lation is found to apply satisfactorily we declare that we have dealt with a "freely falling body." When it does not so apply we declare 126 COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS that, due to the action of some "extraneous force," the fall has not been "free." Thus safeguarded from all possibility of failure, the law is then nothing but a convention? Nonsense! We lack absolutely de- iiniti\'e criteria for the recognition in advance of a perfectly freely falling body— just as we do for an ideal lever or pure sulfur— but we do not lack all criteria. We need not then wait until after the fact to rush in with postulated extraneous forces that explain away cases to which Galileo's law should not have been applied in the first place. Instead, as Poincare observes, generally we can recognize, in the world of experience, those real systems sufficiently approximating the ideal systems to which the law applies by definition. It would do me no good to have given the name of free fall to falls which happen in conformity with Galileo's law, if I did not know that elsewhere, in such circumstances, the fall will be probably free or approximately free. That then is a law which may be true or false [read "efficient or inefficient"], but which does not reduce to a convention. Because we grasp the denotation of "freely falling body" the law is for us no "mere convention": by it we are invested with power to pre- dict what will be observed, and almost always ( though not invariably or precisely) this is just what is observed. Thus, substituting "rela- tion" for Poincare's first ambiguous use of "fact," we may say with him: . . . all the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not. Might one not still object that some colligative relations are so deeply and generally involved, both in our predictions and in all our observa- tions, that they can give rise to no recognizable predictive failures? Russell recalls what at one time seemed a whole group of such relations : Kant asserted that [Euclidean] geometi\' is based on an a priori intui- tion of space and that experience coukl never contradict it because space constitutes a part of our manner of perceiving the world. COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 127 A relation of Euclidean geometry. "The sum of the angles of a triangle is 180°." With straight lines defined by the paths of light rays, Gauss carefully carried through a large scale triangulation that showed this relation sound within the (narrow) limits of what could legitimately be regarded as experimental error. Kant notwith- standing, Gauss apparently considered that a failure of the relation would be recognizable. Even at the most fundamental level of our conception of space, a colligative relation would not then be so con- ventionalized as to be forever made "true." Indeed, once we agree on the denotations attaching to the conceptual entities of geometry, it becomes possible to prefer one geometry to another. In macrocosmic applications most physicists today prefer to Euclid's a Riemannian geometry in which the relation stated above is no more than an approximation. THE "PROOF" AND ENDURANCE OF COLLIGATIVE RELATIONS What is a legitimate generalization is not given us a priori, but al- ways we seek maximum deployment of each relation. Not content simply to interpolate, we also extrapolate; e.g., we extend a graphed relation into regions where we do not have, and perhaps cannot get, any experimental points whatever. Such extrapolations we recognize as potentially hazardous; for whenever experience takes us into new and unfamiliar realms, as Bridgman observes, . . . we must be prepared to find, and as a matter of fact we have often found, that we encounter phenomena of an entirely novel char- acter for which previous experience has given us no preparation. Yet, so profound is our confidence in the principle of continuity, we still remain bold enough to essay the most extreme extrapolations. At the very worst, we think, the relation will not blow up abruptly but fail only gradually— becoming a progressively poorer approximation. And, such is our faith in continuity, ^ven today we are sometimes lamentably slow to recognize the failure, even as approximations, of apparently plausible extrapolations. A theory may be harmful if it encourages us to forget that such extrapolations may prove fallible. But it is harmful, too, if it too strongly discourages generalization and extrapolation. Provided that we permit no relation to become permanently conventionalized, 128 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS maximum generalization of a relation is clearly the optimal policy. Certainly it is the policy best designed to bring to light any inade- quacies of the relation: "Gi\'e a man enough rope . . ." By generali- zation a relation is put to proof and, as we come sooner or later to recognize its limitations, its value to us is not impaired but very much enhanced. We say: "Two things cannot occupy the same space at the same time." At first sight this statement seems perfectly general and per- fectly reliable. But a great deal depends on how we understand the denotation of "things." We might eliminate some failures of the re- lation by excluding gases from "things"; with increase of pressure two gases can easily be crowded into the container formerly "occupied" by one of them. Some other failures we might eliminate by excluding liquids; still others, by excluding solids (in sodium sulfide the sodium and sulfur together occupy a volume less than that initially occupied by the sodium alone ) . Denying status as "things" to gases, liquids, and solids, out of fear of error we reduce the relation to naught. Actually, of course, we do nothing of the sort. Ordirmrilyy surely, volumes are additive— even in gaseous systems if they are nonreactive and held at constant temperature. Precisely as we recog- nize that the relation has a proper domain of application, it becomes a more reliable guide. Certainly an ill-founded colligative relation may be discarded, as erroneous or fortuitous; and certainly a relation may be extensively reformulated to acknowledge (or surpass) previously unrecognized limits to its applicability. But de Broglie quite correctly stresses that once a relation has been properly authenticated— . . . we have a definitely acquired result which no later speculation is able to undo. If it were not thus, no science would be possible. But it can very well be that, in the light of new experimental facts or of new theoretical conceptions, we are led to consider previously verified laws as being only approximate, that is to assume that, if the precision of the verification were indefinitelv increased, the laws would not be more exactly verified. This has happened many times in the course of the history of science. Thus the laws of geometrical optics— for ex- ample, the rectilinear propagation of light— although having been verified with precision and at first regarded as rigorously true, were seen to be only approximations that day when the phenomena of dif- fraction and the wave character of light were discovered. COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 129 Of course the laws of geometric optics retain all their wonted use- fulness throughout the domain in which they had earlier demon- strated their efficiency. What we have discovered is simply when and where not to apply them and, in Buhem's view, this is the kind of discovery we must expect to make ultimately about any scientific law. It is provisional because it represents the fact to which it applies with an approximation that physicists today judge to be sufficient but will some day cease to judge satisfactory. Such a law is always relative; not because it is true for one physicist and false for another, but be- cause the approximation it involves suffices for the use the first physicist wishes to make of it and does not suffice for the use the sec- ond wishes to make of it. After this we are forewarned not to use the law when we find our- selves in the position of the second physicist, but we continue to use it, as a limiting law, whenever we are in the position of the first. Dalton arrived at his law of partial pressures by way of a theory of the nature of gases we wholly reject, but the law survives. Man-made theories rise and fall; man-made concepts and their denotations prove highly mutable. But colligative relations have generally an immor- tality denied their conceptual formulations. How can tiiis be? Quite simply! The "invention" of human theoreticians who may well be wrong, once "discovered" the law exists independent of their wisdom or folly. By virtue of the denotations attaching to the conceptual terms in which it is formulated, the relation refers to observables that do not change when we change our ideas. Even if a law is given a new conceptual formulation, and new theoretic accommodation, what has correctly been said about the relation of observables by the older law must be said also by the newer. Thus, as Poincare remarks, a law can survive as the imperishable memorial of a theory perhaps long since passed away. At first glance it appears to us that theories last but a day and that ruins heap up on ruins. . . . But there is something in them which endures. If one of them has revealed to us a true relation, this relation has been acquired for all time. We shall find it again under a new cloak in the other theories which will reign successively in its place. The relation of metals. "Metals, however dissimilar in other re- spects, are generally hard, dense, malleable, ductile, lustrous, in- 130 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS soluble, destroyed by corrosive acids, etc." Apparently a definition of what we mean by "metals," this is a genuine colligative relation hav- ing the form of the sulfur relation: If a substance has several of the following properties . . . , theri probably it is a metal and has the other properties. This relation antedates the rise of systematic chem- istry, and survived for millennia without theoretic accommodation. Early in the 18th century the phlogiston theory proposed that metals be viewed as compound bodies with one component, phlogiston, common to all of them. The relation is then rationalized: the presence of the common component "explains" the occurrence of properties common to all. Toward the end of the 18th century, however, the ad\^ent of Lavoisier's new chemical theory destroyed the phlogiston theory. In Lavoisier's system all the metals are distinct elements, ap- parently having nothing in common. The relation is then no longer rationalized, but of course it survives the loss of its theoretic ac- commodation. For more than a century the relation of metals survived, amply useful but an enigma. Only in the last half century has it acquired what we conceive to be an enduring rationalization. Metals, we now suppose, do contain something in common: the company of labile electrons that constitute the metallic bond. Once again we "under- stand " the relation— indeed if we read "electrons" for "phlogiston" we understand it, and many other such relations, in much the same way they were "understood" in the phlogiston theory. But through all such clouds of theoretic speculation the relation itself looms up and endures solid as a rock. Colligative Relations not Wholly Independent of Theories So far in this chapter, and particularly in the last section, we have considered colligative relations as completely independent of their theoretic affiliations. This simplification facilitates discussion, but must not be pressed too far. Typically, a colligative relation is doubly connected. By the denotations of its conceptual terms it is linked widi experience; by its accommodation in a theory it is linked de- ductively to the postulates thereof. Either link may be formed first. The relation may first materialize as an empirical regularity, as did Boyle's law, and only subsequently acquire theoretic accommoda- COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 131 tion; or it may first appear as a theoretic deduction, as did in part Moseley's law, and only subsequently be shown to describe and pre- dict experience. Whichever link is formed first, we rest dissatisfied until both have been forged. Without the link to experience there is no colligative relation. Without the link to theory it remains "unra- tionalized" and, so, hard to "grasp" and manage with the manifold others of its kind. Even strikingly efficient colligative relations may then leave us dissatisfied as long as they remain uncorrelated by any theory. Evoking a determined effort to provide theoretic accommodation for all "purely empirical" relations, this healthy sense of dissatisfac- tion supplies an indispensable element in the internal dynamics that renders the scientific movement self-preservative. For science would surely and rapidly degenerate into natural history— into a chaotic and unmanageable welter of purely empirical relations— were it not for the characteristically strong and enduring endeavor that, in ma- ture sciences, has kept to an absolute minimum the number of these uncorrelated relations. A highly efficient relation, one that cannot possibly be dismissed as something that "just happens," will of course be used, preser\ed, and defended in any case. Thus, having lost its theoretic accommodation, the relation of metals survives until it finds a new one. And thus, though it had never any theoretic accommodation, the relation of inertial and gravitational masses survives during the more than two centuries that separated the work of Newton from that of Einstein. But in marginal cases our opinion of a given relation may be de- cisively influenced, in a way not so far indicated, by the extent to which it has (or has not) achieved theoretic accommodation. With faith in the principle of intelligibility, we believe that for all genuine relations such accommodation must be possible. Failing reasonably promptly to achieve accommodation of some relation of doubtful status, we will be very strongly tempted to dismiss it as an "accident" rather than permit the potentially disastrous accumulation of a mul- titude of unaccommodated relations. As is clearest in solar eclipses, the ratio of the diameters of moon and sun as seen from the earth is almost exactly 1:1. This is certainly a relation of observables, and was at one time held significant. But tliis relation, unattractive in its meagre generality, is also one we find tlieoretically inexplicable; and we simply, and probably quite prop- 132 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS erly, dismiss it as an "accident." As another example, consider how in the early 19th century Prout called attention to a relation (among chemical atomic weights) which, aside from a few notable excep- tions, seemed too frequently approximated to be dismissed as an "accident." No generally convincing theoretic explanation of this re- lation ha\dng been given by the end of the century, most scientists were then inclined to dismiss it. Today, having acquired a theoretic interpretation, the relation is again deemed of some significance. Following is an even more striking illustration of the influence of theories on the appraisal of laws that seem to hang on the borderline between significance and happenstance. The Bode-Titus law. In 1772 Titus announced the disco\'ery of a relation among die orbital radii of the six planets then known. The nature of this relation is displayed in tlie accompanying table, in which the radial distances are expressed in tenths of an astronomical A series term -\- 4 = Total Observed orbital radius 4 3.9 Mercury 3 7 7.2 Venus 6 10 10.0 Earth 12 16 15.2 Mars 24 28 48 52 52 Jupiter 96 100 95 Saturn 192 196 unit. The near equality of the numbers in die second and third col- umns is amply impressive. Is it significant? Bode, who thought it might be, set out to discover an as yet unobserved planet which, ac- cording to the relation, should be found between Mars and Jupiter. And to be sure Ceres and, subsequently, a multitude of other aster- oids (presumed to be the fragments of an extinct planet) were found, by various astronomers, in precisely the region predicted by the re- lation. This, taken together with the somewhat earlier discovery of Uranus (which has an orbital radius of 192, within 2% of that pre- dicted by the relation) seemed to place the Bode-Titus law beyond all doubt. Subsequently the tide turned. Two outer planets, Neptune and Pluto, were found with orbital radii diverging 20% and 100%, respec- COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 133 tively, from the values predicted by the Bode-Titus law. In the face of these setbacks, and still lacking theoretic justification, the law was then dismissed as "accidental" by many astronomers, though by others it was still held a genuine relation distorted by conjectural "secondary eflFects." Recently the postulates of a revised nebular hypothesis for the origin of the solar system seem to yield the Bode- Titus law as a deduction. If this promise is borne out, the law will no longer be dismissed as an "accident" and, conversely, its accommoda- tion will become one of the strongest bits of evidence for the new hypotliesis. Theory and law have here a powerful mutual interaction. CONNOTATIONS AS WELL AS DENOTATIONS A scientific theory may affect our appraisal of a given relation; con- versely, a relation may help us to the first conception of a theory. Beyond predictively efficient denotations, one then draws from the relation theoretically suggestive connotations. To be sure, these con- notations do not simply inhere in the colligative relation as such: only one, or a very few, of many who know the relation may fully grasp its implications. A Newton reads the connotation of Kepler's laws to be the action on planets of a sun-directed centripetal force; after more than two centuries an Einstein finds in the equivalence of gravitational and inertial masses a connotation previously grasped by no one. In the gifted mind even a crude or fragmentary relation may suffice to spark the flash of insight. But always the connotations of a relation will be most readily grasped when, beyond a discovery, it is also an optimal invention, i.e., cast in an abstract form well suited to theoretic consideration. We saw that by the time we attain even as simple a relation as Boyle's law, we have already traversed a great, if not the greater, part of the road from "concrete fact" to "abstract theory." With the ac- quisition of Boyle's law a chaos is reduced to at least comparative order. Moreover, the law provides the reference standard that first permits us to recognize, and measure, the departure of real gases from ideal behavior. The theoretic connotations of these systematic deviations thus first become accessible only dirough the mediation of the abstract law that contributes to the organization of even the "imperfections" of which it renders no account. Consider now a re- lation of a still more abstract sort. Moseleys law. Let Z represent the "atomic number" of the element 134 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS that, under specified conditions, emits light of "wavelength" A: for the Ka X-ray line we can then write A (Z — 1)- = 1.21 X 10~^. This seems so purely theoretical, so abstract, that our first obligation is to show that it can function as a coUigative relation. By 1869 the concept "relative atomic weight" had acquired a rea- sonably defined denotation. Given certain chemical data, one could compute "relative atomic weights"; given atomic weights, one could predict certain chemical data. Beginning in 1869 Mendeleev, Meyer, and others developed a classificatory chart in which, with a few specific inversions, the chemical elements are arranged in order of increasing atomic weight. The "atomic number" of an element is simply the ordinal number expressing its position in the sequence of the perfected classification. Giving exceedingly compact expression to a great many relations among measurable properties of the ele- ments, Mendeleev's "periodic table" is in part "theoretical," e.g., in its implicit acceptance of the Daltonian atomic theory; and it has very pronounced connotations, e.g., the nonultimacy of the chemical "ele- ments." But through it the concept of "atomic number" acquires a clear enough denotation. Given certain measurements made on an element and its compounds, I can assign it an ordinal number and a place in the chart; given the chart and the number of some element, I can state the probable outcome of certain experiments not before made on it. Turning now to the "wavelength of light," in the X-ray region a denotation is fairly readily established with an instrument like the crystal reflection spectrograph. The "wavelength" of light passed into the instrument is calculated in a specified way from the location(s) at which blackening is produced on a photographic plate that forms part of the spectograph. An immense amount of theoretical work un- derlies the instrument and the calculation. But, once we accept this denotation, the concept has a perfectly clear linkage with experience. \Mien I have seen the plate I can assign a definite wavelength (a) to the light which produced a black mark on it; and when I predict a certain \'alue of A I say where on the plate I expect to see a black mark. Now we can come to grips with Moseley's law. We "excite" an element under the specified conditions and, passing the light so generated into our spectrograph, we find a determinate relation be- tween the ordinal number of that element in the periodic classifica- COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 135 Hon and the position of one identifiable mark on the photographic plate. Were we to decide that matter is non-atomic, and light non- undulatory, presumably our formulation of this relation would no longer be given in terms of "atomic number" and "wavelength." But even such a drastic upheaval could not alter the substance of this re- lation: between the position of the element in the periodic classifica- tion and the position of the mark on the photographic plate there is an indissoluble connection. A physicist might rightly object that this is a preposterous way to put Moseley's law— not wrong but grotesquely insufficient. Dwelling on its denotations, we have wholly ignored the law's weighty theo- retical connotations. Reading the abstract law in the light of the Rutherford-Bohr theory of the atom, we discover the basis for a pro- found rationalization of Mendeleev's "purely empirical" classifica- tion. Z we identify as both the "number of protons" in the "atomic nucleus" and the "number of electrons" attendant thereto. One ap- parent failure of Moseley's law was then taken to connote the prob- able occurrence of an undiscovered element. That element (haf- nium) was indeed discovered some years later, when excitation of a sample in which its presence was suspected did yield a spectro- graphic plate with a spot corresponding to the expected atomic num- ber. This pretty piece of work oflFers a vivid illustration of the inter- play of the connotation and denotation of an abstract law. The Mendelian laws. The following will serve us as a particular example: "In monohybridization experiments conducted on a large scale, in which dissimilar parents are crossed and the first filial gen- eration is intercrossed, three-fourths of the members of the second filial generation will exhibit the dominant forms of the diflFerentiating characteristic." Let us assume what is not at once evident: that the denotations of the many conceptual terms here involved can be made adequately clear. The need for the qualification "conducted on a large scale" at once signifies that we have here to do with a new ( statistical ) kind of relation unlike any so far discussed. No relation furnishes absolutely reliable prediction of a particular event in a particular system. However, when dealing with relations of the kind considered earlier, we find that predictive reliability can be increased without apparent limit— by improving the accuracy with which we determine the conditions defining the state of the system, and/or by broadening our definition of state to take account of a 136 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS greater number of initial conditions. With a statistical relation, on the other hand, we may find that no such increase in the number of spec- ifications of the state of the particular system suffices to increase the reliability of our prediction of the one particular event. Dealing with a statistical relation, we find only one way to improve our perform- ance: we must limit our predictions to comparatively large numbers of events, and the improvement in predictive reliability is in pro- portion to the increase in the number of events. We are powerless to predict the result of a single throw of a well-balanced die, but we predict with confidence that in a long series of throws each of the faces will turn up very nearly one-sixth of the time. Often a statistical relation leaves us profoundly unsatisfied: for example, each man seeks one specific item of prediction no statisti- cal table of life expectancies can ever yield him. In exactly the same way, the Mendelian laws leave undetermined whether a given seed —with a given genetic heritage— will produce a white or a pink flower. But when we work with large numbers of seeds the laws permit us to make excellent predictions of the ratio of white and pink flowers. The table shows Mendel's own results for seven sets of monohybridizations conducted with sweet peas. Differentiating Second Filial Characteristic Generation DOMINANTS RECESSIVES „ ^. DOM. Ratio REG. Form of seed 5474 smooth 1850 wrinkled 2.96 : 1 Color of seed coat 6022 yellow 2001 green 3.01 : 1 Length of stem 787 tall 277 dwarf 2.84 : 1 Color of flowers 705 colored 224 white 3.15 : 1 Position of flowers 651 axial 207 teiTninal 3.14 : 1 Form of pods 882 inflated 299 constricted 2.95 : 1 Color of unripe pods 428 green 152 yellow 2.82 : 1 Total 14949 5010 2.98 : 1 The relation so clearly evident in the table is one of very broad generality. It applies with equal facility to a great number of differ- entiating characteristics displayed by a great variety of plants and animals; and it furnishes a secure predictive guide of profound im- portance to plant hybridists and others who work on a large scale. COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 137 But at this point our chief concern is with the MendeHan laws' con- notations. These are, of course, enormous: from them derive the foundation blocks of classical genetics. And even the predictive fail- ures of the Mendelian laws, in other than a statistical sense, are rich in connotations, e.g., as regards the linkage of genes in chromosomes. COLLIGATIVE RELATIONS IN OTHER GUISES Everything called a scientific law is not necessarily a colligative re- lation; everything serving as a colligative relation is not necessarily restricted to the function of a more or less efficient predictive device. The relation may have connotations that, as we have just seen, sup- ply suggestive pointers for theory construction. Having achieved theoretical accommodation, the relation acquires a new footing in the heuristic apparatus, as something entailed by a theory there estab- lished. There, too, it may appear in generalized form not as deduc- tion from postulates but as in itself a postulate; e.g., the conservation of energy as first conceived by Joule is a colligative relation before it becomes the first principle of thermodynamics. In the heuristic ap- paratus again the law may appear as a substantive principle, taken for granted and temporarily conventionalized while v/e use it in our study of other laws. Yet again, a law may be involved in establishing the denotations, and in particular the alternate "equivalent " denota- tions, of an indicative concept; e.g., Boyle's law becomes part of the definition whenever we rely on a McLeod gauge to measure a "pres- sure" too small to be measured with an ordinary manometer. Apart from any status as colligative relation, a scientific law may thus as- sume manifold guises and functions, some of which we shall ex- amine later. CHAPTER VI Empirical Tools and Empincism ciENCE purports to speak of the world of experience; the devices of empiricism safeguard its contact with that world. To be sure, not all scientific concepts are linked to obser\ables with exactly equal clarity and directness. Thus, for ex- ample, many of the ( explicati\'e ) concepts figuring in the postulates of highly abstract theories will be so linked only indirectly— by way of colligative relations derivative from those postulates. Nevertheless, among scientific concepts generally, we find a remarkable reconcilia- tion, of great abstraction and great clarity of denotation, highly char- acteristic of science— because completely unparalleled in common sense, philosophy, mathematics, or any other human endeavor. At the most fundamental level this union develops from the power of the em- pirical devices deployed by scientists: their special materials and specimens, procedures and techniques, instruments and equipment. INSTRUMENTS In Chapter II we saw how instruments may facilitate the concur- rence of multiple observers of the "same thing." You and I will agree on the magnitude of some particular "light intensity" as soon as we agree to adopt a denotation that points us toward a straightforward observable, such as the scale reading of a light meter. Even a notably abstract scientific concept may thus acquire a clarity of denotation 138 EMPIRICAL TOOLS AND EMPIRICISM 139 immeasurably superior to that of the more "obvious" {i.e., famiHar) concepts of common sense. The sophisticated concept of X-ray wavelength is invested with a comparatively unequivocal denota- tion, established around such a device as the crystal diflFraction spectrometer, and "nuclear spin" one established around the NMR spectrometer. Of course, the situation is not completely uncompli- cated: beyond the instrument itself we have also to specify the proto- col for its "proper" operation. The operating protocol. Need any appreciable procedural specifi- cation be given in the simplest of cases, e.g., an accurate measure- ment of "length" with a meter stick? Yes— at least two considerations demand attention. First: If the stick and the object to be measured are not in the same plane, then at oblique angles of view we may read from the meter stick substantially erroneous lengths for the object. Grasping this possibility of (parallactic) error, we easily avoid it— perhaps by bringing into play another instrument. Thus a cathetometer can assure us of a perpendicular line of sight and, by a suitable arrange- ment of lenses, allows us to cast the object and the comparison scale in the same focal plane. But even then we do not attain a purely instrumental denotation: "proper" operation of the cathetometer it- self demands a protocol specifying a considerable variety of pro- cedural details. And so on. Second: The meter scale has a length of one meter only at the specified temperature at which it was graduated. Often, however, we seek an accurate result from measurements we must make at some other temperature. Then, using what we regard as a well- established relation between the temperature and the length of the scale, we calculate and report, as the accurate length of the object, a "corrected" value more or less different from what we actually read from the scale. That such corrections must be made, and the colliga- tive relations with which they are to^ be made, we learn from the protocol thus required to fill out the denotation of "length" even after we have agreed to center that denotation on an instrument, the meter stick. The need for an auxiliary protocol is perfectly general: "length" is an atypical case only in the comparative simplicity of this prescrip- tion. Consider the multiplication of complexities in an instance only slightly less simple. Suppose that, for some liquid, we wish to meas- 140 EMPIRICAL TOOLS AND EMPIRICISM ure accurately the "boiling temperature"— and adopt a thermometer as the instrumental core of denotation. Do we then simply read oflF the temperature shown by a thermometer immersed in the boiling liquid? Not at all! We find that, due to "superheating," a boiling liquid stands at a temperature irreproducibly higher than that of its vapor. We then specify use of a "boiling point apparatus," in which we arrange to measure the vapor temperature, following a procedure designed to minimize superheating of that \^apor. We have now an instrument, an apparatus, and a procedure— but at most only part of the procedure: the actual thermometer readings will require "cor- rection." Using a well-authenticated colligative relation, we make a "stem correction" to allow for the fact that, although the mercury in the thermometer bulb is at the temperature of the saturated vapor, the mercury in the stem is ordinarily at some other, lower, tempera- ture. Another colligative relation warns us that boiling temperature is a function of pressure: we must then correct the thermometer reading to allow for the "barometric pressure." But now, to establish this last, we will require still other corrections. One such correction term is a function of the temperature of the barometer, which af- fects both the density of the mercury and the length of the measur- ing scale; another in\'olves the latitude and elevation of the labora- tory, which aflFects the gravitational acceleration, and hence the formula for the conversion of barometric heights to barometric pres- sures. And so on. Without going any further, we see clearly that establishment of the denotation of "boiling temperature" requires a procedural protocol of substantial complexity. How grave are the risks that the scientist will be led seriously astray by the element of human subjectivity irreducibly involved whenever, by making "corrections," he ventures to "tamper with the facts"? The relations used in making corrections have been inde- pendently checked many times o\'er. Moreover, in some crucial cases we have made more elaborate experiments in which the need for many if not most corrections is eliminated. In these cases we have generally arrived at the very same results obtained much more con- veniently in simpler experiments in\'olving multiple corrections. A second point: corrections may enhance predictive reliability. For example, Dulong and Petit's law we now know to be only a crude approximation. We find it a better approximation when we use as specific heats not the values actually measured, ordinarily at con- EMPIRICAL TOOLS AND EMPIRICISM 141 stant pressure, but corrected values hypothetically representing the results of constant- volume experiments. Conversely, when we make due allowance for this correction, Dulong and Petit's law becomes able to furnish more reliable predictions of what we will observe in new cases, cases not before examined. Third, and perhaps most im- portant: however less objective they may or may not be, the corrected values are certainly very much more impersonal. Different scientists measuring the "same thing" under different conditions observe differ- ent raw values, which each subjects to the corrections appropriate to his own experimental conditions. Only at the level of the corrected values is general agreement reached, and the attainment of such agreement cannot but strengthen our confidence in the correction terms. For there is nothing "artificial" or contrived about this impres- sive concordance: the correction formulae involved in the operating protocol are established before we know the actual values of the measurements reduced with their aid to agreement. No matter how the concurrence of observers is facilitated by use of an instrument, the instrument always constitutes at most the core of denotation. We never achieve completely explicit categorical denota- tions. The denotation always must be filled out with an operating protocol involving words and symbols for proper understanding of which we must, ultimately, rely at least in part on the "good judg- ment" of the investigator. He is trained to such judgment by educa- tion, by the editorial policies of his journals, and by the example of distinguished colleagues. So pervasive are these influences of the international community of organized science that ordinarily tve need not even state the auxiliary protocol that completes an instru- mental denotation. Ordinarily we safely assume that protocol "under- stood" by all competent and responsible scientists— for of course it is simply shaped to take account of colligative relations that find a place in the theories known and accepted by all. In using this par- ticular instrument, I design my experiment and correct its results in a way determined by my awareness of the effect of other variables on the parameter I seek to measure. Thus, for example, knowing the rela- tion between barometric pressure and boiling temperature, all sci- entists will duly allow for the first when determining the second. The denotative uncertainty introduced by the necessary, if wholly tacit, involvement of an operating protocol is, then, ordinarily negligible. Pointer readings. Still yearning to establish completely categorical 142 EMPIRICAL TOOLS AND EMPIRICISM denotations, we may think to do so with the aid of more elaborate "self-sufficient" instruments. Imagine a device in which insertion of a sample at one end is followed by automatic production at the other of a pointer reading giving "the result." The operating procedure is then reduced to plugging in the instrument and inserting the sample; the need for corrections is eliminated because the instrument itself provides stabilization of the conditions of measurement, or contains compensatory mechanisms for making the corrections automatically; and the result given as a pointer reading seems to be the non plus ultra of denotative clarity. Have we then at last arrived at a fully categorical denotation? Alas, we have not. We now require a protocol for detecting and re- pairing malfunction of the "self-sufficient" instrument. Far from elim- inating all auxiliary protocols, we have simply substituted a new one for the old— and the new one is ordinarily much the more difficult. This protocol cannot safely be left to the "good judgment" of the in- vestigator. Through an elaborate instruction manual, the manufac- turer of a complex instrument supplies an operating protocol as ex- plicit as he can make it and, beyond this, he must make available also the services of the specialists required to rectify malfunctions of the instrument. In the long term, then, such an instrument may make demands on human judgment not less but greater than those imposed in use of simpler devices. Through instruments we may first gain access to realms of ex- perience otherwise outside our ken. The microscope "amplifies," the NMR spectrometer "com^erts," hypothetical signals to which our senses are dead into signals to which they are very much dlive. In addition, the automatic pointer-reading instrument may offer great advantages in speed, in sensitivity, and in simplicity of routine op- eration—which can often be entrusted to unskilled technicians. These are immense gains, justifying every effort to achieve them. But, as Bernard well recognized long ago, the introduction of elaborate in- struments where they are not needed is positively disadvantageous. . . . we need to learn that the more complicated the instrument, the more sources of error does it create. Experimenters do not grow great by the number and complexity of instruments. Quite the contrary. The great experimenters, Berzelius and Spallanzani [and Bernard, Pasteur, and Rutherford], made great discoveries by means of simple instruments. EMPIRICAL TOOLS AND EMPIRICISM 143 Even today in certain applications the human eye offers us discrim- inatory capacities unmatched by any instrument or combination of instruments. Why should we hesitate to make the fullest possible use of the sensory faculties with which we are endowed? A vain lust- ing after reduction to instrumental measurements in general, and to pointer readings in particular, seems to rest on complete misconcep- tion of what we gain with their aid. Not categorical denotation, not the complete elimination of human judgment, not "objectivity." The fundamental achievement is this: denotative clarity is enormously enhanced by adoption of an "external" rather than an "internal" standard of reference. Though instruments and pointer readings are generally sufficient to ensure this great advance, they are not always necessary to ensure it. THE EXTERNAL STANDARD OF REFERENCE How shall I establish the denotation of "weight"? That denotation remains highly uncertain for just so long as it is "fixed" only by an internal standard, i.e., the sense of muscular strain felt in lifting. In that case I have always to remember what it felt like to lift other "weights," and my memory is not wholly reliable. Nor are my sensa- tions unaffected by my recent personal history: things may well seem heavier when I am tired. My own estimates of the weight of a given object vary from time to time, and disagree with the estimates made by other persons who rely on their internal standards. The self-consistency of my own reports of weight, and the concur- rence of different reporters, are both enormously improved when we all agree to adopt one particular set of standard weights. "Weighing" is then reduced to making a comparison between one or more of these and the unknown weight. I may, for example, seek to make some combination of standard weights that "feels the same" when it is picked up immediately before or after the unknown weight— the magnitude of which can then be expressed in terms of the stand- ard ( s ) . As already indicated ( p. 51 ) , I can even go somewhat further. Making comparison not through trials by lifting but with an equal- arm balance, I exclude secondary complications that might arise when unknown and standard differ sharply in shape, texture, etc. In this way the role of human judgment, though never completely elim- inated, is still further diminished and simplified— while at the same time we acquire a delicacy of discrimination wholly unknown to the 144 EMPIRICAL TOOLS AND EMPIRICISM unaided senses. To go still furdier— to an elaborate, automatic, pointer-reading device— may win us gains in sensitivity and conven- ience, but can afford us no further fundamental gain in clarity of denotation. Consider the analogous case of "temperature." Our thermal sensi- bility, quite limited at best, is also notoriously unreliable; it is, for example, heavily dependent on the recent history of the sensing surface. The denotation of temperature is immensely clarified and refined with the aid of a thermometer. At first sight this instrument (unlike the equal-ann balance) seems to involve no comparison with an external standard. The balance is a null-reading instrument in- volving an explicit comparison, but scale-reading instruments like the thermometer normally involve implicit comparisons. The scale is constructed by comparison ( direct, indirect, or by way of colligati^'e relations) with certain external standards. Thus whenever I read a temperature from a thermometer scale, I make an implicit compari- son with, say, tlie temperatures of melting ice and boiling water. This state of affairs remains unaltered when the instrument is more deeply involved, in amplifying and/or converting an otherwise undetectable signal. An ohmeter gives a direct pointer reading of "resistance," but ultimately it yields a comparison of this resistance with that of a particular spool of manganin wire. Denotations depending on "absolute" judgments— that is, judg- ments made relative to more or less uncertain internal standards— suf- fice for many purposes, e.g., counting. For some purposes, e.g., psy- chiatric diagnosis, they may well be indispensable. But, in general, denotations are most firmly established when we need make only relative judgments, i.e., comparisons with external standards. Thus, for example, the human eye is thoroughly ineffectual in judging the absolute intensity of illumination, but highly adept at distinguishing small differences in intensities that occur, or can be brought together, in the same visual field. Given one "standard candle," comparisons founded on use of even so primitive a device as the Bunsen grease- spot photometer in\'est "light intensity" with a well-defined denota- tion. Hebb's comment amply suggests that we here encounter no trivial shortcoming of optic physiology but, rather, a general psy- chological phenomenon: Man or animal tends to perceive relative rather than absolute in- tensity, extent, or frequency. One can readily train an animal to EMPIRICAL TOOLS AND EMPIRICISM 145 choose the larger of two surfaces; it is extraordinarily hard to get him to choose a particular size, except when differences are very great. Just so, many of us easily detect a flat note in a continuing melody, but very few of us possess absolute pitch. At one extreme of the spectrum of denotative clarity, the concepts of physics most often have precise, instrumentally established denota- tions. At the other extreme, few instruments are deployed in psy- chiatry, but the notorious nebulosity of its fundamental concepts stems ultimately from an almost complete (and unavoidable?) fail- ure to create an acceptable body of external standards of reference. In the broad spectrum of denotative clarity the position of a given concept is then primarily correlated with the availability of such standards, and only secondarily with the availability of the instru- ments that make comparisons. There is no magic in the instrument as such. Where no external standard exists, no instrument can help us; and, however convenient in practice, the instrument is wholly super- fluous in principle where we do not need it to make adequate comparisons. ''Things" as standards. A standard weight is a reference "thing" used in quantitative comparisons, but in many other cases only qualitative comparison is required, or even meaningful. Wishing to know whether a given specimen "belongs" to some previously de- scribed species or subspecies, the taxonomist supplements his mental image of the possibilities by making point-by-point comparisons be- tween his specimen and tliose available in museum collections. Due to the intrinsic variability of living organisms, high-precision quanti- tative comparisons are here unlikely to be helpful. The taxonomist must then exercise his judgment within a penumbra of uncertainty the extent of which is, however, very much reduced by the avail- ability of reference "things." Sometimes almost purely qualitative comparison is completely definitive. Consider an organic chemist who wishes to know whether a synthetic compound (X) in his test tube is or is not a certain previously isolated natural product (P). With the aid of elaborate in- struments he can compare various properties of X and P, but actually he regards as most definitive a procedure involving only the simplest of instruments, and not even requiring quantitative measurements. This is the technique of the "mixed melting point." Ha\'ing found 146 EMPIRICAL TOOLS AND EMPIRICISM that X and P melt at the same temperature, the chemist prepares a mixture of X and P and determines its melting point. If this is un- changed he concludes that X and P are identical. To determine the melting points a thermometer is ordinarily used, but this is super- fluous in principle. The chemist need only prepare three similar tiibes containing respectively X, P, and a mixture of X and P. If he finds that they all melt at very nearly the same time in a slowly-heated and well-stirred "melting point bath," he then feels well justified in iden- tifying X as a specimen of P. With or without use of the thermometer, the denotation of the concept of P is firmly established by the one reference specimen of P and the technique of mixed melting point. Techniques as standards. Even in the absence of a reference "thing," a technique or group of techniques can constitute an ade- quate external standard— as when Lavoisier established the denota- tion of "element" as follows : The last term at which analysis arrives, all the substances which we have as yet been unable to decompose by any means, are elements as far as we are concerned. What is to pass as an element is here fixed in terms of the techniques for analysis available at the time. What is taken to be an element may thus become a function of time, but at any one time we well know what does pass as an element. Invented in antiquity, the concept "element" developed its full usefulness only after Lavoisier thus pro- vided a firm link between the abstract concept and the world of ex- perience. Often deceptively simple in retrospect, the forging of such a link can, as here, represent a major step forward. A similar if less spectacular advance was wrought by Proust, who first suggested that techniques of analysis can serve also to establish the denotation of the concept "compound": a material is a compound if, wherever and however it is obtained, analysis finds it to contain its component ele- ments in an invariant proportion. Like all other denotations, those established in terms of techniques fall short of absolute clarity. Ordinarily the modern chemist still chooses to treat as an "element" a material that analysis, broadly conceived, finds resolvable into distinct (isotopic) components; and as a "compound," a material slightly variable in composition for this and other reasons. These usages present no real problems, but borderline cases severely strain the denotative precision of some EMPIRICAL TOOLS AND EMPIRICISM 147 Other concepts. Asked to decide whether a given specimen is a "hving organism," the microbiologist apphes various culturing techniques to obtain results that ordinarily support an unequivocal answer. But when the crystalline viruses were first encountered, a latent indefi- niteness of the denotation of "living organism" became quite pain- fully manifest. Colligative relations as standards. Although we have discussed separately different species of external standards, most typically what we loork with is a mixed standard. Beyond "things" and tech- niques a mixed standard involves colligative relations, which may in- deed constitute the ultimate foundation of the entire standard. If an instrument of comparison is used, such relations determine its design and operating protocol. "Things" accepted as standards are selected with a view to the relations in which they figure, and techniques ac- cepted as standards are shaped by such relations. Ultimately the denotation of "living organism" is established on the group of colliga- tive relations expressing certain uniformities in the behavior of "living organisms" in various circumstances. (Perhaps this is the useful sense of the otherwise completely circular "law of definite proportions": A compound contains its component elements in an invariant pro- portion. ) Ordinarily I can safely rely on my judgment, i.e., on an internal standard, in deciding that a particular object is a "lever" or a par- ticular spot of light is a "planet." But in doubtful cases a suitable re- lation can by itself constitute an exemplary external standard. One or a very few trials suflBce to show whether the object does act in accordance with the law of the lever; a relatively small number of observations suffice to show whether the spot of light moves in accord- ance with Kepler's first and second laws. Assuming affirmative indica- tions, we identify the object as a lever and the light as a planet. Serving thus as reference standards, the relations are not in any sense "lost" to us: with them we can now go on to hazard predictions be- yond what we have observed. PRIMARY AND SECONDARY DENOTATIONS There is only one standard kilogram, but many kilogram (and sub- kilogram) "weights" are actively in use. All these are, ultimately, referred to the mass of a particular platinum cylinder kept in the vaults of the International Bureau of Weights and Measures, near 148 EMPIRICAL TOOLS AND EMPIRICISM Paris. With this standard are compared the kilogram masses main- tained by the various national bureaus of weights and measures; with these masses, in turn, are compared the standards used by commer- cial manufacturers of "weights"; and so on in a kind of apostolic succession. Even as we thus multiply our standards, we multiply our instruments, taking care to assure their mutual consistency by simi- lar cross-comparisons. Generally we venture much further still, bring- ing into play entirely new kinds of instruments that yield us powerful new secondary denotations. Calibration. Taking as example the concept "electric charge," I simplify by considering only comparatively large charges passed in D.C. systems. The fundamental unit, the coulomb, is defined (tempo- rarily) as the charge which deposits 0.00112 gram of metallic silver when passed under specified conditions through a specified device: the silver coulometer. Smaller or larger charges are measured as pro- portionately smaller or larger deposits of silver. The specifications of the apparatus and procedure are so clear and complete that the con- cept "electric charge" here acquires all the unequi\'Ocality one hopes to find conveyed by a well-contrived primary denotation. But— as everybody who has used a silver coulometer will testify— operation of the device demands the expenditiire of a good deal of time, effort, and irritation. The silver coulometer is not a highly practical device. Often we prefer to use in its place an instrument as different as, say, some type of integrating galvanometer in which charge is determined by the measurable extent of the mechanical displacements its passage produces. A sophisticated electromagnetic theory may be required first to suggest the possibility of such an instrument. But entangle- ment of this theory with the denotation of "charge" is readily avoided —by the simple expedient of calibration. We connect an integrator-galvanometer "in series" with a silver coulometer, so that the "same charge" passes through both. The ob- servable correlation of the results yielded by the coulometer and by the galvanometer supplies the sought-for calibration of that particu- lar galvanometer. From the galvanometric measurement we can then calculate the result that would be given by the less convenient coulometric measurements we need now no longer undertake. Con- tinuing our studies, we arrive ultimately at a general result of still greater value. We find that the values yielded by the coulometer cor- relate with the readings afforded by all galvanometers of the same EMPIRICAL TOOLS AND EMPIRICISM 149 type, through relations involving only certain independently deter- minable characteristics of the galvanometer, e.g., the dimensions, ar- rangement, and number of windings in its coil, the strength of its magnet, the disposition of its mechanical system, and so forth. With these colligative relations in hand we can now establish an inde- pendent secondary denotation for "electric charge." That is, making no reference to silver coulometers, we can build integrating galva- nometers and graduate their scales to read directly and accurately in coulombs. Extrapolation. The way now lies open to a gain far weightier than mere operational convenience. Each "equivalent" denotation reflects the existence of one or more colligative relations joining different sets of data. Throughout the broad range in which galvanometric and coulometric results can be compared, we find them well correlated by relations we then dare extrapolate to situations in which only galvanometric measurements can be made. Provisionally conven- tionalizing the relations— incorporating them in my definition of charge— I graduate my galvanometer dial to read "electric charge" on a scale I assume everywhere consistent with that originally estab- lished with the coulometer. I can now extend the application of that concept to systems in which the charges are too large, too small, or too abruptly delivered to be measured with the silver coulometer. All colligative relations somewhere fail of reliability. With the ac- commodation of the relations in theories, we may acquire some help- ful indications. We may thus be warned not to extend "equivalent" denotations in circumstances demanding extrapolations that would run counter to approximations used in the theoretical derivation of the relations of equivalence (see p. 59). Our theories may encourage us to risk certain other extrapolations, but some element of risk per- sistently remains. We accept that risk to make this notable gain: im- portant concepts may thus be made available for use far beyond the domains of their original applications. Consider the case of "temperature." Today our scale of tempera- tures is pinned to certain fixed points established with the aid of gas thermometers. Applying certain corrections, suggested by theoretical (thermodynamic) considerations, we use such thermometers through- out the range from ca. — 265°C to ca. +1200°C. For the sake of con- venience, we accept also many alternate denotations established with such devices as liquid-in-glass thermometers, resistance ther- 150 EMPIRICAL TOOLS AND EMPIRICISM mometers, thermocouples, and the hke. Cahbrating these at the fixed points, we contrive to assure the equivalence of the alternate denota- tions of "temperature." How shall we extend the range of application of the concept "temperature"? The extension above 1200° C presents no serious problems. Here we use a radiation pyrometer diat can be calibrated, at fixed points established with the gas thermometer, over a range of several hundred degrees. We then extrapolate the relation between pyrometric and thermometric readings into the range where only pyrometric measurements are possible. This extrapolation proves ex- tremely useful and generally satisfactory; i.e., the data so obtained "make sense." But now consider the extension below ca. — 265 °C. As before, we extrapolate a relation, between the readings of some de- vice and the readings of the gas thermometer, into the range in which only the new device can be used. Here a drastically different situation materializes: most of the attempted extrapolations prove un- satisfactory, and we easily recognize their inadequacy. That is, the "temperatures" so secured "don't make sense." We encounter discon- tinuities, inversions, and anomalies difficult to explain save on the assumption tliat most of the extrapolations were ill advised. Fortu- nately some extrapolations survive this test, and with them we make a deep penetration of the region close to absolute zero. Many such cases give abundant evidence that in die long term any failures of denotative equivalence, due to unsound extrapolations of the relations of equivalence, will become recognizable and rectifiable. Thus even a primary denotation may be called into question. Today we adopt the gas thermometer to establish a scale of temperature we consider far superior to those of the liquid-in-glass thermometers originally primary only as a matter of historical accident. A com- paratively recent revision of the primary denotation of "electric charge" now pins it to an electromechanical device (distantly re- lated to an integrator-galvanometer) instead of the silver coulom- eter. What is primary and what is secondary may thus change with time, and often the distinction loses its clarity. To be sure ii—i1^side the range in which both primary and secondary denotations are deploy- able— we encounter some inconsistency between the measurements they yield, we will adjust the relation between them to bring the second into conformity with the first. But, meeting contradictions and anomalies outside the range in which direct comparison of suppos- EMPIRICAL TOOLS AND EMPIRICISM 151 edly equivalent denotations is possible, we are thrown back on our own appraisals of the reliability of different extrapolations. We seek then to readjust the denotations we have assigned to our concepts until once again the data collected do "make sense." Proceeding so we do not wholly give way to human caprice: to "make sense" of ex- perience is, after all, the business of science. Nor do we in any way turn our backs on "hard reality": readjusting our denotations, we simply find that we can make sense of the data collected in one way and not in another. And always, whatever the risks that in future we may have further to reconstruct the denotations of our indicative concepts, we hold firm that indispensable bridge that science ever maintains between the conceptual realm and the perceptual realm— however vertiginous may become the first, and however extended the second. Observation and Experiment Epistemologically the distinction between observation and experi- ment is a thin one. However complicated the equipment we bring to bear in the laboratory, the ultimate operation in any experiment is always the making of one or more observations. The ancient astrono- mer, making naked-eye observations of the sky, and the modern phys- icist, taking "pointer readings" from his "counter," are engaged in epistemologically equivalent undertakings. However, the important point is not this trivial equivalence but the enormous advancement of our conceptual powers produced when we pass from observation to experiment. In observation we can note only what occurs in the "natural course of events." Passing to experiment, we can for the first time observe what happens in a multitude of other circumstances we ourselves contrive. Though these conditions be "unnatural," the data we obtain may notably advance our understanding of what happens "naturally." Thus we learn much about the normal function of the endocrine glands by studying the abnormal conditions of organisms from which the glands have been removed by surgery. Experiment cannot produce, but sometimes practically evokes, the concepts we alone can create. Thus movement observed in nature, rapidly suppressed by frictional effects, suggested the thought that rest is the "natural state" of bodies. Had it been possible to observe movement in the laboratory under conditions that minimize fric- 152 EMPIRICAL TOOLS AND EMPIRICISM tional effects, the creation of the modern (Newtonian) concept of in- ertia might not have been so long deferred. Today such laboratory experiments help even the novice to a firm grip on the concept which, without the aid of experiment, was not fully grasped even by Galileo. Of course the creation of this concept long antedated the laboratory production of any approximation to inertial motion. But sometimes simple laboratory experiences have clearly furnished powerful and suggestive stimuli to concept-creation. Boyle's conception of a "spring of the air"— a springiness later quantitatively expressed in Boyle's law— is prompted by the physical sensations felt when operat- ing a laboratory vacuum pump. Faraday's concept of "lines of force" seems fairly to leap from the pattern observed in die distribution of iron filings around a magnet and, more generally. Born remarks that: The revolutionary conception which distinguished electrodynamics from classical mechanics is that of the field. One can see in Faraday's work how it sprang from his observations of dielectric, paramagnetic and diamagnetic properties; . . . Such clean-cut cases are presumably quite rare, but in another sense experiment practically always renders our thinking easier and more secure. We gain new conceptual power as we pass on from observation to experiment but, Sambursky notes, we will essay that passage only when we have come to accept the principle of dissolubility much more fully than did the Greeks. The essential thing in an experiment is the isolation of a certain phe- nomenon in its pure form, for the pui-pose of studying it systemati- cally. Herein lies its artificiality. Natural phenomena occur as part of a web of intei-woven and interconnected processes; their continuity in time and space makes them appear to us a single complete unit. . . . [Early experiments in mechanics by Galileo and Newton] were all based on the notion that friction or the resistance of environment are to be considered as incidental interferences with the study of the phe- nomenon that illustrates a natural law or principle in its pure form. This conception is as different as could be from Aristotle's. For him the environment was actually an integral part of the phenomenon itself, and he regarded the very idea of isolation as untenable. Pushing to the extreme that dissection of Nature envisioned by Bacon, in the laboratory we leave behind us the complexity of the EMPIRICAL TOOLS AND EMPIRICISM 153 interlocked phenomena of nature, and seek escape to experimental systems that better approximate the simple "ideals" figured in our conceptual abstractions. From raw phenomena— complicated by multiple accessory effects and subject to the action of a host of vari- ables difficult to identify, much less to evaluate— we seek escape to experimental systems in which, by isolation and control, we suppress the accessory effects, diminish the number of active variables, and make the remaining variables amenable to our adjustment. How much more easily we grasp the function in nature of a biochemical intermediate when, in the laboratory, we can study it in a wholly un- natural state of high purity! How much easier it becomes to establish the conjectural effect of a hypothetical variable when we can make it the onlij variable! And, more generally still, given reproducible laboratory data, we must always find it simpler "to see the thing" because, to some degree, at last we can see the simple thing. By such experimentation on "parts" we acquire the understanding with which, often, we can mount a successful attack on the still formi- dable problem of giving a complete conceptual reconstruction of the integral phenomenon— which is so completely refractory when sub- ject only to observation as such. Consider Pasteur. He finds the sour- ing of milk far too complex and irreproducible to study directly. He elects to study this fermentation in a medium constituted of chalk, water, sugar, and yeast extract, to which he adds no more than a pin- point's worth of material derived from milk. He proposes to grasp the essence of what happens in milk by studies made on the more controllable medium that, in effect, contains no milk. But then, hav- ing completed his studies on "sugared yeast water," Pasteur finds it possible to return to the souring of milk with an understanding made manifest by his ability to predict its vagaries and, most important of all, to conceive the possibility of something wholly new: the process we know as pasteurization. Precisely in the overivhelming success of such a return— from an ever-so-remote realm of superficially absurd conceptual and experimental abstractions— the scientist's capacity ever to maintain contact with the natural world is most convincingly demonstrable. Goethe criticizes Newton for having gone into a darkened room to study light. This criticism was made when the empirical tools of sci- ence were still relatively simple. Today, when scientists devote so much of their attention to subtle effects unobservable without the aid 154 EMPIRICAL TOOLS AND EMPIRICISM of complex machinery— today Goethe's criticism can be put with much greater force. Do scientists grope in the dark for a conception of hght? Do they turn their backs on the "real world" to study a world of purely synthetic phenomena artificially produced in a laboratory purposively cut oflF from the light of day? Can it be that what they study experimentally are not "natural" phenomena, but some artifi- cially contrived experience they do not even accept as such, but "cor- rect" as they deem necessary? Undeniably scientists sometimes confuse an artifact of their labora- tory machinery with a manifestation of nature. Eddington suggests a vivid illustration of this possibility: a hypothetical naturalist draws a net with one-inch mesh through the oceans of the world, and concludes from his catch that nowhere in the oceans are there crea- tures less than one inch in length. That scientists have suffered analo- gous, if more sophisticated, delusions is readily demonstrable. But the crucially important thing is that such delusions ultimately be- come recognizable as such. We learn, for example, to make "correc- tions": a half -fish in die net need not connote a half -fish in the ocean, but only a whole fish the other half of which has disappeared into some voracious companion with which, in the net, the victim has been brought in "unnatural" propinquity. Even more to the point, only a hypothetically stupid naturalist could forever content himself with superficial observation. The smallest modicum of experimentation reveals that inside the smaller fish in the net there are still smaller fish. Unpacking the Chinese box of successively smaller organisms, we would then ultimately obtain, from the catch of the one-inch net, a quite substantial knowledge of the microflora and fauna of the ocean. Our experimental tools do not of themselves manufacture ex- perience. The otherwise unattainable experience they make acces- sible to us must derive ultimately from nature. Consider, as an ex- ample, how we seek clues to life in the ashes of death. To discover what makes a plant thrive, we pluck it from the field, carry it to the lab- oratory, kill it, incinerate it, and analyze the ashes to find an answer. How absurd. But such studies, made by de Saussure and others, did indicate the chemical elements that figure in the composition of plants. With this knowledge we return from the laboratory to the fields, bringing with us artificial fertilizers that work a notable in- crease in agricultural productivity. The "unnatural" endeavors of the laboratory have then taught us something about nature. Surely we EMPIRICAL TOOLS AND EMPIRICISM 155 have not yet found the "secret of Hfe." But in the ashes of dead plants, in the dark of the laboratory, we have found the ideas that permit us to attain for plants a more vigorous growth, and for ourselves a life of greater abvmdance. EMPIRICISM AND THE INTERNAL DYNAMICS OF SCIENCE By determining the accessible elements of experience, and the quality of attainable data, empirical tools contribute to the shaping of scien- tific history. A new tool can reveal a whole domain of experience the very existence of which was previously unsuspected. Here the tele- scope and microscope are paradigmatic. Note, however, the far more recent unforeseen discovery of that world of bizarre phenomena taking place at ultra-low temperatures. That science has been the "endless frontier" is due in no small measure to the function of its empirical tools in reconstructing its horizons. No scientific Alexander need sigh for new worlds to conquer. Nor need he even await the discovery of new worlds: always there are known lands to which we first gain entry only with the development of new empirical tools. For long the geologist could only hypothesize certain phenomena inside the earth, but with the development of laboratory equipment generating extremely high pressures and tem- peratures many of these processes became observable in detail. The physiologist was aware that electrical phenomena accompanied the function of the brain long before the development of adequate elec- tronic instrumentation finally made these phenomena accessible to study. Science may be given a dramatic turn even by tlie quite modest empirical innovation that offers no more than easy entry in practice to a realm of data already accessible in principle. Consider as example the recent development of high-speed computing machinery. What is the magic of the computer? This elaborate machinery can perform no mathematical operation previously unperformable by a human mathematician provided with pad, pencil, and plenty of time. Plenty of time, and that is the point: the computing machine can do in sec- onds what a human computer would need years to accomplish. And from this advance in speed many major lines of theoretical investiga- tion have derived immense impetus. As an instance totally different in character, yet intimately related in effect, consider what progress was opened to genetics when it was fortunate enough to choose as its 156 EMPIRICAL TOOLS AND EMPIRICISM prime experimental subject the fast-breeding Drosophila melanogas- ter, possessed also of giant chromosomes and many diflferentiating traits. Consider finally how whole areas of modern biochemical re- search have been galvanized by the development of the extraordi- narily simple but powerful techniques of filter-paper chromatog- raphy. The devices of empiricism represent a major factor in the internal dynamics of science. From them the scientific movement gains not only general trends and directions but also specific foci. A new em- pirical device draws attention to itself. At the frontier of knowledge to which it provides access, great prizes may be won by the hardi- hood of pioneers. A potentially powerful tool then produces the state of mind of the gold-rush: from all contiguous areas "everbody" hastens into the country newly opened. Today "everybody" interested in structural chemistry seeks to exploit the novel powers of NMR and EPR spectrometers. Some two centuries ago "everybody" was at- tracted to the study of certain "odd" materials {e.g., phosphorus, mercuric oxide, hydrogen ) , and in such studies "everbody" sought to deploy the simple apparatus and techniques of pneumatic chemistry. Out of this high local concentration of activity developed the "Chem- ical Revolution." Bartlett remarks that: It is vastly important to realize how much experimental thinking is controlled by experimental method and by experimental instrumenta- tion and how hard it is, once methods and instruments have become accepted and established, to break away from their use. No small part of the history of science is written in the history of the devices of empiricism. But to suppose empiricism self-sufficient is surely absurd. Empirical devices help to establish the application of our ideas, the denotations of our concepts; but judgment and "good sense" are still requisite. By widening the realm of our experience, by providing us widi experience of peculiarly simple ( experimental ) systems, empirical devices can function even as aids to thought. But never can they function as substitutes for thought. Without Tycho's fundamental improvements in the instruments and techniques of ob- servational astronomy, and without the wonderful body of data col- lected by Tycho, Kepler could not have discovered his celebrated EMPIRICAL TOOLS AND EMPIRICISM 157 laws. But Tycho's empirical data do not themselves proclaim Kepler's laws: to discover them the conceptual insight of a Kepler is requisite. The Scientific Method Empiricism, fact, and logic loom large enough in science to give some color to the popular conception of a "scientific method" ( sometimes even The Scientific Method) infallible because it relies on nothing but systematic empiricism, hard fact, and cold logic. But this alluring conception of routinized Method is indefensible in the face of mul- tiple objections, not the least being Polanyi's comment on just those great turning points that have made the history of science what it is. Major discoveries change our interpretative framework. Hence it is logically impossible to arrive at these by the continued application of our previous interpretative framework. ... by the diligent perfonn- ance of any previously known and specifiable procedure. Consider too that, given Method, the advance of science should be as smooth and unfaltering as, indeed, it may appear in the long-term perspective of textbook presentations which are analytical rather than historical. Conant, however, remarks that: The stumbling way in which even the ablest of the scientists in every generation have had to fight through thickets of erroneous ob- servations, misleading generalizations, inadequate formulations, and unconscious prejudice is rarely appreciated by those who obtain their scientific knowledge from textbooks. It is largely neglected by those expounders of the alleged scientific method who are fascinated by the logical rather than the psychological aspects of experimental investigations. Even cursory scrutiny of the actual historical record— the modern no less than the ancient— yields ample evidence that in close-up perspec- tive the advance of science is sporadic, laborious, tortuous. Given Method, there should be a major element of sameness in the practice of those to whom science is indebted for its major advances. Examination of the historical record reveals not sameness but over- whelming diversity. At the very least we might expect to find unani- mous acceptance of the basic tenet of empiricism: the supreme authority of brute fact. But quite the contrary situation is implied by 158 EMPIRICAL TOOLS AND EMPIRICISM Polanyi's striking juxtaposition of the achievements of two 'Tieroes" of scientific history. . . . Vesalius is praised as a hero of scientific scepticism for boldly re- jecting the traditional doctrine that the dividing wall of the heart was pierced by invisible passages; but Harvey is acclaimed for the very opposite reason, namely for boldly assuming the presence of in- visible passages connecting the arteries with the veins. We praise Vesalius for so cleaving to the "testimony of the senses" that he could reject what all since Galen had accepted. But we also praise Harvey (though we condemn Galen) for going beyond the sensory evidence— to a degree denying its authority— in order thereby to "make sense" of the observables. And both Vesalius and Harvey (but not Galen) will ordinarily be claimed for the sacred flock of practitioners of Method. Certainly scientists are responsive to the authority of facts; pre- sumably in this they are much more responsive than the generality of men. But the absolute authority of facts has been denied— and, we say, most nobly denied— by some who could not otherwise have made the scientific advances for which we honor them. Science is irreduc- ible to a "safe" fealty to "indubitable facts." Often, to advance, men must venture boldly, sustained by nothing stronger than a human faith in human ideas that might well prove wrong— preconceived ideas defended warmly even in the teeth of contrary evidence. We do right to honor Mendeleev who— to sustain his periodic classification- had to reverse the positions of tellurium and iodine on the optimistic ( and quite erroneous ) assumption that major errors had been made in determining their atomic weights. Facts are not enough; empiricism is not enough. Consider the evi- dence gained by asking: Who advances science? Among the early members of the Royal Society were many who sought to conduct sci- ence as an exercise in Baconian empiricism. But the most notable ad- vances in the science of that age were not the work of these faithful cataloguers of facts: de Maistre indeed suggests that generally those who have taken Bacon most seriously have had the poorest success. Might one then argue that what fails here is not Method, but only men holding an imperfect conception of Method? One will then pre- dict that among moderns the older scientists, with a lifetime's ex- perience of Method, should far excel dieir younger colleagues in the EMPIRICAL TOOLS AND EMPIRICISM 159 production of important discoveries. Well-known facts contravene that prediction. Consider further: important experimental discoveries are made by but one of a hundred men equally trained in Method— equally in command of empirical techniques and of the elementary deductive operations which are all that experimental discovery or- dinarily requires of logic. Moreover, the discoverer is often not the most skillful experimentalist nor he most abundantly supplied with experimental devices. Is he simply "lucky"? How very painful to re- duce Method to chance! Du Noiiy finds the great discoverer distinguished from the pedes- trian fact-collector in this : The man of science who cannot formulate a hypothesis is only an accountant of phenomena. An hypothesis is an idea: beyond facts and the logical analysis thereof, the creation of ideas demands imagination. And imaginative capacity I suppose is precisely the faculty weaker in the old than in the young, precisely that so sparsely and unevenly distributed even among men amply trained in Method. Sometimes all too prolific of speculations that harden disastrously into preconceived ideas, imag- ination remains always the irreplaceable source of the hypotheses that power the successes of empiricism. Bernard writes: The experimental method, then, cannot give new and fiTiitful ideas to men who have none; it can serve only to guide the ideas of men who have them, to direct their ideas and to develop them so as to get the best possible results. The idea is a seed; the method is the earth furnishing the conditions in which it may develop, flourish, and give the best of fruit according to its nature. But as only what has been sown in the ground will ever grow in it, so nothing will be developed by the experimental method except the ideas submitted to it. The method itself gives birth to nothing. . . . . . . Consequently, there can be ho method for making discov- eries, because philosophic theories can no more give inventive spirit and aptness of mind, to men who do not possess them, than knowl- edge of the laws of acoustics or optics can give a correct ear or good sight to men deprived of them by nature. Neither Bernard nor I would for a moment deny that some methodo- logical precepts guide the practice of scientists: my present concern is only to show the vacuousness of the textbook stereotype of Method. 160 EMPIRICAL TOOLS AND EMPIRICISM FINDING THE PROBLEM At every stage, eflFective scientific investigation demands more than Method can supply. Beginning at the very beginning, observe that empirical devices are themselves but rarely the fruits of pure empiri- cism. The first creation of an NMR spectrometer demanded highly sophisticated theoretical work. But even the humble Dewar flask is an insulating device shaped to its purpose by a theoretical conception of three modes of heat transfer. A similarly abstract pedigree stands be- hind the startling simplicity of modern chromatographic techniques. Waive all such considerations. Suppose ourselves presented at the outset with an abundance of empirical tools. We have then to decide "only" how those tools shall be deployed. In a brand new field, random casts may be sufficiently rewarding: we learn what there is to be seen, and even to learn that certain effects are absent is some gain of knowl- edge. But ultimately we reach the stage of having seen enough, and then we have to ask what is worth observing. Random experiments now become vastly inefficient; from the vast majority of them we learn nothing of value. Thus we come to seek "promising" deployments of our empirical resources. Shall I use my machines to count the pebbles on the beach? Absurd! But why absurd? Because I judge their number irrelevant to any significant problem. How identify such a problem? Often a highly individualized ca- pacity seems here involved. Others before Newton had seen, and dis- missed, the elongation of the prismatic spectrum: to Newton that elongation represented a major problem, one through which he ar- rived at a new conception of light and color. For millennia men knew of "fanciful" dreams and "trivial" slips of the tongue: in just these Freud saw a substantial problem. So to detect a significant problem, long concealed under pseudo-explanations or in the trivial, demands intuition. Indeed, often it is the discovery and formulation of the problem that demands insight, whereas the solution demands no more than routine mathematical or experimental skill. The identifica- tion of a problem both solvable and worth solving is then a matter of prime importance. In this identification "experimental method" can- not help us: what we seek is necessarily prior to our experiments. Nor can we look for support to any Method that denies us the use of pre- conceived ideas. Problems can emerge only within contexts of presupposition that EMPIRICAL TOOLS AND EMPIRICISM 161 define the "ordinary" or "natural." Lacking such a context everything and nothing in our experience is a source of wonder and perplexity, everything and nothing is a problem. Given such a context, a problem becomes recognizable as a particular something that seems "unnat- ural," "incomplete," "irregular," "unsatisfactory." Thus, for example, the retrograde motion of the planets was a problem for the ancients who believed in the perfect uniformity of celestial motions, and not so very long ago the photoelectric eflFect posed a problem for those who accepted the view of classical electrodynamics. To be sure, if our theoretical preconceptions are wrong, they may lead us to study problems as unrewarding for us as were for them the chemical prob- lems studied by the alchemists. Outlawing preconceived ideas, Method would save us from such error; but then we could not even begin the work of science. The "illicit" context of presupposition dis- charges the indispensable function of making the difficulty that con- stitutes a problem, and so first permits the initiation of inquiry. Not all difficulties pose acceptable problems. Thus I refuse to treat as a problem some "odd" datum I consider likely to prove no more than a trivial experimental error. Making such peremptory dismissal, I draw again on (potentially fallible) theoretical presuppositions. And, if I am to advance any farther, I must now bring into play not only these but some very highly speculative hypotheses as well. Among many possible problems, I can first select one, as a good problem, only as I exercise my imagination to guess its answer. That premonitory intuition, or "educated guess," is then required to sup- port all subsequent stages of inquiry. Thus, attacking my problem, I seek first to collect the already-available data relevant to its solution. Even to begin that collection, I must use a criterion of relevance that finds its sole foundation in my own hypotheses about the form(s) solution to my problem will take. Is the orientation of the tails of comets relevant to the study of light? It first becomes so with the conception of an hypothesis associating that orientation with a "light pressure." THE DESIGN AND CONDUCT OF EXPERIMENTS Proceeding to experiment, I confront the problem of relevance in a new and aggravating form. Abstracting a simple experimental system from the complexity of natural events, what assurance have I that my system in any way "represents" the situation in nature? Is the be- 162 EMPIRICAL TOOLS AND EMPIRICISM havior of balls rolling on an inclined plane relevant to understanding of free fall? Can I hope to gain understanding of the souring of milk by studying a sugared yeast water that contains no milk? How shall I design an artificial system that is relevant, what variables shall I control, what observables shall I note? Before ever I make an experi- ment on my problem I must bring fully to bear my speculative ideas about its solution ( s ) . The choice of variables. In an experiment we study a phenomenon in circumstances that are narrowly determined, but never totally de- fined or definable. In practice we seek to measure and/or control only the relevant variables. To do more is a pointless waste of time; to do less is to aggravate unnecessarily the conceptual (interpretive) problems we will later face. Which are the relevant variables? Pre- sumably just those found relevant in previous studies of closely re- lated phenomena. However, unless we are concerned only with phenomena already thoroughly explored, such relation is only some- thing we hypothesize. Even striking resemblance may here be a wholly insufficient clue: the similar array of colors displayed by rain- bow and by peacock tail we find, to our surprise, represent very dif- ferent phenomena of light. No matter how we are guided by careful observation and long experience, a judgment of "close relation"— and the identification of relevant variables it implies— rest alike on the insecure but essential foundation of those of our preconceptions that dare forecast the results of experiments we have yet to begin. Can we not entirely bypass so unnervingly uncertain an identifica- tion of relevant variables? Rather than dealing with them explicitly, in a controlled experiment, might we not resort instead to use of an experimental control? That is, let us contrive two experimental sys- tems identical in all respects save one. Could we not then conclude that any difiPerences in the results obtained are certainly attributable to the action of the one variable in which the systems diflFer? Let us then go on to set up mantj systems, each pair differing only in some one of the many variables conceivably relevant. Could we not then easily establish, by experiment, the identity (and also the specific eflFect) of each relevant variable? Indisputably, use of an experimental control gives us an enor- mously powerful technique. Probably that power is most evident in biological work where— built into the experimental subject itself— a multitude of ill-defined variables elude our control. We cope with EMPIRICAL TOOLS AND EMPIRICISM 163 this major complication by setting up our paired experimental sys- tems with pairs of experimental subjects exactly alike— thus (hope- fully, and often actually) arranging to cancel the effects of variables not even known to us as such. Powerful though it is, however, use of an experimental control is no panacea. Literally identical specimens, in systems literally identical in all save one respect, we do not have and cannot secure. We have at most specimens and systems matched in those (relevant) characteristics that, on conceptual grounds, we regard as assuring effective identity. The use of experimental con- trols makes the problem of relevant variables somewhat less oppres- sive, but ultimately the problem remains just as real here as when we seek to control the variables explicitly and directly. Whether in a controlled experiment or in one with experimental controls, we sometimes encounter erratic fluctuations in our results. When these fluctuations substantially exceed our estimate of experi- mental error, they teach us that we have overlooked some relevant variable(s). But however our data may assist us, neither they nor Method then proclaim the identity of the relevant but uncontrolled variable(s). Always it is ive who must go on to guess that. Such guessing is not always easy. Those shrewd investigators Scheele and Priestley long failed to grasp what shortly after was realized by Ingen-Housz: intensity of illumination is a highly relevant variable in the chemical interaction of plants with the atmosphere. The choice of observables. I cannot control, or even match, all the variables possibly relevant to experimental production of a given phenomenon. But also, among myriad possibilities presented to view, I cannot possibly note all the observables. As early as the 16th cen- tury Tycho Br ahe— himself neither theoretician nor even experi- menter but simply observer— recognized the utter impossibility of "pure" obsers^ation. One must have a lead indicating where to look for something worth observing. This essential role of premonitory hypotheses is generalized by Cohen in the following emphatic state- ment. Accidental discoveries of which popular histories of science make mention never happen except to those who have previously devoted a great deal of thought to the matter. Observation unillumined by theoretic reason is sterile. . . . Wisdom does not come to those who gape at nature with an empty head. Fruitful observation depends not as Bacon thought upon the absence of bias or anticipatory ideas, but 164 EMPIRICAL TOOLS AND EMPIRICISM rather on a logical multiplication of them so that having many possi- bilities in mind we are better prepared to direct our attention to what others have never thought of as within the field of possibility. Guided by an acute surmise founded on the Rutherford-Bohr quantum theory of the nuclear atom, Moseley contrived a particular juxtaposition of equipment: a discharge tube, a series of substances to be put in that tube, a spectrometer containing a photographic plate, etc. These components were assembled for the sole purpose of obser\ing what was in fact found: a simple relation between the position of blackening on the plate and the identity of the substance present in the discharge tube. Something more than a purely empiri- cal genius diflFerentiates the few like Moseley from the many plodders who never make any such important discoveries. Beyond knowing how to measure, he knew also what to measure. If I err in my selection of relevant variables, a fluctuation of my results may alert me to my error; but if I err in my choice of ob- servables no such indication is vouchsafed me. I simply fail to make headway with my problem— which failure may indeed stimulate, though it cannot supply, the creation of some new hypothesis that directs my attention to hitherto neglected observables. No pat for- mula for success is to be found in systematic selection of observables quantitati^'ely determinable. Measurement is not co-extensive with science: measurement is but a tool of science and, though often a notably powerful tool, sometimes one entirely inappropriate. Stephen Hales, highly talented scientist and con\dnced practitioner of the quantitative method— made hundreds of meticulous measurements of tlie volumes of gases released from various specimens. Never did he sense the much deeper significance of the qualitative differences easily demonstrable in these gases— which included such still "un- disco\ered" species as oxygen and hydrogen. A more profound in- sight was won only when, bringing to bear only the very crudest of tests, Priestley and others demonstrated the highly distinctive chemi- cal properties of certain of Hales' specimens of "air." Today superior theories pro^'ide superior bases for choice of signif- icant obser\^ables. In any genuinely pioneering study, however, that choice is alwavs and una\oidablv hazardous. In Fermi's classic in- vestigation of the interaction of neutrons with uranium, for example, he noted a product he identified as radium. Only the flimsiest experi- I EMPIKICx\L TOOLS AND EMPIRICISM 165 mental evidence justified this identification, but it was powerfully supported by theoretical considerations. The more extended qualita- tive examination of the reaction products suggested in 1934, by Ida Noddack, was dismissed as an utterly pointless waste of time and eflFort. Only Rve years later did an adequate chemical characteriza- tion discover the "radium" to be barium— and this discovery at once evoked the wholly novel concept of nuclear fission. DRAWING CONCLUSIONS FROM EXPERIMENTS Postponing for later consideration the chimeras of methodical induc- tion and crucial experiments, I venture here only a few remarks on the obvious. And surely it is obvious that any harvest of the fruits of empiricism will demand more than logic and empiricism can them- selves supply. Like the facts themselves, a general conclusion yields itself only to him who, instructed by his hypotheses, brings to his study a particular query couched in particular conceptual terms. As- sume all "errors" properly rejected, all "corrections" properly made: even then what we will be able to find in our data is ordinarily de- limited by just what our ideas have prompted us to seek. Possessed by certain theoretic ideas, Dalton found the law of multiple propor- tions in published data available for several years to all; in precisely similar situations Gay-Lussac discovered his law of combining vol- umes, Petit and Dulong the law of atomic heats, and Balmer. . . . Hear Poincare: The isolated fact attracts all eyes, those of the layman as well as of the scientist. But what the genuine physicist alone knows how to see is the bond which unites many facts whose analogy is profound but hidden. The story of Newton's apple is probably not true, but it is symbolic; let us then speak of it as if it were tiiie. Well then, we must believe that before Newton plenty of men had seen apples fall; not one knew how to conclude anything therefrom. Facts would be sterile were there not minds capable of choosing among them, discerning those behind which something is hidden, and of recognizing what is hiding, . . . . . . We are [then] no longer in the presence of a fact but of a law. And upon that day the real discoverer will not be the workman who has patiently built up certain of these combinations; it will be he who brings to light their kinship. The first will have seen merely the crude fact, only the other will have perceived the soul of the fact. Often to fix this kinship it suffices him to make a new word, and this 166 EMPIRICAL TOOLS AND EMPIRICISM word is creative. The historv of science furnishes us a multitude of examples familiar to all [e.g., universal gravitation, energy, field]. How materialize "the soul of the fact"? The latent meaning of experi- mental data appears only with the application of a complex concep- tual developer, the formulation of which is irreducible to Method. THE POWER OF STATISTICAL METHODS The elaboration in recent years of refined techniques of statistical analysis may be thought to rehabilitate Method. Teaching us a su- perior design for empirical studies, and showing us how to get more out of empirical data, the statistical techniques generally simplify the empiricist's tasks. Consider, for example, the use of experimental controls. To investigate one \'ariable we ordinarily seek a pair of systems diflFering in that variable but matched in all others possibly relevant. When many such variables come in question, we are then committed to the huge e£Fort of preparing great numbers of paired systems matched in all but one variable. Furthermore, hewing to this pattern, we must inevitably fail ever to observe such possible effects as those "synergisms" that materialize only from simultaneous variation of at least two variables. Finally, and most important, we are entirely debarred from certain investigations in which no match- ing of all the potentially interesting variables is possible: in agricul- tural studies, for example, often we simply cannot find two sizable plots of land exactly matched in soil, exposure, drainage, and every other significant detail. The pioneering studies of Fisher and others have taught us how to meet these problems; taught us how, by statistical analysis, to ex- tract meaningful results from the examination of multi-v SLriant sys- tems. With the aid of such analysis the requisite number of trials is sharply reduced, and conclusions otherwise uncertain or wholly in- accessible are brought firmly widiin our grasp. Recall the co-ordi- nated simplification and complication we earlier found to accompany the shift from observation to experiment. To win simplification of our conceptual problems we accept the empirical complications of con- triving experimental systems tliat match or control die relevant vari- ables. Now Fisher and his colleagues have forged for us a new con- ceptual tool of unprecedented power. When strictly controlled ex- periment is impossible or inconvenient, tliis tool permits us to extract EMPIRICAL TOOLS AND EMPIRICISM 167 the knowledge we seek from the superficially more obscure data yielded by what might be described as controlled observation. The limitation of statistical methods. Undeniably powerful, the statistical tools of thought provide us with notably important new criteria for appraising the relevance or irrelevance of possible varia- bles, and for distinguishing between "error" and the action of some uncontrolled variable. But in neither case does statistical analysis ever identify tliose \'ariables for us: always these can be suggested only by our own hypotheses. Statistical analysis may reveal in our data some subtle relation we might otherwise overlook. But such analysis never supplants the insight of the investigator: always he must supi^ly the concepts in terms of which alone the analysis can be conducted and its results expressed. Like specific empirical tools, these explicit conceptual tools are powerful aids to human thought and judgment. But never can they stand in lieu of diought or eliminate the need for judgment. Simplify- ing judgment at one level, they demand it more heavily at another. Thus, for example, the whole opplicahilitij of statistical analysis de- pends on a judgment that our experimental design suffices to pro- vide results that will constitute a sample truly "random"— and this is no light undertaking when, as is usual, we have access to only a few results. Nothing frees the scientist from an omnipresent, need for such judgments. And generally he makes these decisions rather well, without even thinking of elaborate statistical analyses. Quite clearly he relies then on other than statistical criteria— most clearly when, as often he does, he overrides the statistical indications. Thus he may attach great importance to data statistical analysis would entirely discount: Meyerson, Planck, and many others have commented on the complete inadequacy of tlie data from which Mayer, Joule, and Colding boldly inferred the invariant equivalence of heat and work. Contrariwise, the scientist may totally reject, as meaningless, data which meet searchmg tests of statistical adequacy. If Rhine's data on ESP met ( or meet ) all such tests, still most scien- tists would reject them out of hand. A case perhaps parallel in point is noted by Polanyi, who refers to ... a table of figures published in Nature {146 (1940), p. 620) purporting to show that the days of gestation of difi^erent rodents is an integer multiple of the number tt, . . . no amount of such evi- dence could convince us today that this relationship is real . . . 168 EMPIRICAL TOOLS AND EMPIRICISM Statistical considerations alone can never be decisive because scientists always rely more heavily on quite a different criterion of judgment. Cohen points to that criterion while citing yet another case where the statistics are (and rightly, I suppose) simply held irrelevant. . . . for a number of years the membership in the International As- sociation of Machinists shows a very high correlation (86 per cent) with the death rate in the state of Hyderabad. If instances of this sort do not come to our attention more often it is because we do not look for them. We generally look for correlations where we have some reason to suppose that there is a real connection [and we reject cor- relations whenever we feel that no such reason exists]. But it is ive who make the theories and hypotheses which furnish us with "reasons," and ice who appraise their adequacy. In such cases our ultimate reliance is patently what indeed it is everywhere. Al- ways in the end we are brought back to human judgments dependent on fallible preconceived ideas. THE MYTH OF METHOD Speaking of self-sufficient Method— scientific, experimental, statisti- cal, or what you will~we speak of a chimera. A Method, seeking to invest the construction of science with an inhuman certainty, must seek a dehumanization of science that ends inevitably by making sci- ence humanly impossible. Potential danger then lurks in die myth of Method— danger that working scientists might actually come to take it seriously. In the social sciences credulity of this myth exacts a hea\'y toll— as on occasion it does even in psychology, presumably it- self a natural science. Clipping the wings of inspiration, strictures of Method must cripple the flight of science. Born writes: I believe that there is no philosophical highroad in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed. We do not jind signposts at crossroads, but our own scouts erect them, to help the rest. Methodological scruples endanger the bold, lawless enterprise of scouts, which has made science what it is today— which will again be required to make it all it hopes to become. However shockingly, awk- EMPIRICAL TOOLS AND EMPIRICISM 169 ward facts may on occasion be tvisely ignored; and, in making a be- ginning, irreducibly vague concepts prove often immeasurably su- perior to logically impeccable categories that presuppose all need for investigation is at an end. An obsessive concern with methodological chastity does not often eventuate in scientific fecundity. Great scientists practice not Method but success. Determined to get on with his difficult job, however best he can, the working scien- tist, in Einstein's words, . . . must appear to the systematic epistemologist as a type of un- scrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as the free inven- tions of the human spirit (not logically derivable from what is em- pirically given ) ; as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the view- point of logical simplicity as an indispensable and eff^ective tool of his research. The growth of the natural sciences utterly defies reduction to Method, to the constellation empiricism-fact-logic. I have distin- guished the empirical and conceptual lobes of the heuristic apparatus to facilitate discussion, and because between them there is all the distinctness of facts from ideas. But ultimately we find the facts in- separable from the ("subjective") ideas with which we seek, recog- nize, express, and appraise the relevance of ("objective") facts. Then strikes the hour to move on beyond empiricism: however large it looms in the history of science, Langer accurately remarks the some- thing else that looms still larger. The limits of thought are not so much set from outside, by the ful- ness or poverty of experiences that meet the mind, as from within, by the power of conception, the wealth of formulative notions with which the mind meets experiences. ... A new idea is a light that illuminates presences which simply had no form for us before the light fell on them. CHAPTER VII The Princip les of Science BEGIN by distinguishing two cate- gories of principles: a small group of regulative principles, with im- plications for the conduct of science; and a much larger group of substantive principles constituting "established knowledge" for the scientists of an age. The substantive principles supply a point of de- parture for scientific thought; the regulative principles sketch the goals of such thought and, very tentatively, routes thereto. Thus, in eflFect, the regulative principles assert something about the optimal construction of science, whereas the substantive principles assert something about the actual construction of the world. To be sure, this distinction is not perfectly clean-cut. If we accept a particular regu- lative principle, and seek to build scientific knowledge in certain ways, we do so only because we also accept a certain conception of the object of knowledge: the construction of the world. Nonetheless I will maintain what seems to me this useful distinction between sub- stantive and regulative principles: some haziness of classification must, I think, be tolerated when we have to deal with the funda- mental principles constituting that integral context of science of which Nicod says : It stays in the shadow and yet guides us to the light; we know how to use it, but we do not know how to analyze it. Beginning with the regulative principles, observe that they have the function (but not the status) of Kant's a priori ideas. Kant sug- gests that the multifarious data of human experience are in them- 170 THE PRINCIPLES OF SCIENCE 171 selves formless, inchoate, inapprehensible— that they can be "taken in" only as the human mind imposes on them its own patterns of com- prehension. To the contemplation of experience we thus bring our own ways of seeing: e.g., we "see" an ordered world close bound in chains of causal connection. Such ways of seeing or knowing are not imposed upon us by our experience. On the contrary, they are pre- suppositions of human experience. These patterns of thought consti- tute the co-ordinate system in which we view and measure our ex- perience, the ledger form in which we enter our findings as we "take stock" of that experience. Kant felt that men must always view the world in terms of certain unchanging forms innate to their very humanity: for him these forms were a priori absolutely. Contrariwise, I will regard the regulative principles of science as a priori only relatively. The efflorescence of human minds in some particular age and clime, they remain forever susceptible to change under the coercive pressure of an ever-widen- ing human experience. To be sure, we are very slow to admit any such coercion. The regulative principles are the most essential of the heuristic tools we bring to bear on our experience. Perforce, we make the tool harder than that on which it is to work. But it is not infinitely harder: slowly the tool is itself reshaped by the uses to which it is put. The status of the regulative principles defies simple categorization. Indubitable in the short term, none of them is today entertained in quite the form it had some centuries ago, or will probably have some centuries hence. Metaphysical in that they go far beyond all possi- bility of empirical demonstration, yet are they diflFerent from the perennially disputed abstractions of philosophy and theology: though metaphysical, they elicit the general consensus of scientists who find them justified by and in experience. Maintained with deep convic- tion, they are appraised by pragmatic criteria which are, of their very nature, provisional. Normally implicit, and never clearly for- mulated as such, these principles may seem instinctive feelings (re- flection of the scientific instinct of an age); but they are also judg- ments (no less so because they may be unconscious judgments) in that they change as new evidence comes within our experience. Cos- mologic, as covert expressions of a conception of the world, their primary function is methodologic, though they constitute no concrete Method. Perhaps they are best described, as some of them were by Newton, as "Rules of Reasoning in [Natural] Philosophy." They are 172 THE PRINCIPLES OF SCIENCE "rules of the road," presupposing certain characteristics of earthly roads and human drivers, but they do not teach us to drive. The Existence of a Real World For such as Occam, Berkeley, and Eddington, the reality of an ex- ternal world poses a major problem; but for others, like Bronowski, that world is simply given. We do not construct the world from our experiences; we are aware of the world in our experiences. In exactly the same vein Brain writes ; We do not need to ask how we become aware of things ouside our- selves because it is with that awareness that we begin. Whether it is a something postulated or a something given, an exist- ing real world is assuredly a something taken for granted by scien- tists. To what was said of this principle in Chapter II I have now to add one note of emphasis. I seek only to state, and indicate the appli- cation of, this principle and all other regulative principles treated hereafter. Never do I seek to justify them: taken as methodological principles, they are amply accredited by the demonstrable triumphs of the science that acknowledges them. I recognize no need (or way?) to justify them on any other grounds. The Principle of Intelligibility The real world having been constituted a "something," the principle of intelligibility asserts man's capacity— perhaps even his obligation— to understand that something. No Kantian necessity of thought, the first full conception of man's capacity for understanding appeared only with the coming of the Greeks. That the search for understand- ing is in any sense an obligation is a much later conception, even to- day rarely acknowledged outside the community of scholars. In some part inspirational, the principle of intelligibility has profound meth- odological implications. FOUR METHODOLOGICAL COROLLARIES Seeking to understand the world, we are driven beyond colligative relations— beyond "natural laws" the principle of intelligibility as- THE PRINCIPLES OF SCIENCE 173 sumes both existent and discoverable— in quest of explanation of those laws. This quest seeks consummation in the construction of postulational system(s) in which the laws are demonstrated to be necessary consequences of theoretical premises we accept. But now- having learned to reject, as delusive, the hope that theoretical prem- ises are, or can be made, self-evident— we cannot but recognize that always our explanations are incomplete. Hall attributes to Galilea and Newton the opinion that: The explanation of phenomena at one level is the description of phe- nomena at a more fundamental level, . . . Complete understanding then fails by the margin of those theoretical premises which are stipulated, perhaps "described," but certainly not themselves explained or explicable for so long as they remain our ultimate premises. Parsimony. Resolved to maximize our understanding, we find our- selves committed to a highly characteristic eflFort to minimize the number of theoretical premises required for explanation. Einstein speaks of: . . . the grand aim of all science, which is to cover the greatest pos- sible number of empirical facts by logical deductions from the small- est possible number of hypotheses or axioms. Some centuries earlier Newton had expressed the same "grand aim" in the first of his Rules of Reasoning: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. This is in turn the millennially remote echo of the "master of those who know," writing when the principle of intelligibility was in its infancy. That is done in vain by many means -which may equally well be done with fewer. Major differences of attitude and meaning presumably underlie these statements. Quite clearly, however, acceptance of the principle of intelligibility has always provoked, must always provoke, a con- tinuing endeavor to devise theories of ever-increasing comprehen- siveness founded on ever-narrower postulational foundations. Of many specific manifestations of this endeavor, a particularly signifi- 174 THE PRINCIPLES OF SCIENCE cant example is the enduring eflFort to construe the variety of the world in terms of a very few "elements." That attempt begins with Thales, the earliest of the Ionian philosopher-scientists; and the modern physicist, with his "fundamental particles," presses on in the same endeavor. Generalizing "elements" to include intangibles like force and energy, we find in Newton's Principia an expression of the same striving, for he says: . . . the whole burden of [natural] philosophy seems to consist in this— from the phenomena of motions to investigate the forces of na- ture, and then from these forces [small in number and taken as axioms] to demonstrate the other phenomena. Sambursky emphasizes the absolute continuity of the endeavor while citing yet another example of it: The laws of conservation are now so essential a part of science that it is hardly conceivable that we should be able to do without them or that science should take any form which does not allow for the formu- lation of such laws. The possibility of such foraiulation is implied in the premise which the Milesian School considered self-evident: that nature is capable of a rational explanation which reduces the number of variables and replaces some of them by constant quantities in- dependent of time or of the particular form of a given process. Penury. Each "quality" imputed to a premised entity figures as an additional postulate. Our desire for parsimony of postulates thus evokes a search for theoretical posits having the slenderest possible qualitative endowment. But this last quest derives more fundamen- tally and directly from the principle of intelligibility. Dingle makes it a principle of rational thought that: . . . an entity which is postulated to explain a general propeiiy of observable entities must necessarily lack that propeiiy. We reject theories that offer no more than a first step in a poten- tially infinite regress. We find no sense of explanation in the attribu- tion of the wetness of water to the wetness of water molecules, or of the hardness of iron to the hardness of iron atoms. As well, we think, explain the soporific action of opium by a dormative virtue inherent in it. Today Heisenberg remarks diat: It is impossible to explain . . . qualities of matter except by tracing them back to the behavior of entities which themselves no longer THE PRINCIPLES OF SCIENCE 175 possess these qualities. If atoms are really to explain the origin of color and smell of visible material bodies, then they cannot possess properties like color and smell. But close to the beginning of the era of modern science we find the same insight in Newton, though not in all of his contemporaries ( or ours ) . Having in mind a further question ( What is responsible for the cohesive strength of an "atomic hook"? ) , he remarks : The parts of all homogeneal hard bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked atoms, which is begging the ques- tion; . . . The qualities for us "explained" by a theory can only be those not imputed to the primary entities of that theory. The greater their penury— the fewer the qualities they possess— the more numerous become the qualities rendered potentially explicable by the theory. Any quality so explained is then shown comprehensibly emergent ( in a sense presently to be examined) from the deportment in a context of entities lacking precisely that quality. Evolutionary theories have in this respect immense explanatory appeal. Carrying this line of thought to its extreme, we set out from Gamow's concept of a qualitatively undiflFerentiated super-hot super- dense plasma in which, some billions of years ago, a nuclear explosion on a cosmic scale was followed by a physical evolution of elements. That development he supposes followed (and completed) by an astronomical evolution of galaxies, suns, planets, etc.; and that in turn by such a geological evolution as has produced the varied topog- raphy of our planet. Instructed by Oparin and others, we may then conceive a chemical evolution, yielding moderately complex mole- cules, and carrying on through some step(s) as yet unknown to the production of one or more rudimentary forms of life. By a further biological evolution we may, with Darwin, suppose higher animals like ourselves produced, then to undergo a sociologic evolution, and so on and on. In this chain of theories many links are at present little more than speculations. But such an evolutionary development does propose a potentially acceptable scientific explanation— conspicuously charac- terized by the continual emergence of diverse qualities and com- plexity from systems having fewer qualities and less complexity. 176 THE PRINCIPLES OF SCIENCE Complexity and diversity are so explained as they never can be by the theological view of original creation, in detail, of all the universe and its denizens. That view requires postulation of a god unimagi- nably more complex than the universe to be explained. The evolu- tionary sequence, contrariwise, traces the infinitely variegated world of our experience back to ylem— the undifferentiated plasma with most meagre of qualitative endowments. Ylem itself is describable, but certainly not explained. We might postulate its creation by a god— himself self-created that the regress may be cut off. As well invest ylem with power of self-creation! In the current development of science, ylem is simply that posit which is for us ultimate. Recognizing that, I recognize no failure. In ylem the quests for parsimony and penury are notably gratified. Beyond this, ylem has also the incomparable virtue of clarity. Though unex- plained, ylem can be described as a divine creator cannot be. We seek explanation through deduction of laws from premises: obviously we must seek premises clearly enough describable to support straightforward derivation of conclusions. Clarity. Whatever appearance of clarity they may make, the prem- ises of some theories prove, on closer inspection, far too obscure to reason from, far too exiguous to support any genuine explanation. Of this kind, Bernard remarks, is the premise that characterizes all vitalist theories. Life is nothing but a word which means ignorance, and when we characterize a phenomenon as vital, it amomits to saying that we do not know its immediate cause or its conditions. Science should always explain obscurity and complexity by clearer and simpler ideas. Now since nothing is more obscure, life can never explain anything. Scientists find notably repugnant all theories of this vitalist stamp— and correspondingly attractive those mathematically constructed theories that seem to turn on only the simplest of ideal entities stand- ing to each other in the clearest of relations. Most often the posits are eminently penurious and, beyond that, in such theories we seem to achieve the very utmost of postulational parsimony. From the small group of premised relations a veritable myriad of derivative theorems seem unequivocally and effortlessly produced. The superb power of correlation so displayed awakes in such as Newton a compelling sense of aesthetic splendor. THE PRINCIPLES OF SCIENCE 177 ... it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things. Does this sense of glory have another, deeper root? Beyond the exemplary clarity they oflFer, do mathematical representations of the world have for us another antipodal appeal rooted in an obscure mysticism holding number to be the essence of things? However paradoxically, this mysticism is close kin to the principle of intelligi- bility—as when the Pythagorean philosopher Philolaus argues that: . . . Number, fitting all things into the soul through sense-percep- tion, makes them recognizable and comparable with one another. . . . Actually, everything that can be known has a Number; for it is im- possible to grasp anything with the mind or to recognize it without this. Even numerical laws (as distinct from theories) then take on a special meaningfulness. Koestler remarks that: The Pythagorean discovery that the pitch of a note depends on the length of the string which produces it, and that concordant intervals in the scale are produced by simple numerical ratios (2:1 octave, 3 : 2 fifth, 4 : 3 fourth, etc.), was epoch-making: it was the first re- duction of quality to quantity, . . . . . . The gross strings of the lyre are recognized to be of subordi- nate importance; they can be made of different materials, in various thicknesses and lengths, so long as the proportions are preserved: what produces the music are the ratios, the numbers, the pattern of the scale. Numbers are eternal while everything else is perishable; they are of the nature not of matter, but of mind; they permit mental operations of the most surprising and delightful kind without refer- ence to the coarse external world of the senses— which is how the di- vine mind must be supposed to operate. Pythagorean mysticism can be deleterious, for example in encour- aging neglect of the "coarse external world of the senses." But it also inspires an extraordinarily fruitful effort to construe phenomena of nature in terms of simple mathematical "harmonies," both numerical and geometric. That inspiration informs the work of Archimedes in the ancient world, and plays a decisive role in the rebirth of science in the modern world at the hands of such as Copernicus, Kepler, and Galileo. For such men the discovery of mathematical harmony in natural phenomena was in itself an explanation of those phenomena, 178 THE PRINCIPLES OF SCIENCE to be prized beyond all other possibilities of explanation. In our own age this spirit still moved in Einstein, who expressed a very deep- seated conviction in writing that: I feel sure that pure mathematical construction allows us to discover the concepts, and the laws connecting them, which supply the key to the understanding of natural phenomena. ... In a certain sense, therefore, I hold it to be true that pure thought can comprehend reality, as the ancients dreamed. Those who share this conviction find explanation in the mathematical form of a physical theory. Of course, not all scientists share this con- viction, and not all accepted scientific theories have this form. More- over, we shall find in the next chapter that a theory cannot be purely mathematical if it is to function at all as a physical theory. We must be able to find in its abstract postulates something more than the epit- ome of clarity: in them we must find also some sense of analogy. Analogy. "Explain" laws by derivations from theoretical postulates unexplained and inexplicable in the context of the theory they con- stitute? To wield the dieory eflFectively, clearly we must somehow learn to grasp its postulates— and this we always seek to do by relat- ing them analogically to things or situations that serve us as "models." Thus, Bridgman observes, . . . the model is a useful and indeed unescapable tool of thought, in that it enables us to think about the unfamiliar in terais of the familiar. The lonians perforce sought models outside the science they were first to create— and found them everywhere, e.g., in the action of the winnower's sieve, and the operation of felting. However, by the middle of the 19th century, one particular privileged class of scien- tific models was established by the rise of classical mechanics. The major scientific synthesis extant, it was thoroughly familiar, ap- parently simple, and superbly competent to give a convincing ac- count of just those purely mechanical systems of which man had had the longest and widest experience, and now felt the deepest under- standing. A Kelvin might then understandably assert: I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot make a mechanical model all the way through I THE PRINCIPLES OF SCIENCE 179 cannot understand; and that is why I cannot get the electromagnetic theory. ... I want to understand hght as well as I can without in- troducing things that we understand even less of. Even today many still prefer mechanical models: of all models they are the most directly linked with both familiar everyday experience and the events actually observed in the laboratory. But today few in- deed adhere to Kelvin's opinion that only mechanical models are ac- ceptable. Thoroughly justified for so long as mechanics was the one established scientific system, his conception becomes altogether too narrow as soon as there appear other well developed sciences with which we feel enough at ease to frame our models on them. Today, for example, we happily found "field theories" on a model supplied by precisely that classical electrodynamics Kelvin still found unintel- ligible in itself. A century ago men dealt only in mechanical models formulated explicitly. Today we deploy a diversified array of physi- cal models that, in some cases, may figure only implicitly in a theory constituted by little more than a set of equations. However vague, distant, or incomplete may be the analogy— however deeply hidden in the mathematical formalism may be the physical model— always they are indispensable to our grasp of the theory. But, having forged on beyond mechanical models, we now recognize our capacity to pass beyond any predetermined set of "acceptable" models. CONGRUITY Accepting the principle of intelligibility, we set ourselves to under- stand a world we assume humanly understandable. We may bolster our courage with the assertion that "nature is simple," so that even feeble human reason may comprehend it. The eflFect is the same if we assert the complexity of nature and the vast power of human reason. Actually of course we need, and can, assert neither simplicity nor complexity of world and mind: our basic assumption is the congruity of world and mind. For the earliest scientists the assumption of con- gruity was justifiable only as, for the religious, Pascal's wager might justify faith in his God. Today that assumption is buttressed by a prog- ress of science Einstein holds ample to demonstrate that nature is humanly comprehensible. One may say "the eternal mystery of the world is its comprehensi- bility." . . . 180 THE PRINCIPLES OF SCIENCE In speaking here concerning "comprehensibility," the expression is used in its most modest sense. It imphes: the production of some sort of order among sense impressions, this order being produced by the creation of general concepts, relations between these concepts, and by [various determinate] relations between the concepts and sense experi- ence. ... It is in this sense that the world of our sense experiences is comprehensible. The fact that it is comprehensible is a miracle. The "miracle" can, of course, be taken in various ways. Edelstein writes in a somewhat Kantian vein that: On the basis of the hypothesis that the world can be understood by reason some men in Ionia in the early 6th century created a world that reason understands. Here congruence would arise from "construction" of the world by mind. Galileo thought diflFerently, rejecting the view that: . . . Nature had first made men's brains and then disposed all things in conformity to the capacity of their intellects. But I incline rather to think that Nature first made the things themselves, as she best liked, and afterwards framed the reason of man capable of conceiving (though not without great pains) some part of her secrets. Today we incline very strongly to Galileo's opinion, thinking to have found, in the theory of evolution by natural selection, a mechanism competent so to have "framed the reason of man." By that mechanism Einstein's miracle is toppled into a class with so many others that once loomed large in the argument from design. Hear Sherrington: Our stock is the vertebrate stock; our body is the vertebrate body; our mind is the vertebrate mind. If the vertebrates be a product of the planet, our mind is a product of the planet. Its activities and pro- clivities declare it so. Its senses each and all gear into the ways and means of our planet which is its planet. They are adapted to it, as a fish's bodv to water. . . . Ours is an earthlv mind which fits our earthly body. It produces percepts of earthly things from an earthly viewpoint. It helps the besouled body to deal with terrestrial things, thereby to live. Our mind constructs "time" and its time's rate is that of its besouled body's terrestrial habitat; although it, not unnaturally, has supposed it to be an universal and absolute Time. The last pre- ceding turn of its planet is its "yesterday" and the next expected turn will be its "tomorrow," . . . . . . We are, in biological phrase, reactions. The situation creates THE PRINCIPLES OF SCIENCE 181 the life which fits it. The dry land created the feet which walk it. Our situation has created the mind which deals with it. It is an earthly situation. Along with the sea it has created in us the wonder of the sea. The situation engenders the reaction to it. If the agent is terres- trial and the reaction is terrestrial is not the medium of the reaction terrestrial? The medium is the mind. Simplicity sigillum veri. Newton still assumed some absolute sim- plicity of the world when he wrote : . . . Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes. But even when we posit no more than congruity of world and mind, we must continue to impute special status to what we judge "simple." If our scrutiny of nature seems to show any "superfluous causes," we then come quite naturally to suppose our examination defective or incomplete. Thus in biology each diflFerentiated tissue or organic man- ifestation is confidently assumed to have, if not a purpose, then a function we set ourselves to discover. Von Frisch's entire epoch- making study of bees took departure, he tells us, from his flat rejection of the claim that the colors of flowers have no biological significance. Teleology, today not longer acceptable as an argument, conserves its power as heuristic guide. Von Bruecke, indeed, draws the general conclusion that, although teleology is a lady with whom the contem- porary biologist is reluctant to be seen in public, he finds it impossible to live without her. A number of more "respectable" implications attach to our convic- tion that we must find nature simple when we see her truly. Consider for example JefiFreys' comment: The actual behavior of physicists in always choosing the simplest law that fits the observations therefore corresponds exactly to what would be expected ... if they considered the simplest law as hav- ing the greatest prior probability. Finding difficulty with JefiFreys' whole concept of prior probability, I regard the characteristic behavior he so accurately reports as just one more direct consequence of our acceptance of the principle of intelli- gibility. The simple law is just that species of law we know how to explain by theoretical derivation. Supposing that all genuine laws are 182 THE PRINCIPLES OF SCIENCE SO explicable, we are then at once predisposed to see the simplest law as that most probably genuine. However this may be, the same strain of thought active in determining the laws we seek, and choose, seems also acti\'e when laws fail unexpectedly. Always we seek to under- stand such failure in terms of one or a very few "complicating factors." Of our theories, as of our laws, we hold simplicity the mark of truth. But here the situation becomes very difficult. Using this touchstone for the assay of scientific theories, all too often we obtain highly equiv- ocal results. Retrospecti\^ely we see that simplicity cannot supply a decisi\'e criterion of judgment, for a perfectly obvious reason: there is complexity to the whole idea of simplicity. Simplicities differ in kind as well as in degree. Perhaps we may distinguish the "simplicity" of great explanatory appeal ( e.g., the strong sense of analogy aroused by a convincing model ) from the "simplicity" of great correlative power (e.g., "the glory of geometry"). Probably, however, the two categories are seldom wholly distinct: e.g., is the "glory" ever without explana- tory appeal? And, certainly, in judging simplicity we always face the problem of somehow weighing together (if only against each other) two qualitatively different species of simplicity— within which lurk still further orders of complexity I examine hereafter. In time we learn to attach greater weight to one type of simplicity than to another. But then, all the more clearly, as sigillum veri, sim- plicity becomes a non-absolute criterion of judgment— an unknown function of a whole shifting climate of opinion, both scientific and cosmologic. Nevertheless, however difficult and insecure may be our judgment, and however insufficient in the short term may be this criterion, no scientist ever doubts that simplicity is a criterion for the judgment of theories. Given the principle of intelligibility, that could not be doubted. And, however our ideas of simplicity change in time, we have consistently set a high value on that particular species of simplicity we call "sameness." If for no other reason, we would prize this just because we are so certain that, awaiting our discovery, there is sameness in nature. Acceptance of the principle of intelligibility renders inadmissible any doubt on this point. Consider: in humans knowledge presupposes learning, and learning necessarily presup- poses in nature some degree of sameness in time, place, and species. Human knowledge thus presupposes precisely that uniformity Mill regarded as the ultimate major premise of all inductions. But now the principle of intelligibility asserts human capacity for knowledge of THE PRINCIPLES OF SCIENCE 183 nature, and so has as corollary Mill's ultimate premise. So important and complex is this corollary that I will treat it as a separate principle. The Principle of Continuity Heraclitus found in nature no continuity beyond that of absolute flux, continuous nonrecurrence. And even of those Greeks who descried a stable order in nature, Sambursky finds few who conceived the extent of that order as Anaxagoras did. Anaxagoras' astronomical hypotheses are throughout dominated by a "terrestrial" approach which makes no distinction between phenom- ena "there" in the sky and those "here" on the earth, and gives a purely physical evaluation of astronomical data and their possible causes. The heavenly bodies are nothing more than flaming stones; "the sun is larger than the Peloponnesus"— what uninhibited freedom of thought is revealed by this comparison of the mightiest of the celes- tial bodies, apotheosized by the deep-rooted irrational beliefs of myth- ology, with a geographical object, a part of the inhabited earth! Some two millennia were yet to pass before this view would find its match, and consummation, in Isaac Newton. Extending his concepts to earth and cosmos (and hypothetical microcosm) alike, Newton acts always on this premise: This is the quality of all bodies within the reach of our experiments; and therefore . . . to be aflirmed of all bodies whatsoever. To this conception of continuity Newton attached so much impor- tance that he makes of it a second Rule of Reasoning, corollary to the first. Conceiving nature as "wont to be simple and always consonant to itself," Newton takes it as a matter of principle that: Therefore to the same natural effects we must, as far as possible, assign the same causes. As to respiration in a man and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun; the reflection of light in the earth, and in the planets. Newton's successors applaud, and act upon, this principle— holding its soundness attested by Newton's successes and their own. By those successes ( and co-ordinate failures ) we have, indeed, been taught a revulsion from uniqueness and abruptness that carries us far beyond 184 THE PRINCIPLES OF SCIENCE the idea of sameness in time and place. Always now we would con- ceive nature as a contimium in which gradualism is the predominant (though not invariable) order of things. That conception is brought to bear, as earlier indicated, even in the elementary operation of fitting to our experimental "points" lines along which we interpolate and extrapolate. Active here at the very instant we make a first apprecia- tion of our data, the same conception remains active also right through to the highest levels of theoretical analysis. CONTINUITY AND EXPLANATION The connection of intelligibility and continuity, though asymmetric, is reciprocal. We seek a species of knowledge that presupposes con- tinuity, and with us the recognition of continuity passes as knowledge. The abrupt outbreak of flames from a pile of oily rags constitutes for us a problem. To it we find a satisfactory solution in the conception ( and detection ) of a slow process of oxidation, autoaccelerative as it produces a continuous gradual rise of temperature. That rise simply culminates in the appearance of flames, and these signify only a more rapid progress of an oxidative process we conceive different only in degree and not in kind from that taking place earlier. Passing from the trivial to the cosmic, observe that no small part of the appeal of a cos- mogony of continuous creation derives from the analogous suppres- sion of a unique ( and unfathomable ) "beginning." Forever seeking continuity where continuity is not apparent, we show ourselves still responsive to what was, even in the infancy of science, taken as of principle by Democritus : Nothing can be created out of nothing, nor can it [something, pre- sumably] be destroyed and returned to nothing. If a something seems to disappear into nothing, understanding or explanation requires the conception of a posterior something into which it has been metamorphosed. If a something seems to appear out of nothing, understanding or explanation requires the conception (and, if possible, detection) of an anterior something responsible for its production. The sudden appearance of a positron-electron pair per- plexes us until we can responsibly hypothesize the antecedent pres- ence of an unperceived gamma ray from which they have been pro- duced. Likewise we refuse to suppose that light is generated only to vanish at its source and subsequently to reappear at its destination. THE PRINCIPLES OF SCIENCE 185 Instead we constitute light a "something" which travels from source to destination, thus achieving continuity of connection in space as well as continuity of existence in time. Some half-century ago quantum phenomena began increasingly to breach the conception of continuity so long taken for granted. Secure in that conception, we reject out of hand the suj^position of some early societies that the sun is annihilated at dusk and reborn at dawn; but Bohr's conception of "quantum jumps" may be held to imply that an electron disappears here and reappears there without any inter- mediary "existence." As a matter of record this denial of continuity proved highly oflFensive to many physicists of the early 20th century, and even today a few are deeply disturbed by what Schrodinger called "the nightmare that physical events consist in continual se- quences of little fits and jerks." That this should seem a "nightmare" is testimony to the strength of the abiding human concern with con- tinuity. Indeed this nightmare parallels ( perhaps even in futility? ) a problem that, in a very diflFerent age, agitated the scholastics: when angels move from place to place, do they pass through the intermedi- ate space? In any case, whatever the ultimate outcome of attempts to dispel Schrodinger 's nightmare, quantum mechanics still preserves absolutely intact those major elements of continuity embodied in the various conservation laws. Energy. For Anaximenes "motion is from eternity." Today "kinetic energy" has become one measure and expression of the quantity of motion. But clearly kinetic energy is not constant even for one single oscillation of a simple pendulum. To maintain constancy of "energy'^ we then introduce a term representing "potential energy," hypothe- sizing that the sum (but not the distribution) of energies remains constant. Of course, kinetic and mechanical potential energies are insufficient to maintain the constancy we seek in all the cases with which ultimately we must deal. In the 19th century, conservation of energy required the postulation of multiple species of interconvert- ible energies— thermal, chemical, electric, magnetic, radiant, etc. At the beginning of the 20th century, the apparently limitless evolution of heat by the then-newly-discovered radioactive elements posed a problem resolved only with the conception of an interconvertibility of mass and energy— mass becoming itself a species of energy. Little more than a quarter of a century ago, what seemed a genuine crisis was averted only with the postulation of the neutrino. A purely ad 186 THE PRINCIPLES OF SCIENCE hoc contrivance, this "particle" was purposively designed to be the undetected, and then undetectable, vehicle for the con\Tyance of energy from experimental systems in which the conservation law ( and others of its kind ) apparently fail. Some two centuries ago, close to the beginning of this \^ery complex development, its leitmotif was voiced by Bernoulli in a statement which echoes Democritus : To try to demonstrate this law would be to obscure it. Indeed, every- one regards this as an incontestable axiom, that an efficient cause cannot perish, either as a whole or in part, without producing an effect equal to its loss. That axiom being held incontestable, we have throughout pursued an elusive constancy in the absolute conviction that some such con- stancy exists. Thus, as Meyerson emphasizes, we have perfectly con- sistently multiplied species of energies if and as required for con- stancy of "energy." The quest for continuity we hsive found so imperious, and so highly profitable, here yields a conservation principle like all other conser\^a- tion principles. By dint of conceptual invention and empirical dis- covery, at last we reveal— underlying even the most drastic change- one perfect invariance. Invariance in hand, we now sense within reach that incomparably satisfying absolute continuity we call iden- tity. But here, alas, what remains identical is an exceedingly abstract "essence" difficult to conceive and, if Poincare is right, impossible to define. In each particular case it is clearly seen what energy is and at least a provisional definition of it can be given; but it is impossible to find a general definition for it. If we try to enunciate the [conservation] principle in all its gen- erality and apply it to the universe, we see it vanish, so to speak, and nothing is left but this: There is something which remains constant. The conservation principle is then an incomplete consummation of the quest for absolute identity in nature, which, however, we can pursue in another direction. This particular pursuit is indeed perhaps the most ancient and compelling effort spawned by the principle of continuity, and also one to which modern science owes much of its cachet. W'e sacrifice continuity in space to gain a perfectly genuine identity in time. THE PRINCIPLES OF SCIENCE 187 Atomism. Of the appearances of change and permanence in our world, Herachtus dismisses permanence as ilkisory, while Parmenides so dismisses change. Wishing to dismiss neither, we forever seek to found on permanence— on some element(s) of timeless identity we willingly take for granted— our conceptualization of whatever is ob- served to change with time. Change in the medium-sized world of our experience we seek then to derive from permanence in either macrocosm or microcosm, respectively enfolding or underlying the everyday world. Initially the first possibility may seem more plau- sible: the cycles of tides and seasons are obviously correlated with cycles of moon and sun respectively. And astrology seeks the origin of most or all terrestrial change in the macrocosm, in "influences" aris- ing from the shifting juxtapositions of eternal bodies pursuing their eternally appointed rounds. Mutability then derives from the im- mutable, the "local" motions and changing dispositions of which are not for us inconceivable. Only the millennial incompetence of astrol- ogy finally discredits this possibility. The second alternative is the one Leucippus and Democritus ex- plored. Again qualitative change is construed in term.s of local dis- placements of the unchanging— here in a hypothetical microcosm, the world of atoms. Thus, in Newton's phrasing, . . . the changes of corporeal things are to be placed only in the various separations and new associations and motions of these per- manent particles; . . . Slightly earlier, but some two millennia after Parmenides, Boyle had maintained that: If an angel himself should work a real change in the [qualitative] nature of a body, 'tis scarce conceivable to men, how he could do it, without the assistance of local motion. Two centuries later du Bois-Reymond still saw things the same way: The scientific cognition of nature ... is the reduction of changes in the physical world to the motions of atoms in accordance with cen- tral forces independent of time ... It is a fact of psychological ex- perience that our yearning for causal understanding is, for the time, well satisfied whenever we succeed in making that reduction. Beyond conceptual attractiveness, the corpuscular view today offers proven power. In all chemistry qualitative change is conceived in 188 THE PRINCIPLES OF SCIENCE terms of alterations in the (molecular) groupings of unaltered (atomic) particles, now including electrons and nucleons. In biology the fluctuating appearance of heritable traits is similarly referred back to the fluctuating combinations of "atomic" genes ( and, today, to the sequences of "atomic" base groups in DNA molecules). And so on and on. The invariance expressed in a conservation law is, in very strong form, just such a recognition of continuity as passes with us as knowl- edge. And then, quite naturally, recognition of what invariance de- mands will count with us as explanation. So it is that we couple the atomic theory with conservation laws to explain the occurrence (or nonoccurrence) of certain qualitative appearances, corresponding to particular states or structural arrangements. Leibniz considered atomism a theory flagrantly, and unacceptably, in violation of the dominant concept of continuity. But we find no irremediable incom- patability between the discreteness of atoms and the element of con- tinuity so prominent in the conservation principles. Continuity and discreteness are, after all, only imaginary conceptual polarities never wholly separated in practice. We use them to designate modes of thought (e.g., particle theories and field theories) in which one or the other polarity seems dominant. The separation of the polarities may then be highlighted by occasional spectacular conflicts of such theories— ^.g., the ancient strife of atomist with Stoic, the modern strife of morphologist with neo-Darwinian— but no scientific theory fails to embody and unite, in some degree, both polarities. Beginning with (common-sense) concepts of discrete objects, scientists may go on multiplying "things": galaxies, stars, planets, atoms, electrons, photons, etc. But ultimately they seek somehow to re-establish the spatial continuity these concepts will seem to set at nought. Thus, for example, having begun by conceiving a sharp boundary between stationary pipe and fluid e\'erywhere flowing at some bulk velocity, ultimately we conceive ( and find ) a gradient of flow velocities bridging the gap between a maximum value, along the axis of the pipe, and a minimum, next to its walls. Analogous dis- sipations of abrupt discontinuities occur at the furthest reach of scientific thought. Newton first attacks the problem of celestial dynamics with a con- cept of mutually attracting discrete bodies. Rebelling against the idea of action at a distance, ultimately we seek to re-establish continuity THE PRINCIPLES OF SCIENCE 189 by filling interplanetary space with a "field." This endeavor, as Sam- bursky observes, reaches its supreme expression in Einstein's general theory of relativity, where ... a physical point is simply a singularity in the "metric field" which surrounds it. Again, this field is not at all an empty space, but a kind of emanation of the matter in it, just as matter is a kind of "materialization" of the field. At the very opposite end of the scale of magnitudes, we find in modern microphysics an entirely analogous reduction of what once appeared an absolute dichotomy. To the discrete corpuscular "elec- tron" of the 19th century we now impute also some of the character- istics of a continuous wave and, conversely, to the purely undulatory "light" of the 19th century we now impute some of the properties of a corpuscle. Again there is a marriage of continuity and discontinuity and, though quantum mechanics has so far provided only a shotgun wedding, the union has been fruitful and enduring. DISSOLUBILITY AND SUPERPOSITION Superposability, the possibility of reconstituting wholes from parts, I regard as corollary to the principle of continuity. Dissolubility, the separability of parts from wholes, is taken as a principle even by common sense. Already examined from various aspects in Chapters II, III, and V, the principle of dissolubility was seen in Chapter VI as the keystone of all experiment. The immense power attainable by work with artificial controlled systems becomes ours only as we bring that principle to bear to isolate and subdivide our problems. Quite recently we first learned that at the microcosmic level the "part" we can hope to isolate is not an event as such, but only the unit of event and apparatus required to render it as some observable large-scale eflFect. Aside from this minor qualification, however, quantum mechanics leaves untouched our habitual exploitation of dissolubility in the design of experiments. In thought we proceed exactly as we do in experiment. Beginning with concepts of discrete objects and distinct phenomena, we resolve the world into "parts" we consider in abstraction from the whole. By way of superposition of these more comprehensible parts, we seek the whole that is often conceptually inaccessible in itself. But the superposability this program confidently assumes may well fail to 190 THE PRINCIPLES OF SCIENCE materialize if the parts considered are insufficiently "natural." And du Noiiy underlines this difficulty with his vigorous assertion that completely natural parts are completely unattainable, just as Aris- totle contended ( see p. 152 ) : When we speak of a phenomenon, we speak only of an event, or of a succession of events, arbitrarily isolated from the universe whose evolution they share. By isolating a fact in order to study it, we give it a beginning and an end, which are artificial and relative. In relation to the evolution of the universe, birth is not a beginning, and death is not an end. There are no more isolated phenomena in nature than there are isolated notes in a melody. Undeniably, our first eflForts at theoretical comprehension ordinarily center not on the complex general case actually encountered, but on some highly restricted special case— an ideal "phenomenon" con- spicuously artificial in its simplicity. To begin almost any theoretical problem may then demand something of that ruthlessness, reckless- ness, noted in one case by Pirie. Nowadays most thoughtful biologists realize that the evolutionary origin of species is bound to give intermediate types and there may be a transient continuity between adjacent species. But anyone com- batively aware of this in the eighteenth century was a nuisance. Then the most useful approach was a certainty that this is this and that that, and that the trouble with the small proportion of doubtful specimens was simply due to lack of knowledge. So slashing away with conceptual scalpels, we can count as success only an operation in which we do recover our patient alive, entire. We know we have succeeded when, after thinking about parts, we can in thought reconstitute wholes. After abstracting from "non- essential complications," we must in the end render just account even of them— precisely as in the case just noted, where we do at last re- integrate the intermediate types, and so grasp both the distinctness and the continuity of "species." Superposition, not summation. The whole we seek to comprehend may well differ from any sum of parts. Even common sense recog- nizes that a mob is no mere sum of constituent individuals: it has certain new "qualities," and lacks others found in individuals. Thus a correct superposition may sometimes deiucind— beyond addition of parts— due attention to the mutual interactions of those parts. En- THE PRINCIPLES OF SCIENCE 191 counter with such a case is always something of a surprise— so gen- eral is our success in distinguishing substantially independent parts. To mark our surprise we usually give a special name to the "co- operative phenomenon" that redresses the balance of sum and whole. But, however it may surprise us, such a phenomenon does not dismay us: frequently it represents nothing more than some element(s) intrinsic to our problem, but purposively ignored in our first sketch of a solution. Consider the "perturbations" of planetary orbits. The word may be seriously misleading: what we call perturbations are no more than artifacts of our own approach to the problem of calculating a planetary orbit. Ordinarily we begin with the simplifying assumption that planet and sun can be treated as completely independent of all other bodies in the system. This assumption yields a tractable two- body problem, but of course it is an oversimplification: there must also be gravitational attractions among planet, sun, and all other planets in the system. Directly to attack the total problem is hope- less: even a three-body problem defies exact mathematical analysis. We proceed then by solving the central two-body problem, and later re-introduce ( as "perturbations" ) the generally minor systemic inter- actions previously ignored. And our success in thus reconstituting the whole from its parts is at least partially attested by the exquisitely accurate predictions we found on our celestial mechanics. This instance has nothing unique about it. Thus we first approach the problems of nuclear physics with concepts of independent parti- cles. However, among "particles" present in the narrow compass of the nucleus there might well be strong interactions. These do indeed manifest themselves in the difference between the mass of the nucleus and the sum of the masses of the particles of which we suppose it con- stituted. We call this difference a "mass defect," but we readily under- stand that the "defect" arises simply from the interaction of particles we formerly treated as wholly independent. Quite similarly, in chem- istry we begin the study of molecular structure with a conception of bonds having characteristics dependent only on the identities of the two atoms directly linked by each bond. But ultimately we recognize co-operative effects of "parts" in the context of the molecule as a whole— systemic interactions for which we must make allowance, e.g., as "resonance." How often we meet this situation in work with living organisms! 192 THE PRINCIPLES OF SCIENCE We seek to understand the characteristics of hchens by viewing them as aggregates of algae and fungi, which parts we study in abstraction from each other. But of course the properties of a hchen are not simply the sum or average of alga and fungus properties. There is a co-operative phenomenon to which, as usual, we give a special name: symbiosis. Symbiosis is not something new and mys- terious; it symbolizes just those interactions originally neglected. In pharmacy we come to consider ( as "synergism" ) the special features of the joint action of two drugs originally considered singly; in medi- cine to consider (as "psychosomatic") phenomena that seem to in- volve the interaction of the two polarities— mind and body— physi- cians ordinarily treat in complete abstraction from one another. A very few modern investigators have joined Driesch in maintain- ing that, by its approach through "parts," science condemns itself to eternal ignorance of wholes clearly more than any sum of parts. Whatever superficial plausibility this argument may present, I hold it fundamentally specious. Given "parts," often the able scientist can conceive wholes! What could be more outrageously arbitrary than the parts into which the embryologist's microtome cleaves his specimen? But from hundreds of these flat "sections" the skilled embryologist recreates in thought the three-dimensional totality of the intact embryo. Far more than that, by carrying through the same operation with a whole series of embryos of different age, he at last grasps the entire course of development of the single intact embryo. Behold the completed superposition of parts that could scarcely be more "unnatural"! I find no basis whatever for the happy confidence with which ob- scurantists predict the defeat of science in the face of "the great prob- lem of life." The life of an organism we seek to comprehend in terms of parts: anatomical, histological, and molecular. But no scientist is simple enough to suppose that the organism can in thought be re- constituted without due attention to the interactions of these parts on macroscopic, microscopic, and molecular levels. We hope ulti- mately to find "life" emergent from chemical systems the components of which are not alive in any meaningful sense; this alone could for us represent a rational explanation. Far from being an annoyance or disaster, the co-operative phenomena that make superposition differ- ent from summation are, in fact, the essential presupposition of every attempt to explain the qualities of wholes. THE PRINCIPLES OF SCIENCE 193 Superposition and explanation. The emergence of new qualities demands context{s) of interaction: certainly the interactions of one or more "entities" with an environment, and usually also the inter- actions of multiple entities ( like or different in kind ) with each other. A gas molecule has mass and motion, but no "springiness." A large number of such molecules in a particular context {e.g., a closed cylin- der with movable piston) do manifest that behavior described by Boyle as "the spring of the air." And now, however clearly we may formerly have grasped the denotation of "gas pressure," so conceived emergent from molecular impact "gas pressure" acquires for the first time an explanation. Here, to a first approximation, the "outer" (en- vironmental) context provides the only interaction required for emergence of a new "quality" from molecules present in bulk. Con- sider, however, another case. Water is "wet," we say, but there is no wetness to a water molecule. The emergence of wetness demands the presence of many water molecules in an "outer" context providing, at least, the conditions of temperature and pressure in which water is liquid, as well as any other circumstances required for the manifesta- tion of wetness ( we observe no wetness if all surfaces in contact with the water are waxed, for instance). But now we must consider also the "inner" context of interaction among water molecules present in bulk. Wetness indeed depends on the dominance of one interaction over the other, i.e., the attraction of water molecule and test-surface molecule outweighing the attraction of water molecule for others of its kind. Wetness thus at last emerges from a double context of electric interactions not meaningfully "wet" or "dry." The qualities of the Sahara may be supposed "emergent" from the interactions, with the environment and with each other, of an im- mense multitude of grains of sand. The individual grain has no dunes —the quality of being duned develops from the presence of an outer context {e.g., winds) and an inner context {e.g., rolling friction be- tween grains of sand ) . Dunes are so e^tplained— and I do not venture beyond that to the much more ambitious contention of Sherlock Holmes: From a drop of water a logician could infer the possibility of an At- lantic or a Niagara without having seen or heard of one or the other. This Watson at least held "ineffable twaddle," and perhaps it is. Holmes' claim is one I neither affirm nor deny: I hold it completely 194 THE PRINCIPLES OF SCIENCE irrelevant to the conception of emergence I have sketched. From such emergence I seek not the prediction of quahties or phenomena unhke any I have previously known to exist but, on the contrary, explanation of known qualities or phenomena for the existence of which I seek some "sufficient reason." This is, I think, just the sense in which corpuscular hypotheses may be said to explain qualitative change. They sketch for us mechanisms of change involving die col- lective deportment {e.g., relative displacements) in certain contexts of certain unchanging entities. So taught to understand how change may come about, we grasp a "sufficient reason" we may call the cause of change. And with that dread word we enter now a new area of discourse. The Principle of Determinism, and Causality Though treated here as a separate principle, determinism may per- haps be regarded as further corollary to the principle of continuity. The argument might run thus: Acting on the principle of dissolu- bility, we suppose the condition or state of a finite system adequately defined by specification of a small number of parameters. If a state A of some such system is forever succeeded by state A, we have the perfect continuity of identity. However, if instead state A is once succeeded by some other state B, we expect to find continuity main- tained at least to the extent that, in other such systems, in other times and places, state A will ahcays be succeeded by state B. The princi- ple of determinism asserts that this element of continuity will be found if "proper" specifications of the states are given. We then at- tack the problem of establishing such specifications: each particular change we would show determined by a distinct antecedent state recognizable in advance of the event. When change occurs state B is the effect and, in whole or in some part, state A is the cause. But the idea of causality transcends any such trivial matter of naming and, however closely associated with the idea of determinism, it transcends that as well. Establishment of continuity in determinism satisfies the Egyptian quest for order that change may be rendered predictable. But the causal concept is rooted in the deeper and more difficult Greek quest, for understand- ing, broached in the principle of intelligibility. That is, if determin- ism expresses the conformity of phenomena to laws, in a universe THE PRINCIPLES OF SCIENCE 195 ruled by "necessity," then causality expresses the aspiration to grasp the nature of that necessity as distinct from the form of those laws. Some modern physicists, like Weizsacker, seek to reduce causality to nothing more than determinism. The criterion for the fact that one really knows the efficient cause, is that one can predict correctly the event produced by it. Thus the concept of cause has been so transformed, that the causal principle in modern natural science has been identified precisely with the com- plete predictability of natural phenomena. But though understanding may be manifested in the capacity to meet this "criterion," it is not realized in, or constituted by, that capacity. Through causality we seek, beyond knowledge of lohat-when- tvhere, a grasp of the how of phenomena. The aspiration to grasp how was, we saw earlier, entirely respon- sible for the naturalistic construction the Greeks put upon the prin- ciple of determinism. And observe now in another instance at the very beginning of the modern era that, once again, it is clearly the conception of causality which controls application of the principle of determinism. Thus Galileo laughs to scorn an alleged determinist order simply on the ground that the causal connection it implies is absurd: If Sarsi [Grassi] wants me to believe with Suidas that the Babylon- ians cooked their eggs by whirling them in slings, I shall do so; but I must say that the cause of this effect was very different from what he suggests. To discover the true cause I reason as follows: "If we do not achieve an effect which others formerly achieved, then it must be that in our operations we lack something that produced their success. And if there is just one single thing we lack, then that alone can be the true cause. Now we do not lack eggs, nor slings, nor sturdy fellows to whirl them; yet our eggs do not cook, but merely cool down faster if they happen to be hot. And since nothing is lacking to us except being Babylonians, then being Babylonians is the cause of the harden- ing of eggs, and not friction of the air." Today, as noted at the end of Chapter VI, strictly analogous causal considerations dominate our appraisals of statistical correlations of data. Because we readily conceive a causal mechanism, we are pre- disposed to judge significant a statistical correlation between cigaret smoking and the incidence of lung cancer; and equally predisposed 196 THE PRINCIPLES OF SCIENCE to judge non-significant statistical data alleged to indicate an extra- sensory perception (ESP) for which we can imagine no causal ex- planation. The view of causality here proposed is, of course, kin to Leibniz' principle of sufiicient reason. However, this principle can assume two quite diflFerent variants. Leibniz himself adopted the cosmologic variant that asserts something about nature, e.g., for each obserx^ed eflFect there exists an assignable physical cause or causes. Far dif- ferent is the methodologic variant that, to guide us, asserts a heuristic maxim, e.g., for each observed e£Fect seek to assign a physical cause or causes. A covert cosmologic implication attaches, we saw, to any recommendation of policy for dealing with nature; but in this horta- tory sense "sufficient reason" becomes the primarily methodologic principle I equate with the conception of causality. Causality as heuristic max'tm. Planck considered causality ... a heuristic principle, a signpost— and in my opinion, our most valuable signpost— which helps us find our bearings in a bewildering maze of occurrences, and indicates the direction in which scientific research must advance in order to arrive at fruitful results. The "direction" is simply that in which, setting out from an observed efiFect, we pursue the search for a causal mechanism competent to produce that efiFect. Hume's long-standing demonstration that causes cannot be assigned with certainty is, fortunately, much easier to ig- nore than to refute. And, however far "true causes" may (or may not) lie beyond our grasp, the search for such causes has pro\^ed im- mensely rewarding. One might then say of the idea of causality what Bacon said of alchemy: Alchemy may be compared to the man who told his sons that he had left them gold buried somewhere in his vineyard; where they by dig- ging found no gold but, by turning up the mold about the roots of the vines, procured a plentiful vintage. Just so, we discover the conditioned reflex while seeking the cause(s) of behavior. The word "cause" has a highly variable status in the scientist's \'Ocabulary. Talking about his work in progress, he is apt to voice, and act on, various speculations about the causes of certain observ- able efiPects. But when his work is completed the word "cause" may THE PRINCIPLES OF SCIENCE 197 not even appear in his statement of findings. Imagine, for example, that I am a pre-Copernican astronomer puzzled by the striking fact that when an exterior planet retrogrades it always stands in oppo- sition to the sun. Finding this correlation inexplicable within the framework of the Ptolemaic system, I set myself to discover its ori- gin, and perhaps ultimately I hit upon the Copernican theory. I then see how the odd correlation of retrograde and opposition may be caused and, in my exposition of the Copernican system, I may well cite this convincing explanation as an argument for acceptance of that theory. But, quite emphatically, I will not state that the Co- pernican system is the cause of this notable correlation. In some- what the same fashion, first tidings of the existence of the Andes mountains may at last explain for me a previously known occurrence of a large high-altitude city like Quito, but I am unlikely to say that the Andes cause Quito's high altitude. The scientist's search for causes is but means to the end of understanding and, that under- standing once achieved, his grasp of an entire system of phenomena and explanations can no longer be expressed in necessarily fragmen- tary statements about particular causes of particular phenomena. This curious disappearance of "cause" from the ultimate statements of knowledge achieved through pursuit of causes encourages misin- terpretation of the historical record— misinterpretation all the more likely because several of the earlier scientists seem expressly to dis- claim any interest in causes. Thus Galileo puts into the mouth of Salviati the statement that: The present does not seem to be the proper time to investigate the cause of the acceleration of natural motion, concerning which various opinions have been expressed. ... At present it is the purpose of our Author merely to investigate and to demonstrate some of the properties of accelerated motion (whatever the cause of this accelera- tion may be ) . . . In entirely similar fashion Boyle mentions the two models (plenist and kinetic) that might explain the origin of the law that bears his name, but he declines "to declare peremptorily for either of them against the other" on the ground that: I shall decline meddling with a subject, which is much more hard to be explicated than necessary to be so by him, whose business it is not, in this letter, to assign the adequate cause of the spring of the air, but 198 THE PRINCIPLES OF SCIENCE only to manifest, that the air hath a spring, and to relate some of its effects. In their time these passages expressed a novel and important idea: the value of even fragmentary knowledge, i.e., isolated laws. Both authors also imply that a search for more complete understanding then seemed unpropitious, but neither implies that such understand- ing is unattainable. As a matter of fact, Newton did of course find causes for the acceleration of falling bodies and the springiness of air. We construe the second case in a very different manner, but the "adequate cause" is for us, as for Newton, an explanation in terms of forces. What of the celebrated Newtonian disclaimer: hypotheses non fingo? What Newton actually says is this : But hitherto I have not been able to discover the cause of those prop- erties of gravity from phenomena, and I feign no hypotheses; ... to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly sei-ves to account for all the motions of the celestial bodies, and of our sea. The word "hitherto" is illuminating. Like Galileo and Boyle, Newton wisely declines speculation when, for the purpose in hand, he felt the need as clearly insufficient as the evidence. But this is a renunciation neither final nor complete. Far from it! In the very next (concluding) paragraph of the scholium in which the above passage appears, New- ton considers certain possible causes of gravity. He remained pas- sionately interested in the problem, and never despaired of solving it. Certain speculations offered in the later editions of the Opticks left him still unsatisfied, but his feelings remain apparent in the words I have italicized in the following famous passage. To tell us that every species of things is endowed with an occult spe- cific quality by which it acts and produces manifest effects, is to tell us nothing: but to derive two or three general principles of motion from phenomena, and afterwards to tell us how the properties and actions of all corporeal things follow from those manifest principles, would be a veiy great step in philosophy, though the causes of those principles were not yet discovered; and therefore I scruple not to pro- pose the principles of motion above mentioned, they being of very general extent, and leave their causes to be found out. THE PRINCIPLES OF SCIENCE 199 If legend may be trusted, Newton's entire gra\dtational theory originated in the speculation that the fall of the apple and the "fall" of the moon in its orbit have one and the same cause. Let no man presume to declare the search for causes unessential to Newton's work. Leaping all the way to Planck, at the beginning of the present centLiry, we find still active in him a concern for causality wholly unsatisfied in the establishment of determinism. Studying blackbody radiation, Planck at last discovered a mathematical expression for the variation of intensity with wavelength and temperature. That law reduces blackbody phenomena to determinist order; but Planck sought, beyond this, a causal explanation of how there is produced the behavior his law describes. Pushing on in this endeavor, he ar- rived at the oscillator model that first suggested the occurrence of a quantum of action. And here we meet the crowning irony: the con- ception so first born matures into a quantum mechanics that chal- lenges not only the idea of causality that inspired Planck's work, but even the concept of determinism. QUANTUM MECHANICS, DETERMINISM, AND CAUSALITY By the testimony of professional metaphysicians, and of scientists who speak as metaphysicians, we are assured that a catastrophe in the domain of microphysics now forces on us a complete re\ision of our concept of causality and determinism. Yet we behold with aston- ishment that scientists still persevere in causal inquiries that, as ever before, terminate fruitfully in conclusions that make no reference to causes. This paradox is at once resolved when we recognize the cosmologic locus of the "catastrophe." The heuristic principle of causality is far less aflFected than a cosmologic conception of deter- minism that, starting perhaps from the God who sees the sparrow's fall, passes on to a Laplacean non-God who precisely foretells the coming of star, dust-mote, and electron. Such an absolute determin- ism of individual events had of course never been attainable in the practice of science, and scientific practice owed but little to it. Sci- ence thus remains undamaged when the cosmologic conception of determinism is toppled by the explosive charge that individual micro- physical events remain forever subject to an irreducible indeter- minacy and unpredictability. But that blast does have some impor- tant repercussions in science. 200 THE PRINCIPLES OF SCIENCE Mendel's laws do not permit us to predict the characteristics of the plant that will grow from a given seed of known hybrid pedigree. This check does not much stir us: lacking knowledge of the exact "state" of the seed concerned, of course we cannot predict. And in microphysics, too, it was argued by Planck and others that a pre- cisely analogous incapacity for prediction derives from a precisely analogous deficiency in practice of knowledge conceivably attainable in principle. Today most physicists reject this view, contending that microphysical indeterminacy is no matter of what we don't know but, rather, what we can't give meaning to even in principle. Precise knowledge of the initial state of a microphysical system is impossible for the simple reason that the defining parameters of state are irre- duciblv statistical in nature. Thus statistical variation of results, leaving the individual event substantially uncertain, arises not from our ignorance of the initial state of the system, but from that state as such. Let us concede this widely accepted opinion. What then? This conception leaves entirely unshaken the dominance by determinism of the kind of large-scale events already known reducible to deter- minist order. Moreover, as Margenau observes, we can still say some- thing meaningful about the initial states even of microphysical systems. ... if the condition of the particle is unspecifiable by statements say- ing where it is and how fast it is going; if it is found sometimes here and sometimes there, then an aggregate of measurements must be performed, and the interesting infonnation is the relative frequency, i.e., the probability, with which it is found here or there. It is difficult to see why an observable should lack the fitness to serve as a variable of state if its determination requires more than one measurement. Even at the microphysical level the initial state of a system can thus be defined, in statistical terms, and so of course we can make predic- tions for statistically large numbers of events. I have now no basis for predicting when some one particular radioactive atom will decay. But I easily predict, and with great exactness, the time required for decay of some given fraction of a very large number of such atoms. E\'en in microphysics, then, determinism is a far from total loss. But what of causality: can we still aspire to know the how of micro- physical phenomena involving parameters only statistically signifi- THE PRINCIPLES OF SCIENCE 201 cant? I believe we can, and do. As science matures, so does our con- ception of causality. At the inception of modern science action-by- contact was the only causal mechanism fully acceptable; and the "unthinkable" notion that celestial bodies can attract each other from a distance, through "empty space," was as repugnant to Newton as to most of his adversaries. But, as earlier suggested, ultimately we learn to find acceptable explanations in models other than those that involve directly only mechanical pushes and pulls. Today, in con- frontation of the phenomena of microphysical indeterminacy, the concept of causality undergoes not destruction but a still further en- largement. For an observed microphysical eflFect we still seek, if not causes, then reasons, e.g., involving "chance" and the law of large numbers. May it be objected that, of its very nature, "chance" cannot furnish a sufficient reason? Suppose I find that in a large number of throws of a well-balanced die each face has turned up very nearly one-sixth of the time. For this observation have I not an amply sufficient reason when I recognize the absence of any cause that favors one face as against another? I feel in this sufficient explanation of how to requite, if not wholly to satisfy, the quest for sufficient reason broached by the concept of causality. For to me it appears, as to Lande, that: . . . random events take place continually, as C. S. Peirce remarked long before the quantum age. There are not sufficient causes for every event. On the other hand, there is sufficient reason for the lack of sufficient causes when one accepts Leibniz's principle of cause-effect continuity. This principle leads first to the conclusion that the reaction "always yes" or "always no" respectively should be bridged by intermediate reactions "sometimes yes and sometimes no," that is, by cases of in- determinacy in an individual test, dominated by statistical averages. The destruction of the cosmological principle of determinism does not, of course, leave even the purely heuristic concept of causality entirely unscathed. Thus Planck observes that: If it is assumed that statistical laws are the ultimate and most pro- found in existence, then there is no reason in theoiy why, when deal- ing with any particular statistical law, we should ask what are tlie causes of the variations in the phenomena? Actually, however, the most important advances in the study of atomic processes are due to 202 THE PRINCIPLES OF SCIENCE the attempt to look for a strictly causal and dynamic law behind every statistical law. If science is genuinely transformed in microphysics, Planck's histori- cal precedents will not compel us to join him in resisting the alleged ultimacy of statistical laws. But a recent statement of de Broglie's suggests that, even yet, there may be some substance to Planck's misgivings. For a quarter of a century the purely probabilistic interpretation of wave mechanics has certainly been of service to physicists because it has kept them from being overwhelmed by the study of very arduous problems . . . and thus has permitted them to advance steadily in the direction of applications, which have been numerous and fruitful. But today the heuristic power of wave mechanics, as it is taught, seems in large measure weakened. Everyone recognizes this . . . However this may be ( for "everyone" does not "recognize this" ) , the widely alleged ultimacy of the statistical view lies open to attack on what seems to me a far more fundamental plane. The target then is not the statistical view as such, but the more vulnerable pretension to knowledge of a final principle. Quantum mechanics produces appreciable changes in our con- ceptions of determinism and causality. But precisely because these are not the first such changes, we may well doubt they are the last. In the general context of his beliefs, the man of the Dark Ages could demonstrate convincingly the absolute unpredictability of the ap- pearance of comets— divinely sent portents of disaster. In much the same way, within the context of early 19th-century science, one could produce an apparently conclusive demonstration that the construc- tion of heavier-than-air flying machines was impossible. Yet behold, we are borne upon the air and we foretell the coming of comets. Presuming the finality of the context of modern quantum mechanics, one can prove the ultimacy of statistical laws, the irreducibility of the wave-particle dualism, and I know not what else. But Bohm cor- rectly emphasizes that the crucial initial presumption is neither dem- onstrated nor demonstrable. . . . conclusions have been drawn concerning the need to renounce causality, continuity, and the objective reality of individual micro- objects, which follow neither from the experimental facts underlying the quantum mechanics nor from the mathematical equations in terms THE PRINCIPLES OF SCIENCE 203 of which the theory is expressed. Rather, they follow from the as- sumption (usually implicit rather than explicit) that certain features associated with the current formulation of the theory are absolute and final, in the sense that they will never be contradicted in future theories . . . Such assumptions have in the past proved groundless often enough to encourage a watchful reservation as regards, for example, the "principle of complementarity" that Lande equates with: . . . the doctrine that a fundamental wave-particle duality is an im- manent feature of the microcosm which must be accepted at face value without peraiitting any further explanation. To my mind, this doctrine relies too much on the policy: if you cannot explain it, call it a principle; then defend it as fundamental and absolutely irreduci- ble, so that speaking of the unsolved "riddle of duality" from here on becomes the mark of naivete if not of heresy. I do not presume to know the outcome of the highly technical dispute still in progress. But I feel quite sure that always scientists must re- sist the finality of assertions about human incapacity for knowledge. Thus, for example, if I accept as final the view of vitalism, I will inevitably make it "true" by foreswearing just that effort, to compre- hend living organisms, which is alone competent to demonstrate the falsity of vitalism. But here I trespass on a much larger matter. The Principle of Corrigible Fallibility We have earlier touched upon a point made with great emphasis by Nietzsche: The assertion that the truth is here, and that an end has been made of ignorance and error, is one of the greatest seductions that there are. Assuming that one believes it, then the will to test, investigate, predict, experiment, is crippled: theJatter can itself become wanton, can doubt the truth. The "truth" is consequently more ominous than error and ignorance because it binds the forces with which one can work for enlightenment and knowledge. To resist "the truth" is difficult. The more deeply an open question concerns us, the more we crave its final resolution. Of all human en- terprises, only science has succeeded in fathering some approxima- tion to that attitude of philosophic doubt of which Cohen says: 204 THE PRINCIPLES OF SCIENCE As the state of doubt is intensely disagreeable, communities try to get rid of it in diverse ways, through ridicule, forcible sunpression, and the like. The method of science seeks to conquer doubt by cul- tivating it and encouraging it to grow until it finds its natural limits and can go no further. Sober reflection soon shows that though very few propositions are in themselves absolutely unquestionable, the pos- sibility of systematic truth cannot be impugned. The last sentence of Cohen's statement is of pivotal importance. A rampant Pyrrhonism was no small factor in the decline of ancient science. Unalloyed doubt, eventuating in nothing but a paralyzing awareness of the possibility of error, is as fatal as the complete as- surance remarked by Nietzsche. Implicit in all action is necessarily the possibility of wrong action: we can be certain we have done nothing wrong only by taking care to do nothing at all. Science can progress in its pursuit of truth only as it passes over from timid avoidance to bold acceptance of the risk— nay, the certainty— of error. LEARNING PRESUPPOSES ERROR We find in Genesis that learning presupposes failure, error; and Carr's maze-running tests show that, for men as for mice, learning occurs only when the subjects are allowed to make and recognize their errors. Learning thus presupposes error and, as itself a process of learning, science presupposes error. Not simply accommodating ourselves to the possibility of error, we actively court error ( e.g., by the extreme generalization of our laws and theories). Only through error, recognized as such, can we hope to learn. "The capacity of learning from experience," says William James, "is one of the rarest gifts of genius." The learning act that both demands and manifests such genius may be precisely that first difficult detection of error in an erstwhile indubitable. The policy of science is to maximize the possibility of learning by minimizing the number of "truths" held permanently beyond any challenge posed by experience. In ener- getic pursuit of the infallibility we confidently suppose humanly approachable, we can advance only to the extent that we deny our- selves the illusion that any item of infallibility is already attained. Popper holds it a point of fundamental importance— to the philos- ophy of science no less than to the methodology of science— that the distinguishing characteristic of an empirical statement is its suscepti- bility to falsification. Stipulating that all scientific beliefs must be THE PRINCIPLES OF SCIENCE 205 potentially falsifiable, we arrive at one belief we can hold compara- tively certain simply because it has survived submission to the many tests that have discredited all known alternative beliefs. However "negative" this approach to scientific truth, it— and it alone— can jus- tify the positive affirmation of Mill's ringing declaration: The beliefs which we have most warrant for, have no safeguard to rest on, but a standing invitation to the whole world to prove them un- founded. If the challenge is not accepted, or is accepted and the at- tempt fails, we are far enough from certainty still; but we have done the best that the existing state of human reason admits of ; . . . and in the meantime we may rely on having attained such approach to truth, as is possible in our own day. This is the amount of certainty attainable by a fallible being, and this the sole way of attaining it. We here approach a characterization of science in negative terms. It is a method of rejection that invests science with the extraordinary power for self -correction Cohen holds to be decisive. The apodictic certainty of science is not the absolute certainty of any specific result or material proposition, but the dialectic demonstration that any inaccuracy or false step can be corrected only by relying on principles inherent in the system of science itself. This is a position unassailable by any argument that can pretend to have any evidence in its favor. Plainly a purely negative system cannot suffice. Any expectation of progress through a method of rejection must always presuppose a positive production of new items thus to be winnowed. However, the human mind seems quite competent to produce new scientific ideas, and its competence most seriously impaired by unavailability or un- acceptability of a reliable criterion of rejection. We are most stim- ulated to produce new ideas by recognition of the inadequacy of ideas we have earlier accepted. Thus for science the negative capac- ity to court, recognize, and reject error is in itself precious. The char- acteristically strong development of that faculty in science is indeed the wellspring nourishing tlie root of scientific progressivism. No longer do we expect science to reach any bedrock of absolutely secure knowledge. Today's conception of science, as endless frontier, was grasped by Bernard a century ago. When we propound a general theory in our sciences, we are sure only that, literally speaking, all such theories are false. They are only par- 206 THE PRINCIPLES OF SCIENCE tial and provisional tiTiths which are necessary to us, as steps on which we rest, so as to go on with investigation; . . . Given faith in the possibility of progress toward superior knowledge, we can aflFord to indulge that scepticism of present knowledge which holds even our best established theories potentially open to review. This is the sense of Thomson's dictum that a theory is "a policy rather than a creed," and the substance of a delightfully matter-of-fact statement by Lewis. The scientist is a practical man and his are practical [i.e., practi- cally attainable] aims. He does not seek the ultimate but the proxi- mate. He does not speak of the last analysis but rather of the next approximation. . . . On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade. THE MUTUAL CONTROL OF FACTS AND THEORIES Science is basically empirical, and all scientists share Newton's opin- ion that: We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; . . . But in the face of what evidence are "true propositions" to be relin- quished as "dreams and vain fictions"? Generally the evidence must be overwhelming. For always it is we who must interpret "the evi- dence of experiments," and always we do so in the uncertain light shed by those "older truths" of which James says: Their influence is absolutely controlling. Loyalty to them is the first principle— in most cases it is the only principle; for by far the most usual way of handling phenomena so novel that they would make for a serious rearrangement of our preconception is to ignore them altogether, or to abuse those who bear witness for them. Just so Galileo was abused for his telescopic observations. Just so we ignore the repeated appearances of microorganisms in media earlier supposed to have been sterile, and thus maintain the nonoc- currence of spontaneous generation. For us these appearances are not the "evidence of experiments" but only the evidence of experi- mental errors. However temptingly simple may be the identification of science with the policy of systematic doubt, we must recognize THE PRINCIPLES OF SCIENCE 207 that science embodies always essential elements of systematic belief. An obdurate defender of his own opinions, Newton is fully aware that no theoretical ideas are susceptible to any perfectly final dem- onstration. And although the arguing from experiments and observations by in- duction be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. Yet Newton also recognizes that, however far beyond possibility of demonstration our best established ideas may lie, it is essential that we cling to them. He indicates the importance he attaches to this view by framing his fourth Rule of Reasoning to run as follows : In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be im- agined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exception. The double thrust of this rule is decisive. From it we gain courage to rely on unprovable theoretical ideas in the design and interpreta- tion of our experiments. In the face of apparent contradictions we defend our theories stoutly, and accept their guidance as we press on to new investigations. But precisely these endeavors, together with Newton's conception that all theoretical ideas are potentially liable to exceptions, may bring us ultimately to a very sceptical re- view of the ideas that have directed our efforts. We arrive here at the very core of the principle of corrigible falli- bility. The sense of fallibility encourages detachment, and the capac- ity to recognize error; the sense of corrigibility allows us to proceed hopefully, in full commitment to the ideas we believe well estab- lished. Commitment and detachment, but on somewhat diffe