SCIENTIFIC METHOD AND INDIVIDUAL THINKER
GEORGE H. MEAD
The scientist in the ancient world found his test of reality in the evidence of the presence of the essence of the object. This evidence came by way of observation, even to the Platonist. Plato could treat this evidence as the awaking of memories of the ideal essence of the object seen in a world beyond the heavens during a former stage of the existence of the soul. In the language of Theatetus it was the agreement of fluctuating sensual content with the thought-content imprinted in or viewed by the soul. In Aristotle it is again the agreement of the organized sensuous experience with the vision which the mind gets of the essence of the object through the perceptual experience of a number of instances. That which gives the stamp of reality is the coincidence of the percept with a rational content which must in some sense be in the mind to insure knowledge, as it must be in the cosmos to insure existence, of the object. The relation of this test of reality to an analytical method is evident. Our perceptual world is always more crowded and confused than the ideal contents by which the reality of its meaning is to be tested. The aim of the analysis varies with the character of the science. In the case of Aristotle's theoretical sciences, such as mathematics and metaphysics, where one proceeds by demonstration from the given existences, analysis isolates such elements as numbers, points, lines, surfaces, and solids, essences and essential accidents. Aristotle approaches nature, however, as he approaches the works of human art. Indeed, he speaks of nature as the artificer par excellence. In the study of nature, then, as in the study of the practical and productive arts, it is of the first importance that the observer should have the idea—the final cause—as the means of deciphering the nature of living forms. Here analysis proceeds to isolate characters which are already present in forms whose functions are assumed to be known. By analogy such identities as that of fish fins with limbs of other vertebrates are assumed, and some very striking anticipations of modern biological conceptions and discoveries are reached. Aristotle recognizes that the theory of the nature of the form or essence must be supported by observation of the actual individual. What is lacking is any body of observation which has value apart from some theory. He tests his theory by the observed individual which is already an embodied theory, rather than by what we are wont to call the facts. He refers to other observers to disagree with them. He does not present their observations apart from their theories as material which has existential value, independent for the time being of any hypothesis. And it is consistent with this attitude that he never presents the observations of others in support of his own doctrine. His analysis within this field of biological observation does not bring him back to what, in modern science, are the data, but to general characters which make up the definition of the form. His induction involves a gathering of individuals rather than of data. Thus analysis in the theoretical, the natural, the practical, and the productive sciences, leads back to universals. This is quite consistent with Aristotle's metaphysical position that since the matter of natural objects has reality through its realization in the form, whatever appears without such meaning can be accounted for only as the expression of the resistance which matter offers to this realization. This is the field of a blind necessity, not that of a constructive science.
Continuous advance in science has been possible only when analysis of the object of knowledge has supplied not elements of meanings as the objects have been conceived but elements abstracted from those meanings. That is, scientific advance implies a willingness to remain on terms of tolerant acceptance of the reality of what cannot be stated in the accepted doctrine of the time, but what must be stated in the form of contradiction with these accepted doctrines. The domain of what is usually connoted by the term facts or data belongs to the field lying between the old doctrine and the new. This field is not inhabited by the Aristotelian individual, for the individual is but the realization of the form or universal essence. When the new theory has displaced the old, the new individual appears in the place of its predecessor, but during the period within which the old theory is being dislodged and the new is arising, a consciously growing science finds itself occupied with what is on the one hand the débris of the old and on the other the building material of the new. Obviously, this must find its immediate raison d'être in something other than the meaning that is gone or the meaning that is not yet here. It is true that the barest facts do not lack meaning, though a meaning which has been theirs in the past is lost. The meaning, however, that is still theirs is confessedly inadequate, otherwise there would be no scientific problem to be solved. Thus, when older theories of the spread of infectious diseases lost their validity because of instances where these explanations could not be applied, the diagnoses and accounts which could still be given of the cases of the sickness themselves were no explanation of the spread of the infection. The facts of the spread of the infection could be brought neither under a doctrine of contagion which was shattered by actual events nor under a doctrine of the germ theory of disease, which was as yet unborn. The logical import of the dependence of these facts upon observation, and hence upon the individual experience of the scientist, I shall have occasion to discuss later; what I am referring to here is that the conscious growth of science is accompanied by the appearance of this sort of material.
There were two fields of ancient science, those of mathematics and of astronomy, within which very considerable advance was achieved, a fact which would seem therefore to offer exception to the statement just made. The theory of the growth of mathematics is a disputed territory, but whether mathematical discovery and invention take place by steps which can be identified with those which mark the advance in the experimental sciences or not, the individual processes in which the discoveries and inventions have arisen are almost uniformly lost to view in the demonstration which presents the results. It would be improper to state that no new data have arisen in the development of mathematics, in the face of such innovations as the minus quantity, the irrational, the imaginary, the infinitesimal, or the transfinite number, and yet the innovations appear as the recasting of the mathematical theories rather than as new facts. It is of course true that these advances have depended upon problems such as those which in the researches of Kepler and Galileo led to the early concepts of the infinitesimal procedure, and upon such undertakings as bringing the combined theories of geometry and algebra to bear upon the experiences of continuous change. For a century after the formulation of the infinitesimal method men were occupied in carrying the new tool of analysis into every field where its use promised advance. The conceptions of the method were uncritical. Its applications were the center of attention. The next century undertook to bring order into the concepts, consistency into the doctrine, and rigor into the reasoning. The dominating trend of this movement was logical rather than methodological. The development was in the interest of the foundations of mathematics rather than in the use of mathematics as a method for solving scientific problems. Of course this has in no way interfered with the freedom of application of mathematical technique to the problems of physical science. On the contrary, it was on account of the richness and variety of the contents which the use of mathematical methods in the physical sciences imported into the doctrine that this logical housecleaning became necessary in mathematics. The movement has been not only logical as distinguished from methodological but logical as distinguished from metaphysical as well. It has abandoned a Euclidean space with its axioms as a metaphysical presupposition, and it has abandoned an Aristotelian subsumptive logic for which definition is a necessary presupposition. It recognizes that everything cannot be proved, but it does not undertake to state what the axiomata shall be; and it also recognizes that not everything can be defined, and does not undertake to determine what shall be defined implicitly and what explicitly. Its constants are logical constants, as the proposition, the class and the relation. With these and their like and with relatively few primitive ideas, which are represented by symbols, and used according to certain given postulates, it becomes possible to bring the whole body of mathematics within a single treatment. The development of this pure mathematics, which comes to be a logic of the mathematical sciences, has been made possible by such a generalization of number theory and theories of the elements of space and time that the rigor of mathematical reasoning is secured, while the physical scientist is left the widest freedom in the choice and construction of concepts and imagery for his hypotheses. The only compulsion is a logical compulsion. The metaphysical compulsion has disappeared from mathematics and the sciences whose techniques it provides.
It was just this compulsion which confined ancient science. Euclidian geometry defined the limits of mathematics. Even mechanics was cultivated largely as a geometrical field. The metaphysical doctrine according to which physical objects had their own places and their own motions determined the limits within which astronomical speculations could be carried on. Within these limits Greek mathematical genius achieved marvelous results. The achievements of any period will be limited by two variables: the type of problem against which science formulates its methods, and the materials which analysis puts at the scientist's disposal in attacking the problems. The technical problems of the trisection of an angle and the duplication of a cube are illustrations of the problems which characterize a geometrical doctrine that was finding its technique. There appears also the method of analysis of the problem into simpler problems, the assumption of the truth of the conclusion to be proved and the process of arguing from this to a known truth. The more fundamental problem which appears first as the squaring of the circle, which becomes that of the determination of the relation of the circle to its diameter and development of the method of exhaustion, leads up to the sphere, the regular polyhedra, to conic sections and the beginnings of trigonometry. Number was not freed from the relations of geometrical magnitudes, though Archimedes could conceive of a number greater or smaller than any assignable magnitude. With the method of exhaustion, with the conceptions of number found in writings of Archimedes and others, with the beginnings of spherical geometry and trigonometry, and with the slow growth of algebra finding its highest expression in that last flaring up of Greek mathematical creation, the work of Diophantes; there were present all the conceptions which were necessary for attack upon the problems of velocities and changing velocities, and the development of the method of analysis which has been the revolutionary tool of Europe since the Renaissance. But the problems of a relation between the time and space of a motion that should change just as a motion, without reference to the essence of the object in motion, were problems which did not, perhaps could not, arise to confront the Greek mind. In any case its mathematics was firmly embedded in a Euclidian space. Though there are indications of some distrust, even in Greek times, of the parallel axiom, the suggestion that mathematical reasoning could be made rigorous and comprehensive independently of the specific content of axiom and definition was an impossible one for the Greek, because such a suggestion could be made only on the presupposition of a number theory and an algebra capable of stating a continuum in terms which are independent of the sensuous intuition of space and time and of the motion that takes place within space and time. In the same fashion mechanics came back to fundamental generalizations of experience with reference to motions which served as axioms of mechanics, both celestial and terrestrial: the assumptions of the natural motion of earthly substances to their own places in straight lines, and of celestial bodies in circles and uniform velocities, of an equilibrium where equal weights operate at equal distances from the fulcrum.
The incommensurable of Pythagoras and the paradoxes of Zeno present the "no thoroughfares" of ancient mathematical thought. Neither the continuum of space nor of motion could be broken up into ultimate units, when incommensurable ratios existed which could not be expressed, and when motion refused to be divided into positions of space or time since these are functions of motion. It was not until an algebraic theory of number led mathematicians to the use of expressions for the irrational, the minus, and the imaginary numbers through the logical development of generalized expressions, that problems could be formulated in which these irrational ratios and quantities were involved, though it is also true that the effort to deal with problems of this character was in no small degree responsible for the development of the algebra. Fixed metaphysical assumptions in regard to number, space, time, motion, and the nature of physical objects determined the limits within which scientific investigation could take place. Thus though the hypothesis of Copernicus and in all probability of Tycho Brahe were formulated by Greek astronomers, their physical doctrine was unable to use them because they were in flagrant contradiction with the definitions the ancient world gave to earthly and celestial bodies and their natural motions. The atomic doctrine with Democritus' thoroughgoing undertaking to substitute a quantitative for a qualitative conception of matter with the location of the qualitative aspects of the world in the experience of the soul appealed only to the Epicurean who used the theory as an exorcism to drive out of the universe the spirits which disturbed the calm of the philosopher.
There was only one field in which ancient science seemed to break away from the fixed assumptions of its metaphysics and from the definitions of natural objects which were the bases for their scientific inferences, this was the field of astronomy in the period after Eudoxus. Up to and including the theories of Eudoxus, physical and mathematical astronomy went hand in hand. Eudoxus' nests of spheres within spheres hung on different axes revolving in different uniform periods was the last attempt of the mathematician philosopher to state the anomalies of the heavens, and to account for the stations, the retrogressions, and varying velocities of planetary bodies by a theory resolving all phenomena of these bodies into motions of uniform velocities in perfect circles, and also placing these phenomena within a physical theory consistent with the prevailing conceptions of the science and philosophy of the time. As a physicist Aristotle felt the necessity of introducing further spheres between the nests of spheres assigned by Eudoxus to the planetary bodies, spheres whose peculiar motions should correct the tendency of the different groups of spheres to pass their motions on to each other. Since the form of the orbits of heavenly bodies and their velocities could not be considered to be the results of their masses and of their relative positions with reference to one another; since it was not possible to calculate the velocities and orbits from the physical characters of the bodies, since in a word these physical characters did not enter into the problem of calculating the positions of the bodies nor offer explanations for the anomalies which the mathematical astronomer had to explain, it was not strange that he disinterested himself from the metaphysical celestial mechanics of his time and concentrated his attention upon the geometrical hypotheses by means of which he could hope to resolve into uniform revolutions in circular orbits the anomalous motions of the planetary bodies. The introduction of the epicycle with the deferent and the eccentric as working hypotheses to solve the anomalies of the heavens is to be comprehended largely in view of the isolation of the mathematical as distinguished from the physical problem of astronomy. In no sense were these conceptions working hypotheses of a celestial mechanics. They were the only means of an age whose mathematics was almost entirely geometrical for accomplishing what a later generation could accomplish by an algebraic theory of functions. As has been pointed out, the undertaking of the ancient mathematical astronomer to resolve the motions of planetary bodies into circular, uniform, continuous, symmetrical movements is comparable to the theorem of Fourier which allows the mathematician to replace any one periodic function by a sum of circular functions. In other words, the astronomy of the Alexandrian period is a somewhat cumbrous development of the mathematical technique of the time to enable the astronomer to bring the anomalies of the planetary bodies, as they increased under observation, within the axioms of a metaphysical physics. The genius exhibited in the development of the mathematical technique places the names of Apollonius of Perga, Hipparchus of Nicaea, and Ptolemy among the great mathematicians of the world, but they never felt themselves free to attack by their hypotheses the fundamental assumptions of the ancient metaphysical doctrine of the universe. Thus it was said of Hipparchus by Adrastus, a philosopher of the first century A. D., in explaining his preference for the epicycle to the eccentric as a means of analyzing the motions of the planetary bodies: "He preferred and adopted the principle of the epicycle as more probable to his mind, because it ordered the system of the heavens with more symmetry and with a more intimate dependence with reference to the center of the universe. Although he guarded himself from assuming the rôle of the physicist in devoting himself to the investigations of the real movements of the stars, and in undertaking to distinguish between the motions which nature has adopted from those which the appearances present to our eyes, he assumed that every planet revolved along an epicycle, the center of which describes a circumference concentric with the earth." Even mathematical astronomy does not offer an exception to the scientific method of the ancient world, that of bringing to consciousness the concepts involved in their world of experience, organizing these concepts with reference to each, analyzing and restating them within the limits of their essential accidents, and assimilating the concrete objects of experience to these typical forms as more or less complete realizations.
At the beginning of the process of Greek self-conscious reflection and analysis, the mind ran riot among the concepts and their characters until the contradictions which arose from these unsystematized speculations brought the Greek mind up to the problems of criticism and scientific method. Criticism led to the separation of the many from the one, the imperfect copy from the perfect type, the sensuous and passionate from the rational and the intrinsically good, the impermanent particular from the incorruptible universal. The line of demarcation ran between the lasting reality that answered to critical objective thought and the realm of perishing imperfect instances, of partially realized forms full of unmeaning differences due to distortion and imperfection, the realm answering to a sensuous passionate unreflective experience. It would be a quite inexcusable mistake to put all that falls on the wrong side of the line into a subjective experience, for these characters belonged not alone to the experience, but also to the passing show, to the world of imperfectly developed matter which belonged to the perceptual passionate experience. While it may not then be classed as subjective, the Greeks of the Sophistic period felt that this phase of existence was an experience which belongs to the man in his individual life, that life in which he revolts from the conventions of society, in which he questions accepted doctrine, in which he differentiates himself from his fellows. Protagoras seems even to have undertaken to make this experience of the individual, the stuff of the known world. It is difficult adequately to assess Protagoras' undertaking. He seems to be insisting both that the man's experience as his own must be the measure of reality as known and on the other hand that these experiences present norms which offer a choice in conduct. If this is true Protagoras conceived of the individual's experience in its atypical and revolutionary form as not only real but the possible source of fuller realities than the world of convention. The undertaking failed both in philosophic doctrine and in practical politics. It failed in both fields because the subjectivist, both in theory and practice, did not succeed in finding a place for the universal character of the object, its meaning, in the mind of the individual and thus in finding in this experience the hypothesis for the reconstruction of the real world. In the ancient world the atypical individual, the revolutionist, the non-conformist was a self-seeking adventurer or an anarchist, not an innovator or reformer, and subjectivism in ancient philosophy remained a skeptical attitude which could destroy but could not build up.
Hippocrates and his school came nearer consciously using the experience of the individual as the actual material of the object of knowledge. In the skeptical period in which they flourished they rejected on the one hand the magic of traditional medicine and on the other the empty theorizing that had been called out among the physicians by the philosophers. Their practical tasks held them to immediate experience. Their functions in the gymnasia gave their medicine an interest in health as well as in disease, and directed their attention largely toward diet, exercise, and climate in the treatment even of disease. In its study they have left the most admirable sets of observations, including even accounts of acknowledged errors and the results of different treatments of cases, which ancient science can present. It was the misfortune of their science that it dealt with a complicated subject-matter dependent for its successful treatment upon the whole body of physical, chemical, and biological disciplines as well as the discovery and invention of complicated techniques. They were forced after all to adopt a hopelessly inadequate physiological theory—that of the four humors—with the corresponding doctrine of health and disease as the proper and improper mixture of these fluids. Their marvelously fine observation of symptoms led only to the definition of types and a medical practice which was capable of no consistent progress outside of certain fields of surgery. Thus even Greek medicine was unable to develop a different type of scientific method except in so far as it kept alive an empiricism which played a not unimportant part in post-Aristotelian philosophy. Within the field of astronomy in explaining the anomalies of the heavens involved in their metaphysical assumptions, they built up a marvelously perfect Euclidian geometry, for here refined and exhaustive definition of all the elements was possible. The problems involved in propositions to be proved appeared in the individual experience of the geometrician, but this experience in space was uniform with that of every one else and took on a universal not an individual form. The test of the solution was given in a demonstration which holds for every one living in the same Euclidian space. When the mathematician found himself carried by his mathematical technique beyond the assumptions of a metaphysical physics he abandoned the field of physical astronomy and confined himself to the development of his mathematical expressions.