Part 8 (1/2)

The incommensurable of Pythagoras and the paradoxes of Zeno present the ”no thoroughfares” of ancient mathematical thought. Neither the continuum of s.p.a.ce 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 s.p.a.ce 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 quant.i.ties 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 a.s.sumptions in regard to number, s.p.a.ce, 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 subst.i.tute a quant.i.tative 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 a.s.sumptions 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 a.s.signed by Eudoxus to the planetary bodies, spheres whose peculiar motions should correct the tendency of the different groups of spheres to pa.s.s 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 ma.s.ses 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 accomplis.h.i.+ng 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 c.u.mbrous 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 a.s.sumptions 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 a.n.a.lyzing 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 a.s.suming the role 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 a.s.sumed that every planet revolved along an epicycle, the center of which describes a circ.u.mference 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, a.n.a.lyzing and restating them within the limits of their essential accidents, and a.s.similating 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 a.n.a.lysis, 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 pa.s.sionate 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 peris.h.i.+ng imperfect instances, of partially realized forms full of unmeaning differences due to distortion and imperfection, the realm answering to a sensuous pa.s.sionate 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 pa.s.sing show, to the world of imperfectly developed matter which belonged to the perceptual pa.s.sionate experience. While it may not then be cla.s.sed 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 a.s.sess 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 att.i.tude 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 a.s.sumptions, 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 s.p.a.ce 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 s.p.a.ce. When the mathematician found himself carried by his mathematical technique beyond the a.s.sumptions of a metaphysical physics he abandoned the field of physical astronomy and confined himself to the development of his mathematical expressions.

In other fields Greek science a.n.a.lyzed with varying success and critical skill only the conceptions found in the experience of their time and world. Nor did Greek thought succeed in formulating any adequate method by which the ultimate concepts in any field of science were to be determined. It is in Aristotle's statement of induction and the process of definition that we appreciate most clearly the inadequacy of their method. This inadequacy lies fundamentally in Aristotle's conception of observation which, as I have already noted, implies the recognition of an individual, that is, an object which is an embodied form or idea. The function of knowledge is to bring out this essence. The mind sees through the individuals the universal nature. The value of the observation lies, then, not in the controlled perception of certain data as observed facts, but in the insight with which he recognizes the nature of the object. When this nature has been seen it is to be a.n.a.lyzed into essential characters and thus formulated into the definition. In Aristotle's methodology there is no procedure by which the mind can deliberately question the experience of the community and by a controlled method reconstruct its received world. Thus the natural sciences were as really fixed by the conceptions of the community as were the exact sciences by the conceptions of a Euclidian geometry and the mathematics which the Greeks formulated within it. The individual within whose peculiar experience arises a contradiction to the prevailing conceptions of the community and in whose creative intelligence appears the new hypothesis which makes possible a new heaven and a new earth could utilize his individual experience only in destructive skepticism. Subjectivism served in ancient thought to invalidate knowledge not to enlarge it.

Zeller has sketched a parallelism between the ideal state of Plato and the social structure of the medieval world. The philosopher-king is represented by the Pope, below him answering to the warrior cla.s.s in the Platonic state stands the warrior cla.s.s of the Holy Roman Empire, who in theory enforce the dictates of the Roman curia, while at the bottom in both communities stand the ma.s.s of the people bound to obedience to the powers above. There is, however, one profound difference between the two, and that is to be found in the relative positions of the ideal worlds that dominate each. Plato's ideal world beyond the heavens gives what reality it has to this through the partic.i.p.ation by the world of becoming in the ideas. Opinion dimly sensed the ideas in the evanescent objects about it, and though Plato's memory theory of knowledge a.s.sumed that the ideas had been seen in former existence and men could thus recognize the copies here, the ideal world was not within the mind but without. In a real sense the Kingdom of Heaven was within men in the medieval world, as was the Holy Roman Empire. They were ideal communities that ought to exist on earth, and it was due to the depravity of men that they did not exist. From time to time men undertook in various upheavals to realize in some part these spiritual and political ideals which they carried within them. And men not only carried within them the ideas of a New Jerusalem in which the interest of one was the interest of all and of an earthly state ordered by a divine decree to fulfil this Christian ideal, but the determining causes of the present condition and the future realization depended also upon the inner att.i.tudes and experiences of the individuals themselves.

Without carrying the a.n.a.logy here too far, this relation between the experience of the individual and the world which may arise through the realization of his ideas is the basis of the most profound distinction between the ancient world and the modern. Before the logic of this att.i.tude could appear in science a long period of intellectual and social growth was necessary. The most essential part of this growth was the slow but steady development of psychological doctrine which placed the objective world in the experience of the individual. It is not of interest here to bring out the modern epistemological problem that grew out of this, or to present this in the world of Leibnitzian monads that had no windows or in the Berkeleyan subjective idealism. What is of interest is to point out that this att.i.tude established a functional relations.h.i.+p between even the subjective experience of the individual and the object of knowledge. A skepticism based upon subjectivism might thereafter question the justification of the reference of experience beyond itself; it could not question knowledge and its immediate object.

Kant formalizes the relation of what was subjective and what was objective by identifying the former with the sensuous content of experience and the latter with the application of the forms of sensibility and understanding to this content. The relations.h.i.+p was formal and dead. Kant recognized no functional relations.h.i.+p between the nature of the _Mannigfaltigkeit_ of sensuous experience and the forms into which it was poured. The forms remained external to the content, but the relations.h.i.+p was one which existed within experience, not without it, and within this experience could be found the necessity and universality which had been located in the world independent of experience. The melting of these fixed Kantian categories came with the spring floods of the romantic idealism that followed Kant.

The starting-point of this idealism was Kantian. Within experience lay the object of knowledge. The Idealist's princ.i.p.al undertaking was to overcome the skepticism that attached to the object of knowledge because of its reference to what lies outside itself. If, as Kant had undertaken to prove, the reality which knowledge implies must reach beyond experience, then, on the Kantian doctrine that knowledge lies within experience, knowledge itself is infected with skepticism. Kant's practical bridge from the world of experience to the world of things-in-themselves, which he walked by faith and not by sight, was found in the postulates of the conduct of the self as a moral being, as a personality. The romantic idealists advance by the same road, though as romanticists not critical philosophers, they fas.h.i.+oned the world of reality, that transcends experience, out of experience itself, by centering the self in the absolute self and conceiving the whole infinite universe as the experience of the absolute self. The interesting phase of this development is that the form which experience takes in becoming objective is found in the nature and thought of the individual, and that this process of epistemological experience becomes thus a process of nature, if the objective is the natural. In Kant's terms our minds give laws to nature. But this nature constantly exhibits its dependence upon underlying noumena that must therefore transcend the laws given by the understanding. The Romanticist insists that this other reality must be the same stuff as that of experience, that in experience arise forms which transcend those which bound the experience in its earlier phase. If in experience the forms of the objective world are themselves involved, the process of knowledge sets no limits to itself, which it may not, does not, by implication transcend. As further indication of the s.h.i.+ft by which thought had pa.s.sed into possession of the world of things in themselves stands the antinomy which in Kantian experience marks the limit of our knowledge while in post-Kantian idealism it becomes the ant.i.thesis that leads to the synthesis upon the higher plane. Contradiction marks the phase at which the spirit becomes creative, not simply giving an empty formal law to nature, but creating the concrete universe in which content and form merge in true actuality.

The relation of the sensuous content to the conceptual form is not dead, as in Kant's doctrine. It is fused as perception into concept and carries its immediacy and concreteness of detail into the concrete universal as the complete organization of stimulation and response pa.s.s into the flexible habit. And yet in the Hegelian logic, the movement is always away from the perceptual experience toward the higher realm of the _Idee_. Thought is creative in the movement, but in its ultimate reality it transcends spatial and temporal experience, the experience with which the natural and mathematical sciences deal. Thought is not a means of solving the problems of this world as they arise, but a great process of realization in which this world is forever transcended. Its abstract particularities of sensuous detail belong only to the finite experience of the partial self. This world is, therefore, always incomplete in its reality and, in so far, always untrue. Truth and full reality belong not to the field of scientific investigation.

In its metaphysics Romantic Idealism, though it finds a place for scientific discovery and reconstruction, leaves these disdainfully behind, as incomplete phases of the ultimate process of reality, as infected with untruth and deceptive unwarranted claims. The world is still too much with us. We recognize here three striking results of the development of reflective consciousness in the modern world:--first, it is a.s.sumed that the objective world of knowledge can be placed within the experience of the individual without losing thereby its nature as an object, that all characters of that object can be presented as belonging to that experience, whether adequately or not is another question; and second, it is a.s.sumed that the contradictions in its nature which are a.s.sociated with its inclusion in individual experience, its references beyond itself when so included, may themselves be the starting-point of a reconstruction which at least carries that object beyond the experience within which these contradictions arose; and third, it is a.s.sumed that this growth takes place in a world of reality within which the incomplete experience of the individual is an essential part of the process, in which it is not a mere fiction, destroying reality by its representation, but is a growing-point in that reality itself.

These characters of philosophic interpretation, the inclusion of the object of knowledge in the individual experience and the turning of the conflicts in that experience into the occasion for the creation of new objects transcending these contradictions, are the characters in the conscious method, of modern science, which most profoundly distinguish it from the method of ancient science. This, of course, is tantamount to saying that they are those which mark the experimental method in science.

That phase of the method upon which I have touched already has been its occupation with the so-called data or facts as distinguished from Aristotelian individuals.

Whenever we reduce the objects of scientific investigation to facts and undertake to record them as such, they become events, happenings, whose hard factual character lies in the circ.u.mstance that they have taken place, and this quite independently of any explanation of their taking place. When they are explained they have ceased to be facts and have become instances of a law, that is, Aristotelian individuals, embodied theories, and their actuality as events is lost in the necessity of their occurrence as expressions of the law; with this change their particularity as events or happenings disappears. They are but the specific values of the equation when constants are subst.i.tuted for variables. Before the equation is known or the law discovered they have no such ground of existence. Up to this point they find their ground for existence in their mere occurrence, to which the law which is to explain them must accommodate itself.

There are here suggested two points of view from which these facts may be regarded. Considered with reference to a uniformity or law by which they will be ordered and explained they are the phenomena with which the positivist deals; as existencies to be identified and localized before they are placed within such a uniformity they fall within the domain of the psychological philosopher who can at least place them in their relation to the other events in the experience of the individual who observes them. Considered as having a residual meaning apart from the law to which they have become exceptions, they can become the subject-matter of the rationalist. It is important that we recognize that neither the positivist nor the rationalist is able to identify the nature of the fact or datum to which they refer. I refer to such stubborn facts as those of the sporadic appearance of infectious diseases before the germ theory of the disease was discovered. Here was a fact which contradicted the doctrine of the spread of the infection by contact. It appeared not as an instance of a law, but as an exception to a law. As such, its nature is found in its having happened at a given place and time. If the case had appeared in the midst of an epidemic, its nature as a case of the infectious disease would have been cared for in the accepted doctrine, and for its acceptance as an object of knowledge its location in s.p.a.ce and time as an event would not have been required. Its geographical and historical traits would have followed from the theory of the infection, as we identify by our calculations the happy fulfilment of Thales' prophecy. The happening of an instance of a law is accounted for by the law. Its happening may and in most instances does escape observation, while as an exception to an accepted law it captures attention. Its nature as an event is, then, found in its appearance in the experience of some individual, whose observation is controlled and recorded as his experience. Without its reference to this individual's experience it could not appear as a fact for further scientific consideration.

Now the att.i.tude of the positivist toward this fact is that induced by its relation to the law which is _subsequently_ discovered. It has then fallen into place in a series, and his doctrine is that all laws are but uniformities of such events. He treats the fact when it is an exception to law as an instance of the new law and a.s.sumes that the exception to the old law and the instance of the new are identical. And this is a great mistake,--the mistake made also by the neo-realist when he a.s.sumes that the object of knowledge is the same within and without the mind, that nothing happens to what is to be known when it by chance strays into the realm of conscious cognition. Any as yet unexplained exception to an old theory can happen only in the experience of an individual, and that which has its existence as an event in some one's biography is a different thing from the future instance which is not beholden to any one for its existence. Yet there are, as I indicated earlier, meanings in this exceptional event which, at least for the time, are unaffected by the exceptional character of the occurrence. For example, certain clinical symptoms by which an infectious disease is identified have remained unchanged in diagnosis since the days of Hippocrates. These characters remain as characters of the instance of the law of germ-origin when this law has been discovered. This may lead us to say that the exception which appears for the time being as a unique incident in a biography is identical with the instance of a germ-induced disease.

Indeed, we are likely to go further and, in the a.s.surance of the new doctrine, state that former exceptions can (or with adequate acquaintance with the facts could) be proved to be necessarily an instance of a disease carried by a germ. The positivist is therefore confident that the field of scientific knowledge is made up of events which are instances of uniform series, although under conditions of inadequate information some of them appear as exceptions to the statements of uniformities, in truth the latter being no uniformities at all.

That this is not a true statement of the nature of the exception and of the instance, it is not difficult to show if we are willing to accept the accounts which the scientists themselves give of their own observation, the changing forms which the hypothesis a.s.sumes during the effort to reach a solution and the ultimate reconstruction which attends the final tested solution. Wherever we are fortunate enough, as in the biographies of men such as Darwin and Pasteur, to follow a number of the steps by which they recognized problems and worked out tenable hypotheses for their solution, we find that the direction which is given to attention in the early stage of scientific investigation is toward conflicts between current theories and observed phenomena, and that since the form which these observations take is determined by the opposition, it is determined by a statement which itself is later abandoned. We find that the scope and character of the observations change at once when the investigator sets about gathering as much of the material as he can secure, and changes constantly as he formulates tentative hypotheses for the solution of the problem, which, moreover, generally changes its form during the investigation. I am aware that this change in the form of the data will be brushed aside by many as belonging only to the att.i.tude of mind of the investigator, while it is a.s.sumed that the ”facts” themselves, however selected and organized in his observation and thought, remain identical in their nature throughout. Indeed, the scientist himself carries with him in the whole procedure the confidence that the fact-structure of reality is unchanged, however varied are the forms of the observations which refer to the same ent.i.ties.[35]

The a.n.a.lysis of the fact-structure of reality shows in the first place that the scientist undertakes to form such an hypothesis that all the data of observation will find their place in the objective world, and in the second place to bring them into such a structure that future experience will lead to antic.i.p.ated results. He does not undertake to preserve facts in the form in which they existed in experience before the problem arose nor to construct a world independent of experience or that will not be subject itself to future reconstructions in experience.

He merely insists that future reconstructions will take into account the old in re-adjusting it to the new. In such a process it is evident that the change of the form in the data is not due to a subjective att.i.tude of the investigator which can be abstracted from the facts.