CREATIVE INTELLIGENCE

ESSAYS IN THE PRAGMATIC ATTITUDE

BY

JOHN DEWEY
ADDISON W. MOORE
HAROLD CHAPMAN BROWN
GEORGE H. MEAD
BOYD H. BODE
HENRY WALDGRAVE STUART
JAMES HAYDEN TUFTS
HORACE M. KALLEN

NEW YORK

HENRY HOLT AND COMPANY

Copyright, 1917,
BY
HENRY HOLT AND COMPANY
Published January, 1917
THE QUINN & BODEN CO. PRESS
RAHWAY, N. J.

PREFATORY NOTE

The Essays which follow represent an attempt at intellectual coöperation. No effort has been made, however, to attain unanimity of belief nor to proffer a platform of "planks" on which there is agreement. The consensus represented lies primarily in outlook, in conviction of what is most likely to be fruitful in method of approach. As the title page suggests, the volume presents a unity in attitude rather than a uniformity in results. Consequently each writer is definitively responsible only for his own essay. The reader will note that the Essays endeavor to embody the common attitude in application to specific fields of inquiry which have been historically associated with philosophy rather than as a thing by itself. Beginning with philosophy itself, subsequent contributions discuss its application to logic, to mathematics, to physical science, to psychology, to ethics, to economics, and then again to philosophy itself in conjunction with esthetics and religion. The reader will probably find that the significant points of agreement have to do with the ideas of the genuineness of the future, of intelligence as the organ for determining the quality of that future so far as it can come within human control, and of a courageously inventive individual as the bearer of a creatively employed mind. While all the essays are new in the form in which they are now published, various contributors make their acknowledgments to the editors of the Philosophical Review, the Psychological Review, and the Journal of Philosophy, Psychology and Scientific Methods for use of material which first made its appearance in the pages of these journals.

CONTENTS

CREATIVE INTELLIGENCE

THE NEED FOR A RECOVERY OF PHILOSOPHY

JOHN DEWEY

Intellectual advance occurs in two ways. At times increase of knowledge is organized about old conceptions, while these are expanded, elaborated and refined, but not seriously revised, much less abandoned. At other times, the increase of knowledge demands qualitative rather than quantitative change; alteration, not addition. Men's minds grow cold to their former intellectual concerns; ideas that were burning fade; interests that were urgent seem remote. Men face in another direction; their older perplexities are unreal; considerations passed over as negligible loom up. Former problems may not have been solved, but they no longer press for solutions.

Philosophy is no exception to the rule. But it is unusually conservative—not, necessarily, in proffering solutions, but in clinging to problems. It has been so allied with theology and theological morals as representatives of men's chief interests, that radical alteration has been shocking. Men's activities took a decidedly new turn, for example, in the seventeenth century, and it seems as if philosophy, under the lead of thinkers like Bacon and Descartes, was to execute an about-face. But, in spite of the ferment, it turned out that many of the older problems were but translated from Latin into the vernacular or into the new terminology furnished by science.

The association of philosophy with academic teaching has reinforced this intrinsic conservatism. Scholastic philosophy persisted in universities after men's thoughts outside of the walls of colleges had moved in other directions. In the last hundred years intellectual advances of science and politics have in like fashion been crystallized into material of instruction and now resist further change. I would not say that the spirit of teaching is hostile to that of liberal inquiry, but a philosophy which exists largely as something to be taught rather than wholly as something to be reflected upon is conducive to discussion of views held by others rather than to immediate response. Philosophy when taught inevitably magnifies the history of past thought, and leads professional philosophers to approach their subject-matter through its formulation in received systems. It tends, also, to emphasize points upon which men have divided into schools, for these lend themselves to retrospective definition and elaboration. Consequently, philosophical discussion is likely to be a dressing out of antithetical traditions, where criticism of one view is thought to afford proof of the truth of its opposite (as if formulation of views guaranteed logical exclusives). Direct preoccupation with contemporary difficulties is left to literature and politics.

If changing conduct and expanding knowledge ever required a willingness to surrender not merely old solutions but old problems it is now. I do not mean that we can turn abruptly away from all traditional issues. This is impossible; it would be the undoing of the one who attempted it. Irrespective of the professionalizing of philosophy, the ideas philosophers discuss are still those in which Western civilization has been bred. They are in the backs of the heads of educated people. But what serious-minded men not engaged in the professional business of philosophy most want to know is what modifications and abandonments of intellectual inheritance are required by the newer industrial, political, and scientific movements. They want to know what these newer movements mean when translated into general ideas. Unless professional philosophy can mobilize itself sufficiently to assist in this clarification and redirection of men's thoughts, it is likely to get more and more sidetracked from the main currents of contemporary life.

This essay may, then, be looked upon as an attempt to forward the emancipation of philosophy from too intimate and exclusive attachment to traditional problems. It is not in intent a criticism of various solutions that have been offered, but raises a question as to the genuineness, under the present conditions of science and social life, of the problems.

The limited object of my discussion will, doubtless, give an exaggerated impression of my conviction as to the artificiality of much recent philosophizing. Not that I have wilfully exaggerated in what I have said, but that the limitations of my purpose have led me not to say many things pertinent to a broader purpose. A discussion less restricted would strive to enforce the genuineness, in their own context, of questions now discussed mainly because they have been discussed rather than because contemporary conditions of life suggest them. It would also be a grateful task to dwell upon the precious contributions made by philosophic systems which as a whole are impossible. In the course of the development of unreal premises and the discussion of artificial problems, points of view have emerged which are indispensable possessions of culture. The horizon has been widened; ideas of great fecundity struck out; imagination quickened; a sense of the meaning of things created. It may even be asked whether these accompaniments of classic systems have not often been treated as a kind of guarantee of the systems themselves. But while it is a sign of an illiberal mind to throw away the fertile and ample ideas of a Spinoza, a Kant, or a Hegel, because their setting is not logically adequate, is surely a sign of an undisciplined one to treat their contributions to culture as confirmations of premises with which they have no necessary connection.

I

A criticism of current philosophizing from the standpoint of the traditional quality of its problems must begin somewhere, and the choice of a beginning is arbitrary. It has appeared to me that the notion of experience implied in the questions most actively discussed gives a natural point of departure. For, if I mistake not, it is just the inherited view of experience common to the empirical school and its opponents which keeps alive many discussions even of matters that on their face are quite remote from it, while it is also this view which is most untenable in the light of existing science and social practice. Accordingly I set out with a brief statement of some of the chief contrasts between the orthodox description of experience and that congenial to present conditions.

(i) In the orthodox view, experience is regarded primarily as a knowledge-affair. But to eyes not looking through ancient spectacles, it assuredly appears as an affair of the intercourse of a living being with its physical and social environment. (ii) According to tradition experience is (at least primarily) a psychical thing, infected throughout by "subjectivity." What experience suggests about itself is a genuinely objective world which enters into the actions and sufferings of men and undergoes modifications through their responses. (iii) So far as anything beyond a bare present is recognized by the established doctrine, the past exclusively counts. Registration of what has taken place, reference to precedent, is believed to be the essence of experience. Empiricism is conceived of as tied up to what has been, or is, "given." But experience in its vital form is experimental, an effort to change the given; it is characterized by projection, by reaching forward into the unknown; connexion with a future is its salient trait. (iv) The empirical tradition is committed to particularism. Connexions and continuities are supposed to be foreign to experience, to be by-products of dubious validity. An experience that is an undergoing of an environment and a striving for its control in new directions is pregnant with connexions. (v) In the traditional notion experience and thought are antithetical terms. Inference, so far as it is other than a revival of what has been given in the past, goes beyond experience; hence it is either invalid, or else a measure of desperation by which, using experience as a springboard, we jump out to a world of stable things and other selves. But experience, taken free of the restrictions imposed by the older concept, is full of inference. There is, apparently, no conscious experience without inference; reflection is native and constant.

These contrasts, with a consideration of the effect of substituting the account of experience relevant to modern life for the inherited account, afford the subject-matter of the following discussion.

Suppose we take seriously the contribution made to our idea of experience by biology,—not that recent biological science discovered the facts, but that it has so emphasized them that there is no longer an excuse for ignoring them or treating them as negligible. Any account of experience must now fit into the consideration that experiencing means living; and that living goes on in and because of an environing medium, not in a vacuum. Where there is experience, there is a living being. Where there is life, there is a double connexion maintained with the environment. In part, environmental energies constitute organic functions; they enter into them. Life is not possible without such direct support by the environment. But while all organic changes depend upon the natural energies of the environment for their origination and occurrence, the natural energies sometimes carry the organic functions prosperously forward, and sometimes act counter to their continuance. Growth and decay, health and disease, are alike continuous with activities of the natural surroundings. The difference lies in the bearing of what happens upon future life-activity. From the standpoint of this future reference environmental incidents fall into groups: those favorable to life-activities, and those hostile.

The successful activities of the organism, those within which environmental assistance is incorporated, react upon the environment to bring about modifications favorable to their own future. The human being has upon his hands the problem of responding to what is going on around him so that these changes will take one turn rather than another, namely, that required by its own further functioning. While backed in part by the environment, its life is anything but a peaceful exhalation of environment. It is obliged to struggle—that is to say, to employ the direct support given by the environment in order indirectly to effect changes that would not otherwise occur. In this sense, life goes on by means of controlling the environment. Its activities must change the changes going on around it; they must neutralize hostile occurrences; they must transform neutral events into coöperative factors or into an efflorescence of new features.

Dialectic developments of the notion of self-preservation, of the conatus essendi, often ignore all the important facts of the actual process. They argue as if self-control, self-development, went on directly as a sort of unrolling push from within. But life endures only in virtue of the support of the environment. And since the environment is only incompletely enlisted in our behalf, self-preservation—or self-realization or whatever—is always indirect—always an affair of the way in which our present activities affect the direction taken by independent changes in the surroundings. Hindrances must be turned into means.

We are also given to playing loose with the conception of adjustment, as if that meant something fixed—a kind of accommodation once for all (ideally at least) of the organism to an environment. But as life requires the fitness of the environment to the organic functions, adjustment to the environment means not passive acceptance of the latter, but acting so that the environing changes take a certain turn. The "higher" the type of life, the more adjustment takes the form of an adjusting of the factors of the environment to one another in the interest of life; the less the significance of living, the more it becomes an adjustment to a given environment till at the lower end of the scale the differences between living and the non-living disappear.

These statements are of an external kind. They are about the conditions of experience, rather than about experiencing itself. But assuredly experience as it concretely takes place bears out the statements. Experience is primarily a process of undergoing: a process of standing something; of suffering and passion, of affection, in the literal sense of these words. The organism has to endure, to undergo, the consequences of its own actions. Experience is no slipping along in a path fixed by inner consciousness. Private consciousness is an incidental outcome of experience of a vital objective sort; it is not its source. Undergoing, however, is never mere passivity. The most patient patient is more than a receptor. He is also an agent—a reactor, one trying experiments, one concerned with undergoing in a way which may influence what is still to happen. Sheer endurance, side-stepping evasions, are, after all, ways of treating the environment with a view to what such treatment will accomplish. Even if we shut ourselves up in the most clam-like fashion, we are doing something; our passivity is an active attitude, not an extinction of response. Just as there is no assertive action, no aggressive attack upon things as they are, which is all action, so there is no undergoing which is not on our part also a going on and a going through.

Experience, in other words, is a matter of simultaneous doings and sufferings. Our undergoings are experiments in varying the course of events; our active tryings are trials and tests of ourselves. This duplicity of experience shows itself in our happiness and misery, our successes and failures. Triumphs are dangerous when dwelt upon or lived off from; successes use themselves up. Any achieved equilibrium of adjustment with the environment is precarious because we cannot evenly keep pace with changes in the environment. These are so opposed in direction that we must choose. We must take the risk of casting in our lot with one movement or the other. Nothing can eliminate all risk, all adventure; the one thing doomed to failure is to try to keep even with the whole environment at once—that is to say, to maintain the happy moment when all things go our way.

The obstacles which confront us are stimuli to variation, to novel response, and hence are occasions of progress. If a favor done us by the environment conceals a threat, so its disfavor is a potential means of hitherto unexperienced modes of success. To treat misery as anything but misery, as for example a blessing in disguise or a necessary factor in good, is disingenuous apologetics. But to say that the progress of the race has been stimulated by ills undergone, and that men have been moved by what they suffer to search out new and better courses of action is to speak veraciously.

The preoccupation of experience with things which are coming (are now coming, not just to come) is obvious to any one whose interest in experience is empirical. Since we live forward; since we live in a world where changes are going on whose issue means our weal or woe; since every act of ours modifies these changes and hence is fraught with promise, or charged with hostile energies—what should experience be but a future implicated in a present! Adjustment is no timeless state; it is a continuing process. To say that a change takes time may be to say something about the event which is external and uninstructive. But adjustment of organism to environment takes time in the pregnant sense; every step in the process is conditioned. by reference to further changes which it effects. What is going on in the environment is the concern of the organism; not what is already "there" in accomplished and finished form. In so far as the issue of what is going on may be affected by intervention of the organism, the moving event is a challenge which stretches the agent-patient to meet what is coming. Experiencing exhibits things in their unterminated aspect moving toward determinate conclusions. The finished and done with is of import as affecting the future, not on its own account: in short, because it is not, really, done with.

Anticipation is therefore more primary than recollection; projection than summoning of the past; the prospective than the retrospective. Given a world like that in which we live, a world in which environing changes are partly favorable and partly callously indifferent, and experience is bound to be prospective in import; for any control attainable by the living creature depends upon what is done to alter the state of things. Success and failure are the primary "categories" of life; achieving of good and averting of ill are its supreme interests; hope and anxiety (which are not self-enclosed states of feeling, but active attitudes of welcome and wariness) are dominant qualities of experience. Imaginative forecast of the future is this forerunning quality of behavior rendered available for guidance in the present. Day-dreaming and castle-building and esthetic realization of what is not practically achieved are offshoots of this practical trait, or else practical intelligence is a chastened fantasy. It makes little difference. Imaginative recovery of the bygone is indispensable to successful invasion of the future, but its status is that of an instrument. To ignore its import is the sign of an undisciplined agent; but to isolate the past, dwelling upon it for its own sake and giving it the eulogistic name of knowledge, is to substitute the reminiscence of old-age for effective intelligence. The movement of the agent-patient to meet the future is partial and passionate; yet detached and impartial study of the past is the only alternative to luck in assuring success to passion.

II

This description of experience would be but a rhapsodic celebration of the commonplace were it not in marked contrast to orthodox philosophical accounts. The contrast indicates that traditional accounts have not been empirical, but have been deductions, from unnamed premises, of what experience must be. Historic empiricism has been empirical in a technical and controversial sense. It has said, Lord, Lord, Experience, Experience; but in practice it has served ideas forced into experience, not gathered from it.

The confusion and artificiality thereby introduced into philosophical thought is nowhere more evident than in the empirical treatment of relations or dynamic continuities. The experience of a living being struggling to hold its own and make its way in an environment, physical and social, partly facilitating and partly obstructing its actions, is of necessity a matter of ties and connexions, of bearings and uses. The very point of experience, so to say, is that it doesn't occur in a vacuum; its agent-patient instead of being insulated and disconnected is bound up with the movement of things by most intimate and pervasive bonds. Only because the organism is in and of the world, and its activities correlated with those of other things in multiple ways, is it susceptible to undergoing things and capable of trying to reduce objects to means of securing its good fortune. That these connexions are of diverse kinds is irresistibly proved by the fluctuations which occur in its career. Help and hindrance, stimulation and inhibition, success and failure mean specifically different modes of correlation. Although the actions of things in the world are taking place in one continuous stretch of existence, there are all kinds of specific affinities, repulsions, and relative indifferencies.

Dynamic connexions are qualitatively diverse, just as are the centers of action. In this sense, pluralism, not monism, is an established empirical fact. The attempt to establish monism from consideration of the very nature of a relation is a mere piece of dialectics. Equally dialectical is the effort to establish by a consideration of the nature of relations an ontological Pluralism of Ultimates: simple and independent beings. To attempt to get results from a consideration of the "external" nature of relations is of a piece with the attempt to deduce results from their "internal" character. Some things are relatively insulated from the influence of other things; some things are easily invaded by others; some things are fiercely attracted to conjoin their activities with those of others. Experience exhibits every kind of connexion[1] from the most intimate to mere external juxtaposition.

Empirically, then, active bonds or continuities of all kinds, together with static discontinuities, characterize existence. To deny this qualitative heterogeneity is to reduce the struggles and difficulties of life, its comedies and tragedies to illusion: to the non-being of the Greeks or to its modern counterpart, the "subjective." Experience is an affair of facilitations and checks, of being sustained and disrupted, being let alone, being helped and troubled, of good fortune and defeat in all the countless qualitative modes which these words pallidly suggest. The existence of genuine connexions of all manner of heterogeneity cannot be doubted. Such words as conjoining, disjoining, resisting, modifying, saltatory, and ambulatory (to use James' picturesque term) only hint at their actual heterogeneity.

Among the revisions and surrenders of historic problems demanded by this feature of empirical situations, those centering in the rationalistic-empirical controversy may be selected for attention. The implications of this controversy are twofold: First, that connexions are as homogeneous in fact as in name; and, secondly, if genuine, are all due to thought, or, if empirical, are arbitrary by-products of past particulars. The stubborn particularism of orthodox empiricism is its outstanding trait; consequently the opposed rationalism found no justification of bearings, continuities, and ties save to refer them in gross to the work of a hyper-empirical Reason.

Of course, not all empiricism prior to Hume and Kant was sensationalistic, pulverizing "experience" into isolated sensory qualities or simple ideas. It did not all follow Locke's lead in regarding the entire content of generalization as the "workmanship of the understanding." On the Continent, prior to Kant, philosophers were content to draw a line between empirical generalizations regarding matters of fact and necessary universals applying to truths of reason. But logical atomism was implicit even in this theory. Statements referring to empirical fact were mere quantitative summaries of particular instances. In the sensationalism which sprang from Hume (and which was left unquestioned by Kant as far as any strictly empirical element was concerned) the implicit particularism was made explicit. But the doctrine that sensations and ideas are so many separate existences was not derived from observation nor from experiment. It was a logical deduction from a prior unexamined concept of the nature of experience. From the same concept it followed that the appearance of stable objects and of general principles of connexion was but an appearance.[2]

Kantianism, then, naturally invoked universal bonds to restore objectivity. But, in so doing, it accepted the particularism of experience and proceeded to supplement it from non-empirical sources. A sensory manifold being all which is really empirical in experience, a reason which transcends experience must provide synthesis. The net outcome might have suggested a correct account of experience. For we have only to forget the apparatus by which the net outcome is arrived at, to have before us the experience of the plain man—a diversity of ceaseless changes connected in all kinds of ways, static and dynamic. This conclusion would deal a deathblow to both empiricism and rationalism. For, making clear the non-empirical character of the alleged manifold of unconnected particulars, it would render unnecessary the appeal to functions of the understanding in order to connect them. With the downfall of the traditional notion of experience, the appeal to reason to supplement its defects becomes superfluous.

The tradition was, however, too strongly entrenched; especially as it furnished the subject-matter of an alleged science of states of mind which were directly known in their very presence. The historic outcome was a new crop of artificial puzzles about relations; it fastened upon philosophy for a long time the quarrel about the a priori and the a posteriori as its chief issue. The controversy is to-day quiescent. Yet it is not at all uncommon to find thinkers modern in tone and intent who regard any philosophy of experience as necessarily committed to denial of the existence of genuinely general propositions, and who take empiricism to be inherently averse to the recognition of the importance of an organizing and constructive intelligence.

The quiescence alluded to is in part due, I think, to sheer weariness. But it is also due to a change of standpoint introduced by biological conceptions; and particularly the discovery of biological continuity from the lower organisms to man. For a short period, Spencerians might connect the doctrine of evolution with the old problem, and use the long temporal accumulation of "experiences" to generate something which, for human experience, is a priori. But the tendency of the biological way of thinking is neither to confirm or negate the Spencerian doctrine, but to shift the issue. In the orthodox position a posteriori and a priori were affairs of knowledge. But it soon becomes obvious that while there is assuredly something a priori—that is to say, native, unlearned, original—in human experience, that something is not knowledge, but is activities made possible by means of established connexions of neurones. This empirical fact does not solve the orthodox problem; it dissolves it. It shows that the problem was misconceived, and solution sought by both parties in the wrong direction.

Organic instincts and organic retention, or habit-forming, are undeniable factors in actual experience. They are factors which effect organization and secure continuity. They are among the specific facts which a description of experience cognizant of the correlation of organic action with the action of other natural objects will include. But while fortunately the contribution of biological science to a truly empirical description of experiencing has outlawed the discussion of the a priori and a posteriori, the transforming effect of the same contributions upon other issues has gone unnoticed, save as pragmatism has made an effort to bring them to recognition.

III

The point seriously at issue in the notion of experience common to both sides in the older controversy thus turns out to be the place of thought or intelligence in experience. Does reason have a distinctive office? Is there a characteristic order of relations contributed by it?

Experience, to return to our positive conception, is primarily what is undergone in connexion with activities whose import lies in their objective consequences—their bearing upon future experiences. Organic functions deal with things as things in course, in operation, in a state of affairs not yet given or completed. What is done with, what is just "there," is of concern only in the potentialities which it may indicate. As ended, as wholly given, it is of no account. But as a sign of what may come, it becomes an indispensable factor in behavior dealing with changes, the outcome of which is not yet determined.

The only power the organism possesses to control its own future depends upon the way its present responses modify changes which are taking place in its medium. A living being may be comparatively impotent, or comparatively free. It is all a matter of the way in which its present reactions to things influence the future reactions of things upon it. Without regard to its wish or intent every act it performs makes some difference in the environment. The change may be trivial as respects its own career and fortune. But it may also be of incalculable importance; it may import harm, destruction, or it may procure well-being.

Is it possible for a living being to increase its control of welfare and success? Can it manage, in any degree, to assure its future? Or does the amount of security depend wholly upon the accidents of the situation? Can it learn? Can it gain ability to assure its future in the present? These questions center attention upon the significance of reflective intelligence in the process of experience. The extent of an agent's capacity for inference, its power to use a given fact as a sign of something not yet given, measures the extent of its ability systematically to enlarge its control of the future.

A being which can use given and finished facts as signs of things to come; which can take given things as evidences of absent things, can, in that degree, forecast the future; it can form reasonable expectations. It is capable of achieving ideas; it is possessed of intelligence. For use of the given or finished to anticipate the consequence of processes going on is precisely what is meant by "ideas," by "intelligence."

As we have already noted, the environment is rarely all of a kind in its bearing upon organic welfare; its most whole-hearted support of life-activities is precarious and temporary. Some environmental changes are auspicious; others are menacing. The secret of success—that is, of the greatest attainable success—is for the organic response to cast in its lot with present auspicious changes to strengthen them and thus to avert the consequences flowing from occurrences of ill-omen. Any reaction is a venture; it involves risk. We always build better or worse than we can foretell. But the organism's fateful intervention in the course of events is blind, its choice is random, except as it can employ what happens to it as a basis of inferring what is likely to happen later. In the degree in which it can read future results in present on-goings, its responsive choice, its partiality to this condition or that, become intelligent. Its bias grows reasonable. It can deliberately, intentionally, participate in the direction of the course of affairs. Its foresight of different futures which result according as this or that present factor predominates in the shaping of affairs permits it to partake intelligently instead of blindly and fatally in the consequences its reactions give rise to. Participate it must, and to its own weal or woe. Inference, the use of what happens, to anticipate what will—or at least may—happen, makes the difference between directed and undirected participation. And this capacity for inferring is precisely the same as that use of natural occurrences for the discovery and determination of consequences—the formation of new dynamic connexions—which constitutes knowledge.

The fact that thought is an intrinsic feature of experience is fatal to the traditional empiricism which makes it an artificial by-product. But for that same reason it is fatal to the historic rationalisms whose justification was the secondary and retrospective position assigned to thought by empirical philosophy. According to the particularism of the latter, thought was inevitably only a bunching together of hard-and-fast separate items; thinking was but the gathering together and tying of items already completely given, or else an equally artificial untying—a mechanical adding and subtracting of the given. It was but a cumulative registration, a consolidated merger; generality was a matter of bulk, not of quality. Thinking was therefore treated as lacking constructive power; even its organizing capacity was but simulated, being in truth but arbitrary pigeon-holing. Genuine projection of the novel, deliberate variation and invention, are idle fictions in such a version of experience. If there ever was creation, it all took place at a remote period. Since then the world has only recited lessons.

The value of inventive construction is too precious to be disposed of in this cavalier way. Its unceremonious denial afforded an opportunity to assert that in addition to experience the subject has a ready-made faculty of thought or reason which transcends experience. Rationalism thus accepted the account of experience given by traditional empiricism, and introduced reason as extra-empirical. There are still thinkers who regard any empiricism as necessarily committed to a belief in a cut-and-dried reliance upon disconnected precedents, and who hold that all systematic organization of past experiences for new and constructive purposes is alien to strict empiricism.

Rationalism never explained, however, how a reason extraneous to experience could enter into helpful relation with concrete experiences. By definition, reason and experience were antithetical, so that the concern of reason was not the fruitful expansion and guidance of the course of experience, but a realm of considerations too sublime to touch, or be touched by, experience. Discreet rationalists confined themselves to theology and allied branches of abtruse science, and to mathematics. Rationalism would have been a doctrine reserved for academic specialists and abstract formalists had it not assumed the task of providing an apologetics for traditional morals and theology, thereby getting into touch with actual human beliefs and concerns. It is notorious that historic empiricism was strong in criticism and in demolition of outworn beliefs, but weak for purposes of constructive social direction. But we frequently overlook the fact that whenever rationalism cut free from conservative apologetics, it was also simply an instrumentality for pointing out inconsistencies and absurdities in existing beliefs—a sphere in which it was immensely useful, as the Enlightenment shows. Leibniz and Voltaire were contemporary rationalists in more senses than one.[3]

The recognition that reflection is a genuine factor within experience and an indispensable factor in that control of the world which secures a prosperous and significant expansion of experience undermines historic rationalism as assuredly as it abolishes the foundations of historic empiricism. The bearing of a correct idea of the place and office of reflection upon modern idealisms is less obvious, but no less certain.

One of the curiosities of orthodox empiricism is that its outstanding speculative problem is the existence of an "external world." For in accordance with the notion that experience is attached to a private subject as its exclusive possession, a world like the one in which we appear to live must be "external" to experience instead of being its subject-matter. I call it a curiosity, for if anything seems adequately grounded empirically it is the existence of a world which resists the characteristic functions of the subject of experience; which goes its way, in some respects, independently of these functions, and which frustrates our hopes and intentions. Ignorance which is fatal; disappointment; the need of adjusting means and ends to the course of nature, would seem to be facts sufficiently characterizing empirical situations as to render the existence of an external world indubitable.

That the description of experience was arrived at by forcing actual empirical facts into conformity with dialectic developments from a concept of a knower outside of the real world of nature is testified to by the historic alliance of empiricism and idealism.[4] According to the most logically consistent editions of orthodox empiricism, all that can be experienced is the fleeting, the momentary, mental state. That alone is absolutely and indubitably present; therefore, it alone is cognitively certain. It alone is knowledge. The existence of the past (and of the future), of a decently stable world and of other selves—indeed, of one's own self—falls outside this datum of experience. These can be arrived at only by inference which is "ejective"—a name given to an alleged type of inference that jumps from experience, as from a springboard, to something beyond experience.

I should not anticipate difficulty in showing that this doctrine is, dialectically, a mass of inconsistencies. Avowedly it is a doctrine of desperation, and as such it is cited here to show the desperate straits to which ignoring empirical facts has reduced a doctrine of experience. More positively instructive are the objective idealisms which have been the offspring of the marriage between the "reason" of historic rationalism and the alleged immediate psychical stuff of historic empiricism. These idealisms have recognized the genuineness of connexions and the impotency of "feeling." They have then identified connexions with logical or rational connexions, and thus treated "the real World" as a synthesis of sentient consciousness by means of a rational self-consciousness introducing objectivity: stability and universality of reference.

Here again, for present purposes, criticism is unnecessary. It suffices to point out that the value of this theory is bound up with the genuineness of the problem of which it purports to be a solution. If the basic concept is a fiction, there is no call for the solution. The more important point is to perceive how far the "thought" which figures in objective idealism comes from meeting the empirical demands made upon actual thought. Idealism is much less formal than historic rationalism. It treats thought, or reason, as constitutive of experience by means of uniting and constructive functions, not as just concerned with a realm of eternal truths apart from experience. On such a view thought certainly loses its abstractness and remoteness. But, unfortunately, in thus gaining the whole world it loses its own self. A world already, in its intrinsic structure, dominated by thought is not a world in which, save by contradiction of premises, thinking has anything to do.

That the doctrine logically results in making change unreal and error unaccountable are consequences of importance in the technique of professional philosophy; in the denial of empirical fact which they imply they seem to many a reductio ad absurdum of the premises from which they proceed. But, after all, such consequences are of only professional import. What is serious, even sinister, is the implied sophistication regarding the place and office of reflection in the scheme of things. A doctrine which exalts thought in name while ignoring its efficacy in fact (that is, its use in bettering life) is a doctrine which cannot be entertained and taught without serious peril. Those who are not concerned with professional philosophy but who are solicitous for intelligence as a factor in the amelioration of actual conditions can but look askance at any doctrine which holds that the entire scheme of things is already, if we but acquire the knack of looking at it aright, fixedly and completely rational. It is a striking manifestation of the extent in which philosophies have been compensatory in quality.[5] But the matter cannot be passed over as if it were simply a question of not grudging a certain amount of consolation to one amid the irretrievable evils of life. For as to these evils no one knows how many are retrievable; and a philosophy which proclaims the ability of a dialectic theory of knowledge to reveal the world as already and eternally a self-luminous rational whole, contaminates the scope and use of thought at its very spring. To substitute the otiose insight gained by manipulation of a formula for the slow coöperative work of a humanity guided by reflective intelligence is more than a technical blunder of speculative philosophers.

A practical crisis may throw the relationship of ideas to life into an exaggerated Brocken-like spectral relief, where exaggeration renders perceptible features not ordinarily noted. The use of force to secure narrow because exclusive aims is no novelty in human affairs. The deploying of all the intelligence at command in order to increase the effectiveness of the force used is not so common, yet presents nothing intrinsically remarkable. The identification of force—military, economic, and administrative—with moral necessity and moral culture is, however, a phenomenon not likely to exhibit itself on a wide scale except where intelligence has already been suborned by an idealism which identifies "the actual with the rational," and thus finds the measure of reason in the brute event determined by superior force. If we are to have a philosophy which will intervene between attachment to rule of thumb muddling and devotion to a systematized subordination of intelligence to preëxistent ends, it can be found only in a philosophy which finds the ultimate measure of intelligence in consideration of a desirable future and in search for the means of bringing it progressively into existence. When professed idealism turns out to be a narrow pragmatism—narrow because taking for granted the finality of ends determined by historic conditions—the time has arrived for a pragmatism which shall be empirically idealistic, proclaiming the essential connexion of intelligence with the unachieved future—with possibilities involving a transfiguration.

IV

Why has the description of experience been so remote from the facts of empirical situations? To answer this question throws light upon the submergence of recent philosophizing in epistemology—that is, in discussions of the nature, possibility, and limits of knowledge in general, and in the attempt to reach conclusions regarding the ultimate nature of reality from the answers given to such questions.

The reply to the query regarding the currency of a non-empirical doctrine of experience (even among professed empiricists) is that the traditional account is derived from a conception once universally entertained regarding the subject or bearer or center of experience. The description of experience has been forced into conformity with this prior conception; it has been primarily a deduction from it, actual empirical facts being poured into the moulds of the deductions. The characteristic feature of this prior notion is the assumption that experience centers in, or gathers about, or proceeds from a center or subject which is outside the course of natural existence, and set over against it:—it being of no importance, for present purposes, whether this antithetical subject is termed soul, or spirit, or mind, or ego, or consciousness, or just knower or knowing subject.

There are plausible grounds for thinking that the currency of the idea in question lies in the form which men's religious preoccupations took for many centuries. These were deliberately and systematically other-worldly. They centered about a Fall which was not an event in nature, but an aboriginal catastrophe that corrupted Nature; about a redemption made possible by supernatural means; about a life in another world—essentially, not merely spatially, Other. The supreme drama of destiny took place in a soul or spirit which, under the circumstances, could not be conceived other than as non-natural—extra-natural, if not, strictly speaking, supernatural. When Descartes and others broke away from medieval interests, they retained as commonplaces its intellectual apparatus: Such as, knowledge is exercised by a power that is extra-natural and set over against the world to be known. Even if they had wished to make a complete break, they had nothing to put as knower in the place of the soul. It may be doubted whether there was any available empirical substitute until science worked out the fact that physical changes are functional correlations of energies, and that man is continuous with other forms of life, and until social life had developed an intellectually free and responsible individual as its agent.

But my main point is not dependent upon any particular theory as to the historic origin of the notion about the bearer of experience. The point is there on its own account. The essential thing is that the bearer was conceived as outside of the world; so that experience consisted in the bearer's being affected through a type of operations not found anywhere in the world, while knowledge consists in surveying the world, looking at it, getting the view of a spectator.

The theological problem of attaining knowledge of God as ultimate reality was transformed in effect into the philosophical problem of the possibility of attaining knowledge of reality. For how is one to get beyond the limits of the subject and subjective occurrences? Familiarity breeds credulity oftener than contempt. How can a problem be artificial when men have been busy discussing it almost for three hundred years? But if the assumption that experience is something set over against the world is contrary to fact, then the problem of how self or mind or subjective experience or consciousness can reach knowledge of an external world is assuredly a meaningless problem. Whatever questions there may be about knowledge, they will not be the kind of problems which have formed epistemology.

The problem of knowledge as conceived in the industry of epistemology is the problem of knowledge in general—of the possibility, extent, and validity of knowledge in general. What does this "in general" mean? In ordinary life there are problems a-plenty of knowledge in particular; every conclusion we try to reach, theoretical or practical, affords such a problem. But there is no problem of knowledge in general. I do not mean, of course, that general statements cannot be made about knowledge, or that the problem of attaining these general statements is not a genuine one. On the contrary, specific instances of success and failure in inquiry exist, and are of such a character that one can discover the conditions conducing to success and failure. Statement of these conditions constitutes logic, and is capable of being an important aid in proper guidance of further attempts at knowing. But this logical problem of knowledge is at the opposite pole from the epistemological. Specific problems are about right conclusions to be reached—which means, in effect, right ways of going about the business of inquiry. They imply a difference between knowledge and error consequent upon right and wrong methods of inquiry and testing; not a difference between experience and the world. The problem of knowledge überhaupt exists because it is assumed that there is a knower in general, who is outside of the world to be known, and who is defined in terms antithetical to the traits of the world. With analogous assumptions, we could invent and discuss a problem of digestion in general. All that would be required would be to conceive the stomach and food-material as inhabiting different worlds. Such an assumption would leave on our hands the question of the possibility, extent, nature, and genuineness of any transaction between stomach and food.

But because the stomach and food inhabit a continuous stretch of existence, because digestion is but a correlation of diverse activities in one world, the problems of digestion are specific and plural: What are the particular correlations which constitute it? How does it proceed in different situations? What is favorable and what unfavorable to its best performance?—and so on. Can one deny that if we were to take our clue from the present empirical situation, including the scientific notion of evolution (biological continuity) and the existing arts of control of nature, subject and object would be treated as occupying the same natural world as unhesitatingly as we assume the natural conjunction of an animal and its food? Would it not follow that knowledge is one way in which natural energies coöperate? Would there be any problem save discovery of the peculiar structure of this coöperation, the conditions under which it occurs to best effect, and the consequences which issue from its occurrence?

It is a commonplace that the chief divisions of modern philosophy, idealism in its different kinds, realisms of various brands, so-called common-sense dualism, agnosticism, relativism, phenomenalism, have grown up around the epistemological problem of the general relation of subject and object. Problems not openly epistemological, such as whether the relation of changes in consciousness to physical changes is one of interaction, parallelism, or automatism have the same origin. What becomes of philosophy, consisting largely as it does of different answers to these questions, in case the assumptions which generate the questions have no empirical standing? Is it not time that philosophers turned from the attempt to determine the comparative merits of various replies to the questions to a consideration of the claims of the questions?

When dominating religious ideas were built up about the idea that the self is a stranger and pilgrim in this world; when morals, falling in line, found true good only in inner states of a self inaccessible to anything but its own private introspection; when political theory assumed the finality of disconnected and mutually exclusive personalities, the notion that the bearer of experience is antithetical to the world instead of being in and of it was congenial. It at least had the warrant of other beliefs and aspirations. But the doctrine of biological continuity or organic evolution has destroyed the scientific basis of the conception. Morally, men are now concerned with the amelioration of the conditions of the common lot in this world. Social sciences recognize that associated life is not a matter of physical juxtaposition, but of genuine intercourse—of community of experience in a non-metaphorical sense of community. Why should we longer try to patch up and refine and stretch the old solutions till they seem to cover the change of thought and practice? Why not recognize that the trouble is with the problem?

A belief in organic evolution which does not extend unreservedly to the way in which the subject of experience is thought of, and which does not strive to bring the entire theory of experience and knowing into line with biological and social facts, is hardly more than Pickwickian. There are many, for example, who hold that dreams, hallucinations, and errors cannot be accounted for at all except on the theory that a self (or "consciousness") exercises a modifying influence upon the "real object." The logical assumption is that consciousness is outside of the real object; that it is something different in kind, and therefore has the power of changing "reality" into appearance, of introducing "relativities" into things as they are in themselves—in short, of infecting real things with subjectivity. Such writers seem unaware of the fact that this assumption makes consciousness supernatural in the literal sense of the word; and that, to say the least, the conception can be accepted by one who accepts the doctrine of biological continuity only after every other way of dealing with the facts has been exhausted.

Realists, of course (at least some of the Neo-realists), deny any such miraculous intervention of consciousness. But they[6] admit the reality of the problem; denying only this particular solution, they try to find some other way out, which will still preserve intact the notion of knowledge as a relationship of a general sort between subject and object.

Now dreams and hallucinations, errors, pleasures, and pains, possibly "secondary" qualities, do not occur save where there are organic centers of experience. They cluster about a subject. But to treat them as things which inhere exclusively in the subject; or as posing the problem of a distortion of the real object by a knower set over against the world, or as presenting facts to be explained primarily as cases of contemplative knowledge, is to testify that one has still to learn the lesson of evolution in its application to the affairs in hand.

If biological development be accepted, the subject of experience is at least an animal, continuous with other organic forms in a process of more complex organization. An animal in turn is at least continuous with chemico-physical processes which, in living things, are so organized as really to constitute the activities of life with all their defining traits. And experience is not identical with brain action; it is the entire organic agent-patient in all its interaction with the environment, natural and social. The brain is primarily an organ of a certain kind of behavior, not of knowing the world. And to repeat what has already been said, experiencing is just certain modes of interaction, of correlation, of natural objects among which the organism happens, so to say, to be one. It follows with equal force that experience means primarily not knowledge, but ways of doing and suffering. Knowing must be described by discovering what particular mode—qualitatively unique—of doing and suffering it is. As it is, we find experience assimilated to a non-empirical concept of knowledge, derived from an antecedent notion of a spectator outside of the world.*[7]

In short, the epistemological fashion of conceiving dreams, errors, "relativities," etc., depends upon the isolation of mind from intimate participation with other changes in the same continuous nexus. Thus it is like contending that when a bottle bursts, the bottle is, in some self-contained miraculous way, exclusively responsible. Since it is the nature of a bottle to be whole so as to retain fluids, bursting is an abnormal event—comparable to an hallucination. Hence it cannot belong to the "real" bottle; the "subjectivity" of glass is the cause. It is obvious that since the breaking of glass is a case of specific correlation of natural energies, its accidental and abnormal character has to do with consequences, not with causation. Accident is interference with the consequences for which the bottle is intended. The bursting considered apart from its bearing on these consequences is on a plane with any other occurrence in the wide world. But from the standpoint of a desired future, bursting is an anomaly, an interruption of the course of events.

The analogy with the occurrence of dreams, hallucinations, etc., seems to me exact. Dreams are not something outside of the regular course of events; they are in and of it. They are not cognitive distortions of real things; they are more real things. There is nothing abnormal in their existence, any more than there is in the bursting of a bottle.[8] But they may be abnormal, from the standpoint of their influence, of their operation as stimuli in calling out responses to modify the future. Dreams have often been taken as prognostics of what is to happen; they have modified conduct. A hallucination may lead a man to consult a doctor; such a consequence is right and proper. But the consultation indicates that the subject regarded it as an indication of consequences which he feared: as a symptom of a disturbed life. Or the hallucination may lead him to anticipate consequences which in fact flow only from the possession of great wealth. Then the hallucination is a disturbance of the normal course of events; the occurrence is wrongly used with reference to eventualities.

To regard reference to use and to desired and intended consequences as involving a "subjective" factor is to miss the point, for this has regard to the future. The uses to which a bottle are put are not mental; they do not consist of physical states; they are further correlations of natural existences. Consequences in use are genuine natural events; but they do not occur without the intervention of behavior involving anticipation of a future. The case is not otherwise with an hallucination. The differences it makes are in any case differences in the course of the one continuous world. The important point is whether they are good or bad differences. To use the hallucination as a sign of organic lesions that menace health means the beneficial result of seeing a physician; to respond to it as a sign of consequences such as actually follow only from being persecuted is to fall into error—to be abnormal. The persecutors are "unreal"; that is, there are no things which act as persecutors act; but the hallucination exists. Given its conditions it is as natural as any other event, and poses only the same kind of problem as is put by the occurrence of, say, a thunderstorm. The "unreality" of persecution is not, however, a subjective matter; it means that conditions do not exist for producing the future consequences which are now anticipated and reacted to. Ability to anticipate future consequences and to respond to them as stimuli to present behavior may well define what is meant by a mind or by "consciousness."[9] But this is only a way of saying just what kind of a real or natural existence the subject is; it is not to fall back on a preconception about an unnatural subject in order to characterize the occurrence of error.

Although the discussion may be already labored, let us take another example—the occurrence of disease. By definition it is pathological, abnormal. At one time in human history this abnormality was taken to be something dwelling in the intrinsic nature of the event—in its existence irrespective of future consequences. Disease was literally extra-natural and to be referred to demons, or to magic. No one to-day questions its naturalness—its place in the order of natural events. Yet it is abnormal—for it operates to effect results different from those which follow from health. The difference is a genuine empirical difference, not a mere mental distinction. From the standpoint of bearing on a subsequent course of events disease is unnatural, in spite of the naturalness of its occurrence and origin.

The habit of ignoring reference to the future is responsible for the assumption that to admit human participation in any form is to admit the "subjective" in a sense which alters the objective into the phenomenal. There have been those who, like Spinoza, regarded health and disease, good and ill, as equally real and equally unreal. However, only a few consistent materialists have included truth along with error as merely phenomenal and subjective. But if one does not regard movement toward possible consequences as genuine, wholesale denial of existential validity to all these distinctions is the only logical course. To select truth as objective and error as "subjective" is, on this basis, an unjustifiably partial procedure. Take everything as fixedly given, and both truth and error are arbitrary insertions into fact. Admit the genuineness of changes going on, and capacity for its direction through organic action based on foresight, and both truth and falsity are alike existential. It is human to regard the course of events which is in line with our own efforts as the regular course of events, and interruptions as abnormal, but this partiality of human desire is itself a part of what actually takes place.

It is now proposed to take a particular case of the alleged epistemological predicament for discussion, since the entire ground cannot be covered. I think, however, the instance chosen is typical, so that the conclusion reached may be generalized.

The instance is that of so-called relativity in perception. There are almost endless instances; the stick bent in water; the whistle changing pitch with change of distance from the ear; objects doubled when the eye is pushed; the destroyed star still visible, etc., etc. For our consideration we may take the case of a spherical object that presents itself to one observer as a flat circle, to another as a somewhat distorted elliptical surface. This situation gives empirical proof, so it is argued, of the difference between a real object and mere appearance. Since there is but one object, the existence of two subjects is the sole differentiating factor. Hence the two appearances of the one real object is proof of the intervening distorting action of the subject. And many of the Neo-realists who deny the difference in question, admit the case to be one of knowledge and accordingly to constitute an epistemological problem. They have in consequence developed wonderfully elaborate schemes of sundry kinds to maintain "epistemological monism" intact.

Let us try to keep close to empirical facts. In the first place the two unlike appearances of the one sphere are physically necessary because of the laws of reaction of light. If the one sphere did not assume these two appearances under given conditions, we should be confronted with a hopelessly irreconcilable discrepancy in the behavior of natural energy. That the result is natural is evidenced by the fact that two cameras—or other arrangements of apparatus for reflecting light—yield precisely the same results. Photographs are as genuinely physical existences as the original sphere; and they exhibit the two geometrical forms.

The statement of these facts makes no impression upon the confirmed epistemologist; he merely retorts that as long as it is admitted that the organism is the cause of a sphere being seen, from different points, as a circular and as an elliptical surface, the essence of his contention—the modification of the real object by the subject—is admitted. To the question why the same logic does not apply to photographic records he makes, as far as I know, no reply at all.

The source of the difficulty is not hard to see. The objection assumes that the alleged modifications of the real object are cases of knowing and hence attributable to the influence of a knower. Statements which set forth the doctrine will always be found to refer to the organic factor, to the eye, as an observer or a percipient. Even when reference is made to a lens or a mirror, language is sometimes used which suggests that the writer's naïveté is sufficiently gross to treat these physical factors as if they were engaged in perceiving the sphere. But as it is evident that the lens operates as a physical factor in correlation with other physical factors—notably light—so it ought to be evident that the intervention of the optical apparatus of the eye is a purely non-cognitive matter. The relation in question is not one between a sphere and a would-be knower of it, unfortunately condemned by the nature of the knowing apparatus to alter the thing he would know; it is an affair of the dynamic interaction of two physical agents in producing a third thing, an effect;—an affair of precisely the same kind as in any physical conjoint action, say the operation of hydrogen and oxygen in producing water. To regard the eye as primarily a knower, an observer, of things, is as crass as to assign that function to a camera. But unless the eye (or optical apparatus, or brain, or organism) be so regarded, there is absolutely no problem of observation or of knowledge in the case of the occurrence of elliptical and circular surfaces. Knowledge does not enter into the affair at all till after these forms of refracted light have been produced. About them there is nothing unreal. Light is really, physically, existentially, refracted into these forms. If the same spherical form upon refracting light to physical objects in two quite different positions produced the same geometric forms, there would, indeed, be something to marvel at—as there would be if wax produced the same results in contact simultaneously with a cold body and with a warm one. Why talk about the real object in relation to a knower when what is given is one real thing in dynamic connection with another real thing?

The way of dealing with the case will probably meet with a retort; at least, it has done so before. It has been said that the account given above and the account of traditional subjectivism differ only verbally. The essential thing in both, so it is said, is the admission that an activity of a self or subject or organism makes a difference in the real object. Whether the subject makes this difference in the very process of knowing or makes it prior to the act of knowing is a minor matter; what is important is that the known thing has, by the time it is known, been "subjectified."

The objection gives a convenient occasion for summarizing the main points of the argument. On the one hand, the retort of the objector depends upon talking about the real object. Employ the term "a real object," and the change produced by the activity characteristic of the optical apparatus is of just the same kind as that of the camera lens or that of any other physical agency. Every event in the world marks a difference made to one existence in active conjunction with some other existence. And, as for the alleged subjectivity, if subjective is used merely as an adjective to designate the specific activity of a particular existence, comparable, say, to the term feral, applied to tiger, or metallic, applied to iron, then of course reference to subjective is legitimate. But it is also tautological. It is like saying that flesh eaters are carnivorous. But the term "subjective" is so consecrated to other uses, usually implying invidious contrast with objectivity (while subjective in the sense just suggested means specific mode of objectivity), that it is difficult to maintain this innocent sense. Its use in any disparaging way in the situation before us—any sense implicating contrast with a real object—assumes that the organism ought not to make any difference when it operates in conjunction with other things. Thus we run to earth that assumption that the subject is heterogeneous from every other natural existence; it is to be the one otiose, inoperative thing in a moving world—our old assumption of the self as outside of things.[10]

What and where is knowledge in the case we have been considering? Not, as we have already seen, in the production of forms of light having a circular and elliptical surface. These forms are natural happenings. They may enter into knowledge or they may not, according to circumstances. Countless such refractive changes take place without being noted.[11] When they become subject-matter for knowledge, the inquiry they set on foot may take on an indefinite variety of forms. One may be interested in ascertaining more about the structural peculiarities of the forms themselves; one may be interested in the mechanism of their production; one may find problems in projective geometry, or in drawing and painting—all depending upon the specific matter-of-fact context. The forms may be objectives of knowledge—of reflective examination—or they may be means of knowing something else. It may happen—under some circumstances it does happen—that the objective of inquiry is the nature of the geometric form which, when refracting light, gives rise to these other forms. In this case the sphere is the thing known, and in this case, the forms of light are signs or evidence of the conclusion to be drawn. There is no more reason for supposing that they are (mis)knowledges of the sphere—that the sphere is necessarily and from the start what one is trying to know—than for supposing that the position of the mercury in the thermometer tube is a cognitive distortion of atmospheric pressure. In each case (that of the mercury and that of, say, a circular surface) the primary datum is a physical happening. In each case it may be used, upon occasion, as a sign or evidence of the nature of the causes which brought it about. Given the position in question, the circular form would be an intrinsically unreliable evidence of the nature and position of the spherical body only in case it, as the direct datum of perception, were not what it is—a circular form.

I confess that all this seems so obvious that the reader is entitled to inquire into the motive for reciting such plain facts. Were it not for the persistence of the epistemological problem it would be an affront to the reader's intelligence to dwell upon them. But as long as such facts as we have been discussing furnish the subject-matter with which philosophizing is peculiarly concerned, these commonplaces must be urged and reiterated. They bear out two contentions which are important at the juncture, although they will lose special significance as soon as these are habitually recognized: Negatively, a prior and non-empirical notion of the self is the source of the prevailing belief that experience as such is primarily cognitional—a knowledge affair; positively, knowledge is always a matter of the use that is made of experienced natural events, a use in which given things are treated as indications of what will be experienced under different conditions.

Let us make one effort more to clear up these points. Suppose it is a question of knowledge of water. The thing to be known does not present itself primarily as a matter of knowledge-and-ignorance at all. It occurs as a stimulus to action and as the source of certain undergoings. It is something to react to:—to drink, to wash with, to put out fire with, and also something that reacts unexpectedly to our reactions, that makes us undergo disease, suffocation, drowning. In this twofold way, water or anything else enters into experience. Such presence in experience has of itself nothing to do with knowledge or consciousness; nothing that is in the sense of depending upon them, though it has everything to do with knowledge and consciousness in the sense that the latter depends upon prior experience of this non-cognitive sort. Man's experience is what it is because his response to things (even successful response) and the reactions of things to his life, are so radically different from knowledge. The difficulties and tragedies of life, the stimuli to acquiring knowledge, lie in the radical disparity of presence-in-experience and presence-in-knowing. Yet the immense importance of knowledge experience, the fact that turning presence-in-experience over into presence-in-a-knowledge-experience is the sole mode of control of nature, has systematically hypnotized European philosophy since the time of Socrates into thinking that all experiencing is a mode of knowing, if not good knowledge, then a low-grade or confused or implicit knowledge.

When water is an adequate stimulus to action or when its reactions oppress and overwhelm us, it remains outside the scope of knowledge. When, however, the bare presence of the thing (say, as optical stimulus) ceases to operate directly as stimulus to response and begins to operate in connection with a forecast of the consequences it will effect when responded to, it begins to acquire meaning—to be known, to be an object. It is noted as something which is wet, fluid, satisfies thirst, allays uneasiness, etc. The conception that we begin with a known visual quality which is thereafter enlarged by adding on qualities apprehended by the other senses does not rest upon experience; it rests upon making experience conform to the notion that every experience must be a cognitive noting. As long as the visual stimulus operates as a stimulus on its own account, there is no apprehension, no noting, of color or light at all. To much the greater portion of sensory stimuli we react in precisely this wholly non-cognitive way. In the attitude of suspended response in which consequences are anticipated, the direct stimulus becomes a sign or index of something else—and thus matter of noting or apprehension or acquaintance, or whatever term may be employed. This difference (together, of course, with the consequences which go with it) is the difference which the natural event of knowing makes to the natural event of direct organic stimulation. It is no change of a reality into an unreality, of an object into something subjective; it is no secret, illicit, or epistemological transformation; it is a genuine acquisition of new and distinctive features through entering into relations with things with which it was not formerly connected—namely, possible and future things.

But, replies some one so obsessed with the epistemological point of view that he assumes that the prior account is a rival epistemology in disguise, all this involves no change in Reality, no difference made to Reality. Water was all the time all the things it is ever found out to be. Its real nature has not been altered by knowing it; any such alteration means a mis-knowing.

In reply let it be said,—once more and finally,—there is no assertion or implication about the real object or the real world or the reality. Such an assumption goes with that epistemological universe of discourse which has to be abandoned in an empirical universe of discourse. The change is of a real object. An incident of the world operating as a physiologically direct stimulus is assuredly a reality. Responded to, it produces specific consequences in virtue of the response. Water is not drunk unless somebody drinks it; it does not quench thirst unless a thirsty person drinks it—and so on. Consequences occur whether one is aware of them or not; they are integral facts in experience. But let one of these consequences be anticipated and let it, as anticipated, become an indispensable element in the stimulus, and then there is a known object. It is not that knowing produces a change, but that it is a change of the specific kind described. A serial process, the successive portions of which are as such incapable of simultaneous occurrence, is telescoped and condensed into an object, a unified inter-reference of contemporaneous properties, most of which express potentialities rather than completed data.

Because of this change, an object possesses truth or error (which the physical occurrence as such never has); it is classifiable as fact or fantasy; it is of a sort or kind, expresses an essence or nature, possesses implications, etc., etc. That is to say, it is marked by specifiable logical traits not found in physical occurrences as such. Because objective idealisms have seized upon these traits as constituting the very essence of Reality is no reason for proclaiming that they are ready-made features of physical happenings, and hence for maintaining that knowing is nothing but an appearance of things on a stage for which "consciousness" supplies the footlights. For only the epistemological predicament leads to "presentations" being regarded as cognitions of things which were previously unpresented. In any empirical situation of everyday life or of science, knowledge signifies something stated or inferred of another thing. Visible water is not a more less erroneous presentation of H₂O, but H₂O is a knowledge about the thing we see, drink, wash with, sail on, and use for power.

A further point and the present phase of discussion terminates. Treating knowledge as a presentative relation between the knower and object makes it necessary to regard the mechanism of presentation as constituting the act of knowing. Since things may be presented in sense-perception, in recollection, in imagination and in conception, and since the mechanism in every one of these four styles of presentation is sensory-cerebral the problem of knowing becomes a mind-body problem.[12] The psychological, or physiological, mechanism of presentation involved in seeing a chair, remembering what I ate yesterday for luncheon, imagining the moon the size of a cart wheel, conceiving a mathematical continuum is identified with the operation of knowing. The evil consequences are twofold. The problem of the relation of mind and body has become a part of the problem of the possibility of knowledge in general, to the further complication of a matter already hopelessly constrained. Meantime the actual process of knowing, namely, operations of controlled observation, inference, reasoning, and testing, the only process with intellectual import, is dismissed as irrelevant to the theory of knowing. The methods of knowing practised in daily life and science are excluded from consideration in the philosophical theory of knowing. Hence the constructions of the latter become more and more elaborately artificial because there is no definite check upon them. It would be easy to quote from epistemological writers statements to the effect that these processes (which supply the only empirically verifiable facts of knowing) are merely inductive in character, or even that they are of purely psychological significance. It would be difficult to find a more complete inversion of the facts than in the latter statement, since presentation constitutes in fact the psychological affair. A confusion of logic with physiological physiology has bred hybrid epistemology, with the amazing result that the technique of effective inquiry is rendered irrelevant to the theory of knowing, and those physical events involved in the occurrence of data for knowing are treated as if they constituted the act of knowing.

V

What are the bearings of our discussion upon the conception of the present scope and office of philosophy? What do our conclusions indicate and demand with reference to philosophy itself? For the philosophy which reaches such conclusions regarding knowledge and mind must apply them, sincerely and whole-heartedly, to its idea of its own nature. For philosophy claims to be one form or mode of knowing. If, then, the conclusion is reached that knowing is a way of employing empirical occurrences with respect to increasing power to direct the consequences which flow from things, the application of the conclusion must be made to philosophy itself. It, too, becomes not a contemplative survey of existence nor an analysis of what is past and done with, but an outlook upon future possibilities with reference to attaining the better and averting the worse. Philosophy must take, with good grace, its own medicine.

It is easier to state the negative results of the changed idea of philosophy than the positive ones. The point that occurs to mind most readily is that philosophy will have to surrender all pretension to be peculiarly concerned with ultimate reality, or with reality as a complete (i.e., completed) whole: with the real object. The surrender is not easy of achievement. The philosophic tradition that comes to us from classic Greek thought and that was reinforced by Christian philosophy in the Middle Ages discriminates philosophical knowing from other modes of knowing by means of an alleged peculiarly intimate concern with supreme, ultimate, true reality. To deny this trait to philosophy seems to many to be the suicide of philosophy; to be a systematic adoption of skepticism or agnostic positivism.

The pervasiveness of the tradition is shown in the fact that so vitally a contemporary thinker as Bergson, who finds a philosophic revolution involved in abandonment of the traditional identification of the truly real with the fixed (an identification inherited from Greek thought), does not find it in his heart to abandon the counterpart identification of philosophy with search for the truly Real; and hence finds it necessary to substitute an ultimate and absolute flux for an ultimate and absolute permanence. Thus his great empirical services in calling attention to the fundamental importance of considerations of time for problems of life and mind get compromised with a mystic, non-empirical "Intuition"; and we find him preoccupied with solving, by means of his new idea of ultimate reality, the traditional problems of realities-in-themselves and phenomena, matter and mind, free-will and determinism, God and the world. Is not that another evidence of the influence of the classic idea about philosophy?

Even the new realists are not content to take their realism as a plea for approaching subject-matter directly instead of through the intervention of epistemological apparatus; they find it necessary first to determine the status of the real object. Thus they too become entangled in the problem of the possibility of error, dreams, hallucinations, etc., in short, the problem of evil. For I take it that an uncorrupted realism would accept such things as real events, and find in them no other problems than those attending the consideration of any real occurrence—namely, problems of structure, origin, and operation.

It is often said that pragmatism, unless it is content to be a contribution to mere methodology, must develop a theory of Reality. But the chief characteristic trait of the pragmatic notion of reality is precisely that no theory of Reality in general, überhaupt, is possible or needed. It occupies the position of an emancipated empiricism or a thoroughgoing naïve realism. It finds that "reality" is a denotative term, a word used to designate indifferently everything that happens. Lies, dreams, insanities, deceptions, myths, theories are all of them just the events which they specifically are. Pragmatism is content to take its stand with science; for science finds all such events to be subject-matter of description and inquiry—just like stars and fossils, mosquitoes and malaria, circulation and vision. It also takes its stand with daily life, which finds that such things really have to be reckoned with as they occur interwoven in the texture of events.

The only way in which the term reality can ever become more than a blanket denotative term is through recourse to specific events in all their diversity and thatness. Speaking summarily, I find that the retention by philosophy of the notion of a Reality feudally superior to the events of everyday occurrence is the chief source of the increasing isolation of philosophy from common sense and science. For the latter do not operate in any such region. As with them of old, philosophy in dealing with real difficulties finds itself still hampered by reference to realities more real, more ultimate, than those which directly happen.

I have said that identifying the cause of philosophy with the notion of superior reality is the cause of an increasing isolation from science and practical life. The phrase reminds us that there was a time when the enterprise of science and the moral interests of men both moved in a universe invidiously distinguished from that of ordinary occurrence. While all that happens is equally real—since it really happens—happenings are not of equal worth. Their respective consequences, their import, varies tremendously. Counterfeit money, although real (or rather because real), is really different from valid circulatory medium, just as disease is really different from health; different in specific structure and so different in consequences. In occidental thought, the Greeks were the first to draw the distinction between the genuine and the spurious in a generalized fashion and to formulate and enforce its tremendous significance for the conduct of life. But since they had at command no technique of experimental analysis and no adequate technique of mathematical analysis, they were compelled to treat the difference of the true and the false, the dependable and the deceptive, as signifying two kinds of existence, the truly real and the apparently real.

Two points can hardly be asserted with too much emphasis. The Greeks were wholly right in the feeling that questions of good and ill, as far as they fall within human control, are bound up with discrimination of the genuine from the spurious, of "being" from what only pretends to be. But because they lacked adequate instrumentalities for coping with this difference in specific situations, they were forced to treat the difference as a wholesale and rigid one. Science was concerned with vision of ultimate and true reality; opinion was concerned with getting along with apparent realities. Each had its appropriate region permanently marked off. Matters of opinion could never become matters of science; their intrinsic nature forbade. When the practice of science went on under such conditions, science and philosophy were one and the same thing. Both had to do with ultimate reality in its rigid and insuperable difference from ordinary occurrences.

We have only to refer to the way in which medieval life wrought the philosophy of an ultimate and supreme reality into the context of practical life to realize that for centuries political and moral interests were bound up with the distinction between the absolutely real and the relatively real. The difference was no matter of a remote technical philosophy, but one which controlled life from the cradle to the grave, from the grave to the endless life after death. By means of a vast institution, which in effect was state as well as church, the claims of ultimate reality were enforced; means of access to it were provided. Acknowledgment of The Reality brought security in this world and salvation in the next. It is not necessary to report the story of the change which has since taken place. It is enough for our purposes to note that none of the modern philosophies of a superior reality, or the real object, idealistic or realistic, holds that its insight makes a difference like that between sin and holiness, eternal condemnation and eternal bliss. While in its own context the philosophy of ultimate reality entered into the vital concerns of men, it now tends to be an ingenious dialectic exercised in professorial corners by a few who have retained ancient premises while rejecting their application to the conduct of life.

The increased isolation from science of any philosophy identified with the problem of the real is equally marked. For the growth of science has consisted precisely in the invention of an equipment, a technique of appliances and procedures, which, accepting all occurrences as homogeneously real, proceeds to distinguish the authenticated from the spurious, the true from the false, by specific modes of treatment in specific situations. The procedures of the trained engineer, of the competent physician, of the laboratory expert, have turned out to be the only ways of discriminating the counterfeit from the valid. And they have revealed that the difference is not one of antecedent fixity of existence, but one of mode of treatment and of the consequences thereon attendant. After mankind has learned to put its trust in specific procedures in order to make its discriminations between the false and the true, philosophy arrogates to itself the enforcement of the distinction at its own cost.

More than once, this essay has intimated that the counterpart of the idea of invidiously real reality is the spectator notion of knowledge. If the knower, however defined, is set over against the world to be known, knowing consists in possessing a transcript, more or less accurate but otiose, of real things. Whether this transcript is presentative in character (as realists say) or whether it is by means of states of consciousness which represent things (as subjectivists say), is a matter of great importance in its own context. But, in another regard, this difference is negligible in comparison with the point in which both agree. Knowing is viewing from outside. But if it be true that the self or subject of experience is part and parcel of the course of events, it follows that the self becomes a knower. It becomes a mind in virtue of a distinctive way of partaking in the course of events. The significant distinction is no longer between the knower and the world; it is between different ways of being in and of the movement of things; between a brute physical way and a purposive, intelligent way.

There is no call to repeat in detail the statements which have been advanced. Their net purport is that the directive presence of future possibilities in dealing with existent conditions is what is meant by knowing; that the self becomes a knower or mind when anticipation of future consequences operates as its stimulus. What we are now concerned with is the effect of this conception upon the nature of philosophic knowing.

As far as I can judge, popular response to pragmatic philosophy was moved by two quite different considerations. By some it was thought to provide a new species of sanctions, a new mode of apologetics, for certain religious ideas whose standing had been threatened. By others, it was welcomed because it was taken as a sign that philosophy was about to surrender its otiose and speculative remoteness; that philosophers were beginning to recognize that philosophy is of account only if, like everyday knowing and like science, it affords guidance to action and thereby makes a difference in the event. It was welcomed as a sign that philosophers were willing to have the worth of their philosophizing measured by responsible tests.

I have not seen this point of view emphasized, or hardly recognized, by professional critics. The difference of attitude can probably be easily explained. The epistemological universe of discourse is so highly technical that only those who have been trained in the history of thought think in terms of it. It did not occur, accordingly, to non-technical readers to interpret the doctrine that the meaning and validity of thought are fixed by differences made in consequences and in satisfactoriness, to mean consequences in personal feelings. Those who were professionally trained, however, took the statement to mean that consciousness or mind in the mere act of looking at things modifies them. It understood the doctrine of test of validity by consequences to mean that apprehensions and conceptions are true if the modifications affected by them were of an emotionally desirable tone.

Prior discussion should have made it reasonably clear that the source of this misunderstanding lies in the neglect of temporal considerations. The change made in things by the self in knowing is not immediate and, so to say, cross-sectional. It is longitudinal—in the redirection given to changes already going on. Its analogue is found in the changes which take place in the development of, say, iron ore into a watch-spring, not in those of the miracle of transubstantiation. For the static, cross-sectional, non-temporal relation of subject and object, the pragmatic hypothesis substitutes apprehension of a thing in terms of the results in other things which it is tending to effect. For the unique epistemological relation, it substitutes a practical relation of a familiar type:—responsive behavior which changes in time the subject-matter to which it applies. The unique thing about the responsive behavior which constitutes knowing is the specific difference which marks it off from other modes of response, namely, the part played in it by anticipation and prediction. Knowing is the act, stimulated by this foresight, of securing and averting consequences. The success of the achievement measures the standing of the foresight by which response is directed. The popular impression that pragmatic philosophy means that philosophy shall develop ideas relevant to the actual crises of life, ideas influential in dealing with them and tested by the assistance they afford, is correct.

Reference to practical response suggests, however, another misapprehension. Many critics have jumped at the obvious association of the word pragmatic with practical. They have assumed that the intent is to limit all knowledge, philosophic included, to promoting "action," understanding by action either just any bodily movement, or those bodily movements which conduce to the preservation and grosser well-being of the body. James' statement, that general conceptions must "cash in" has been taken (especially by European critics) to mean that the end and measure of intelligence lies in the narrow and coarse utilities which it produces. Even an acute American thinker, after first criticizing pragmatism as a kind of idealistic epistemology, goes on to treat it as a doctrine which regards intelligence as a lubricating oil facilitating the workings of the body.

One source of the misunderstanding is suggested by the fact that "cashing in" to James meant that a general idea must always be capable of verification in specific existential cases. The notion of "cashing in" says nothing about the breadth or depth of the specific consequences. As an empirical doctrine, it could not say anything about them in general; the specific cases must speak for themselves. If one conception is verified in terms of eating beefsteak, and another in terms of a favorable credit balance in the bank, that is not because of anything in the theory, but because of the specific nature of the conceptions in question, and because there exist particular events like hunger and trade. If there are also existences in which the most liberal esthetic ideas and the most generous moral conceptions can be verified by specific embodiment, assuredly so much the better. The fact that a strictly empirical philosophy was taken by so many critics to imply an a priori dogma about the kind of consequences capable of existence is evidence, I think, of the inability of many philosophers to think in concretely empirical terms. Since the critics were themselves accustomed to get results by manipulating the concepts of "consequences" and of "practice," they assumed that even a would-be empiricist must be doing the same sort of thing. It will, I suppose, remain for a long time incredible to some that a philosopher should really intend to go to specific experiences to determine of what scope and depth practice admits, and what sort of consequences the world permits to come into being. Concepts are so clear; it takes so little time to develop their implications; experiences are so confused, and it requires so much time and energy to lay hold of them. And yet these same critics charge pragmatism with adopting subjective and emotional standards!

As a matter of fact, the pragmatic theory of intelligence means that the function of mind is to project new and more complex ends—to free experience from routine and from caprice. Not the use of thought to accomplish purposes already given either in the mechanism of the body or in that of the existent state of society, but the use of intelligence to liberate and liberalize action, is the pragmatic lesson. Action restricted to given and fixed ends may attain great technical efficiency; but efficiency is the only quality to which it can lay claim. Such action is mechanical (or becomes so), no matter what the scope of the preformed end, be it the Will of God or Kultur. But the doctrine that intelligence develops within the sphere of action for the sake of possibilities not yet given is the opposite of a doctrine of mechanical efficiency. Intelligence as intelligence is inherently forward-looking; only by ignoring its primary function does it become a mere means for an end already given. The latter is servile, even when the end is labeled moral, religious, or esthetic. But action directed to ends to which the agent has not previously been attached inevitably carries with it a quickened and enlarged spirit. A pragmatic intelligence is a creative intelligence, not a routine mechanic.

All this may read like a defense of pragmatism by one concerned to make out for it the best case possible. Such is not, however, the intention. The purpose is to indicate the extent to which intelligence frees action from a mechanically instrumental character. Intelligence is, indeed, instrumental through action to the determination of the qualities of future experience. But the very fact that the concern of intelligence is with the future, with the as-yet-unrealized (and with the given and the established only as conditions of the realization of possibilities), makes the action in which it takes effect generous and liberal; free of spirit. Just that action which extends and approves intelligence has an intrinsic value of its own in being instrumental:—the intrinsic value of being informed with intelligence in behalf of the enrichment of life. By the same stroke, intelligence becomes truly liberal: knowing is a human undertaking, not an esthetic appreciation carried on by a refined class or a capitalistic possession of a few learned specialists, whether men of science or of philosophy.

More emphasis has been put upon what philosophy is not than upon what it may become. But it is not necessary, it is not even desirable, to set forth philosophy as a scheduled program. There are human difficulties of an urgent, deep-seated kind which may be clarified by trained reflection, and whose solution may be forwarded by the careful development of hypotheses. When it is understood that philosophic thinking is caught up in the actual course of events, having the office of guiding them towards a prosperous issue, problems will abundantly present themselves. Philosophy will not solve these problems; philosophy is vision, imagination, reflection—and these functions, apart from action, modify nothing and hence resolve nothing. But in a complicated and perverse world, action which is not informed with vision, imagination, and reflection, is more likely to increase confusion and conflict than to straighten things out. It is not easy for generous and sustained reflection to become a guiding and illuminating method in action. Until it frees itself from identification with problems which are supposed to depend upon Reality as such, or its distinction from a world of Appearance, or its relation to a Knower as such, the hands of philosophy are tied. Having no chance to link its fortunes with a responsible career by suggesting things to be tried, it cannot identify itself with questions which actually arise in the vicissitudes of life. Philosophy recovers itself when it ceases to be a device for dealing with the problems of philosophers and becomes a method, cultivated by philosophers, for dealing with the problems of men.

Emphasis must vary with the stress and special impact of the troubles which perplex men. Each age knows its own ills, and seeks its own remedies. One does not have to forecast a particular program to note that the central need of any program at the present day is an adequate conception of the nature of intelligence and its place in action. Philosophy cannot disavow responsibility for many misconceptions of the nature of intelligence which now hamper its efficacious operation. It has at least a negative task imposed upon it. It must take away the burdens which it has laid upon the intelligence of the common man in struggling with his difficulties. It must deny and eject that intelligence which is naught but a distant eye, registering in a remote and alien medium the spectacle of nature and life. To enforce the fact that the emergence of imagination and thought is relative to the connexion of the sufferings of men with their doings is of itself to illuminate those sufferings and to instruct those doings. To catch mind in its connexion with the entrance of the novel into the course of the world is to be on the road to see that intelligence is itself the most promising of all novelties, the revelation of the meaning of that transformation of past into future which is the reality of every present. To reveal intelligence as the organ for the guidance of this transformation, the sole director of its quality, is to make a declaration of present untold significance for action. To elaborate these convictions of the connexion of intelligence with what men undergo because of their doings and with the emergence and direction of the creative, the novel, in the world is of itself a program which will keep philosophers busy until something more worth while is forced upon them. For the elaboration has to be made through application to all the disciplines which have an intimate connexion with human conduct:—to logic, ethics, esthetics, economics, and the procedure of the sciences formal and natural.

I also believe that there is a genuine sense in which the enforcement of the pivotal position of intelligence in the world and thereby in control of human fortunes (so far as they are manageable) is the peculiar problem in the problems of life which come home most closely to ourselves—to ourselves living not merely in the early twentieth century but in the United States. It is easy to be foolish about the connexion of thought with national life. But I do not see how any one can question the distinctively national color of English, or French, or German philosophies. And if of late the history of thought has come under the domination of the German dogma of an inner evolution of ideas, it requires but a little inquiry to convince oneself that that dogma itself testifies to a particularly nationalistic need and origin. I believe that philosophy in America will be lost between chewing a historic cud long since reduced to woody fiber, or an apologetics for lost causes (lost to natural science), or a scholastic, schematic formalism, unless it can somehow bring to consciousness America's own needs and its own implicit principle of successful action.

This need and principle, I am convinced, is the necessity of a deliberate control of policies by the method of intelligence, an intelligence which is not the faculty of intellect honored in text-books and neglected elsewhere, but which is the sum-total of impulses, habits, emotions, records, and discoveries which forecast what is desirable and undesirable in future possibilities, and which contrive ingeniously in behalf of imagined good. Our life has no background of sanctified categories upon which we may fall back; we rely upon precedent as authority only to our own undoing—for with us there is such a continuously novel situation that final reliance upon precedent entails some class interest guiding us by the nose whither it will. British empiricism, with its appeal to what has been in the past, is, after all, only a kind of a priorism. For it lays down a fixed rule for future intelligence to follow; and only the immersion of philosophy in technical learning prevents our seeing that this is the essence of a priorism.

We pride ourselves upon being realistic, desiring a hardheaded cognizance of facts, and devoted to mastering the means of life. We pride ourselves upon a practical idealism, a lively and easily moved faith in possibilities as yet unrealized, in willingness to make sacrifice for their realization. Idealism easily becomes a sanction of waste and carefulness, and realism a sanction of legal formalism in behalf of things as they are—the rights of the possessor. We thus tend to combine a loose and ineffective optimism with assent to the doctrine of take who take can: a deification of power. All peoples at all times have been narrowly realistic in practice and have then employed idealization to cover up in sentiment and theory their brutalities. But never, perhaps, has the tendency been so dangerous and so tempting as with ourselves. Faith in the power of intelligence to imagine a future which is the projection of the desirable in the present, and to invent the instrumentalities of its realization, is our salvation. And it is a faith which must be nurtured and made articulate: surely a sufficiently large task for our philosophy.

REFORMATION OF LOGIC

ADDISON W. MOORE

I

In a general survey of the development of logical theory one is struck by the similarity, not to say identity, of the indictments which reformers, since the days of Aristotle, have brought against it. The most fundamental of these charges are: first, that the theory of logic has left it formal and with little significance for the advancement of science and the conduct of society; second, that it has great difficulty in avoiding the predicament of logical operations that are merely labored reproductions of non-logical activities and therefore tautologous and trifling, or of logical operations that are so far removed from immediate, non-logical experience that they are irrelevant; third, that logical theory has had trouble in finding room in its own household for both truth and error; each crowds out the other.

The identity of these indictments regardless of the general philosophical faith, empiricism, or rationalism, realism, or idealism to which the reformer or the logic to be reformed has belonged, suggests that whatever the differences in the doctrines of these various philosophic traditions, they possess a common ground from which these common difficulties spring.

It is the conviction of a number who are at present attempting to rid logic of these ancient disabilities that their common source is to be found in a lack of continuity between the acts of intelligence (or to avoid the dangers of hypostasis, intelligent acts) and other acts; between logical conduct and other conduct. So wide, indeed, is this breach, that often little remains of the act of knowing but the name. It may still be called an act, but it has no describable instruments nor technique of operation. It is an indefinable and often mystical performance of which only the results can be stated. In recent logical discussion this techniqueless act of knowing has been properly enough transformed into an indefinable "external relation" in which an entity called a knower stands to another entity called the known.

For many centuries this breach between the operations of intelligence and other operations has been closed by various metaphysical devices with the result that logic has been a hybrid science,—half logic, half metaphysics and epistemology. So great has been the momentum of the metaphysical tradition that long after we have begun to discover the connection between logical and non-logical operations its methods remain to plague us. Efforts to heal the breach without a direct appeal to metaphysical agencies have been made by attempting a complete logicizing of all operations. But besides requiring additional metaphysics to effect it, the procedure is as fatal to continuity as is an impassable disjunction. Continuity demands distinction as well as connection. It requires the development, the growth of old material and functions into new forms.

Driven by the difficulties of this complete logicization, which are as serious as those of isolation, logical theory was obliged to reinstate some sort of distinction. This it did by resorting to the categories of "explicit" and "implicit." All so-called non-logical operations were regarded as "implicitly" logical. And, paradoxically, logical operations had for their task the transformation of the implicit into the explicit.

An adequate account of the origin and continuance of this isolation of the conduct of intelligence from other conduct is too long a story to be told here. Suffice it to recall that in the society in which the distinction between immediate and reflective experience, between opinion and science, between percepts and universals was first made, intelligence was largely the possession of a special and privileged class removed in great measure from hand-to-hand contact with nature and with much of society. Because it did not fully participate in the operations of nature and society intelligence could not become fully domesticated, i.e., fully naturalized and socialized in its world. It was a charmed spectator of the cosmic and social drama. Doubtless when Greek intelligence discovered the distinction between immediate and reflective experience—possibly the most momentous discovery in history—"the world," as Kant says of the speculations of Thales, "must suddenly have appeared in a new light." But not recognizing the full significance of this discovery, ideas, universals, became but a wondrous spectacle for the eye of reason. They brought, to be sure, blessed relief from the bewildering and baffling flux of perception. But it was the relief of sanctuary, not of victory.

That the brilliant speculations of Greek intelligence were barren because there was no technique for testing and applying them in detail is an old story. But it is merely a restatement, not a solution, of the pertinent question. This is: why did not Greek intelligence develop such a technique? The answer lies in the fact that the technique of intelligence is to be found precisely in the details of the operations of nature and of human conduct from which an aristocratic intelligence is always in large measure shut off. Intelligence cannot operate fruitfully in a vacuum. It must be incarnate. It must, as Hegel said, have "hands and feet." When we turn to the history of modern science the one thing that stands out is that it was not until the point was reached where intelligence was ready (continuing the Hegelian figure) to thrust its hands into the vitals of nature and society that it began to acquire a real control over its operations.

In default of such controlling technique there was nothing to be done with this newly found instrument of intelligence—the universal—but to retain it as an object of contemplation and of worshipful adoration. This involved, of course, its hypostasis as the metaphysical reality of supreme importance. With this, the only difference between "opinion" and "science" became one of the kind of objects known. That universals were known by reason and particulars by sense was of little more logical significance than that sounds are known by the ear and smells by the nose. Particulars and universals were equally given. If the latter required some abstraction this was regarded as merely auxiliary to the immediate vision, as sniffing is to the perception of odor. That universals should or could be conceived as experimental, as hypotheses, was, when translated into later theology, the sin against the Holy Ghost.

However, the fact that the particulars in the world of opinion were the stimuli to the "recollection" of universals and that the latter in turn were the patterns, the forms, for the particulars, opened the way in actual practice for the exercise of a great deal of the controlling function of the universals. But the failure to recognize this control value of the universal as fundamental, made it necessary for the universal to exercise its function surreptitiously, in the disguise of a pattern and in the clumsy garb of imitation and participation.

With perceptions, desires, and impulses relegated to the world of opinion and shadows, and with the newly discovered instrument of knowledge turned into an object, the knower was stripped of all his knowing apparatus and was left an empty, scuttled entity definable and describable only as "a knower." The knower must know, even if he had nothing to know with. Hence the mystical almost indefinable character of the knowing act or relation. I say "almost indefinable"; for as an act it had, of course, to have some sort of conceptualized form. And this form vision naturally furnished. "Naturally," because intelligence was so largely contemplative, and vision so largely immediate, unanalyzed, and diaphanous. There was, to be sure, the concept of effluxes. But this was a statement of the fact of vision in terms of its results, not of the process itself. Thus it was that the whole terminology of knowing which we still use was moulded and fixed upon a very crude conception of one of the constituents of its process. There can be no doubt that this terminology has added much to the inertia against which the advance of logical theory has worked. It would be interesting to see what would be the effect upon logical theory of the substitution of an auditory or olfactory terminology for visual; or of a visual terminology revised to agree with modern scientific analysis of the act of vision as determined by its connections with other functions.

With the act of knowing stripped of its technique and left a bare, unique, indescribable act or relation, the foundations for epistemological and metaphysical logic were laid. That Greek logic escaped the ravages of epistemology was due to the saving materialism in its metaphysical conception of mind and to the steadfastness of the aristocratic régime. But when medieval theology and Cartesian metaphysics had destroyed the last remnant of metaphysical connection between the knowing mind and nature, and when revolutions had torn the individual from his social moorings, the stage for epistemological logic was fully set. I do not mean to identify the epistemological situation with the Cartesian disjunction. That disjunction was but the metaphysical expression of the one which constitutes the real foundation of epistemology—the disjunction, namely, between the act of knowing and other acts.

From this point logic has followed one of two general courses. It has sought continuity by attempting to reduce non-logical things and operations to terms of logical operations, i.e., to sensations or universals or both; or it has attempted to exclude entirely the act of knowing from logic and to transfer logical distinctions and operations, and even the attributes of truth and error to objects which, significantly enough, are still composed of these same hypostatized logical processes. The first course results in an epistemological logic of some form of the idealistic tradition, rationalism, sensationalism, or transcendentalism, depending upon whether universals, or sensations, or a combination of both, is made fundamental in the constitution of the object. The second course yields an epistemological logic of the realistic type,—again, sensational or rationalistic (mathematical), or a combination of the two—a sort of realistic transcendentalism. Each type has essentially the same difficulties with the processes of inference, with the problem of change, with truth and error, and, on the ethical side, with good and evil.

With the processes of knowing converted into objects, and with the act of knowing reduced to a unique and external relation between the despoiled knower and the objects made from its own hypostatized processes, all knowing becomes in the end immediate. All attempts at an inference that is anything more than an elaborated and often confused restatement of non-logical operations break down. The associational inference of empiricism, the subsumptive inference of rationalism, the transcendental inference of objective idealism, the analytical inference of neo-realism—all alike face the dilemma of an inference that is trifling or miraculous, tautologous or false. Where the knower and its object are so constituted that the only relation in which the latter can stand to the former is that of presence or absence, and if to be present is to be known, how, as Plato asked, can there be any false knowing?

For those who accept the foregoing general diagnosis the prescription is obvious. The present task of logical theory is the restoration of the continuity of the act and agent of knowing with other acts and agents. But this is not to be done by merely furnishing the act of knowing with a body and a nervous system. If the nervous system be regarded as only an onlooking, beholding nervous system, if no connection be made between the logical operations of a nervous system and its other operations a nervous system has no logical advantage over a purely psychical mind.

It was to be expected that this movement toward restoration of continuity made in the name of "instrumental" or "experimental" logic would be regarded, alike, by the logics of rationalism and empiricism, of idealism and of realism, as an attempt to rob intelligence of its own unique and proper character; to reduce it to a merely "psychological" and "existential" affair; to leave no place for genuine intellectual interest and activity; and to make science a series of more or less respectable adventures. The counter thesis is, that this restoration is truly a restoration—not a despoliation of the character and rights of intelligence; that only such a restoration can preserve the unique function of intelligence, can prevent it from becoming merely "existential," and can provide a distinct place for intellectual and scientific interest and activity. It does not, however, promise to remove the stigma of "adventure" from science. Every experiment is an adventure; and it is precisely the experimental character of scientific logic that distinguishes it from scholasticism, medieval or modern.

II

First it is clear that a reform of logic based upon the restoration of knowing to its connections with other acts will begin with a chapter containing an account of these other operations and the general character of this connection.[13] Logical theory has been truncated. It has tried to begin and end in the middle, with the result that it has ended in the air. Logic presents the curious anachronism of a science which attempts to deal with its subject-matter apart from what it comes from and what comes from it.

The objection that such a chapter on the conditions and genesis of the operations of knowing belongs to psychology, only shows how firmly fixed is the discontinuity we are trying to escape. As we have seen, the original motive for leaving this account of genesis to psychology was that the act of knowing was supposed to originate in a purely psychical mind. Such an origin was of course embarrassing to logic, which aimed to be scientific. The old opposition between origin and validity was due to the kind of origin assumed and the kind of validity necessitated by the origin. One may well be excused for evading the question of how ideas, originated in a purely psychical mind, can, in Kant's phrase, "have objective validity," by throwing out the question of origin altogether. Whatever difficulties remain for validity after this expulsion could not be greater than those of the task of combining the objective validity of ideas with their subjective origin.

The whole of this chapter on the connection between logical and non-logical operations cannot be written here. But its central point would be that these other acts with which the act of knowing must have continuity are just the operations of our unreflective conduct. Note that it is "unreflective," not "unconscious," nor yet merely "instinctive" conduct. It is our perceptive, remembering, imagining, desiring, loving, hating conduct. Note also that we do not say "psychical" or "physical," nor "psycho-physical" conduct. These terms stand for certain distinctions in logical conduct,[14] and we are here concerned with the character of non-logical conduct which is to be distinguished from, and yet kept in closest continuity with, logical conduct.

If, here, the metaphysical logician should ask: "Are you not in this assumption of a world of reflective and unreflective conduct and affection, and of a world of beings in interaction, begging a whole system of metaphysics?" the reply is that if it is a metaphysics bad for logic, it will keep turning up in the course of logical theory as a constant source of trouble. On the other hand, if logic encounters grave difficulties when it attempts to get on without it, its assumption, for the purposes of logic, has all the justification possible.

Again it will be urged that this alleged non-logical conduct, in so far as it involves perception, memory, and anticipation, is already cognitive and logical; or if the act of knowing is to be entirely excluded from logic, then, in so far as what is left involves objective "terms and relations," it, also, is already logical. And it may be thought strange that a logic based upon the restoration of continuity between the act of knowing and other acts should here be insisting on distinction and separation. The point is fundamental; and must be disposed of before we go on. First, we must observe that the unity secured by making all conscious conduct logical turns out, on examination, to be more nominal than real. As we have already seen, this attempt at a complete logicizing of all conduct is forced at once to introduce the distinction of "explicit" and "implicit," of "conscious and unconscious" or "subconscious" logic. Some cynics have found that this suggests dividing triangles into explicit and implicit triangles, or into triangles and sub-triangles.

Doubtless the attempt to make all perceptions, memories, and anticipations, and even instincts and habits, into implicit or subconscious inference is an awkward effort to restore the continuity of logical and non-logical conduct. Its awkwardness consists in attempting to secure this continuity by the method of subsumptive identity, instead of finding it in a transitive continuity of function;—instead of seeing that perception, memory, and anticipation become logical processes when they are employed in a process of inquiry, whose purpose is to relieve the difficulties into which these operations in their function as direct stimuli have fallen. Logical conduct is constituted by the coöperation of these processes for the improvement of their further operation. To regard perception, memory, and imagination as implicit forms or as sub-species of logical operation is much like conceiving the movements of our fingers and arms as implicit or imperfect species of painting, or swimming.

Moreover, this doctrine of universal logicism teaches that when that which is perfect is come, imperfection shall be done away. This should mean that when painting becomes completely "explicit" and perfect, fingers and hands shall disappear. Perfect painting will be the pure essence of painting. And this interpretation is not strained; for this logic expressly teaches that in the perfected real system all temporal elements are unessential to logical operations. They are, of course, psychologically necessary for finite beings, who can never have perfectly logical experiences. But, from the standpoint of a completely logicized experience, all finite, temporal processes are accidents, not essentials, of logical operations.

The fact that the processes of perception, memory, and anticipation are transformed in their logical operation into sensations and universals, terms, and relations, and, as such, become the subject-matter of logical theory, does not mean that they have lost their mediating character, and have become merely objects of logical contemplation at large. Sensations or sense-data, and ideas, terms and relations, are the subject-matter of logical theory for the reason that they sometimes succeed and sometimes fail in their logical operations. And it is the business of logical theory to diagnose the conditions of this success and failure. If, in writing, my pen becomes defective and is made an object of inquiry, it does not therefore lose all its character as a pen and become merely an object at large. It is as an instrument of writing that it is investigated. So, sense-data, universals, terms, and relations as subject-matter of logic are investigated in their character as mediators of the ambiguities and conflicts, of non-logical experience.

If the operations of habit, instinct, perceptions, memory, and anticipation become logical, when, instead of operating as direct stimuli, they are employed in a process of inquiry, we must next ask: (1) under what conditions do they pass over into this process of inquiry? (2) what modifications of operation do they undergo, what new forms do they take, and what new results do they produce in their logical operations?

If the act of inquiry be not superimposed, it must arise out of some specific condition in the course of non-logical conduct. Once more, if the alarm be sounded at this proposal to find the origin of logical in non-logical operations it must be summarily answered by asking if the one who raises the cry finds it impossible to imagine that one who is not hungry, or angry, or patriotic, or wise may become so. Non-logical conduct is not the abstract formal contradictory of logical conduct any more than present satiety or foolishness is the contradictory of later hunger or wisdom, or than anger at one person contradicts cordiality to another, or to the same person, later. The old bogie of the logical irrelevance of origin was due to the inability to conceive continuity except in the form of identity in which there was no place for the notion of growth.

The conditions under which non-logical conduct becomes logical are familiar to those who have followed the doctrines of experimental logic as expounded in the discussions of the past few years. The transformation begins at the point where non-logical processes instead of operating as direct unambiguous stimuli and response become ambiguous with consequent inhibition of conduct. But again this does not mean that at this juncture the non-logical processes quit the field and give place to a totally new faculty and process called reason. They stay on the job. But there is a change in the job, which now is to get rid of this ambiguity. This modification of the task requires, of course, corresponding modification and adaptation of these operations. They take on the form of sensations and universals, terms and relations, data and hypotheses. This modification of function and form constitutes "reason" or, better, reasoning.

Here some one will ask, "Whence comes this ambiguity? How can a mere perception or memory as such be ambiguous? Must it not be ambiguous to, or for, something, or some one?" The point is well taken. But it should not be taken to imply that the ambiguity is for a merely onlooking, beholding psychical mind—especially when the perception is itself regarded as an act of beholding. Nor are we any better off if we suppose the beholding mind to be equipped with a faculty of reason in the form of the principle of "contradiction." For this throws no light on the origin and meaning of ambiguity. And if we seek to make all perceptions as such ambiguous and contradictory, in order to make room for, and justify, the operations of reason, other difficulties at once beset us. When we attempt to remove this specific ambiguity of perceptive conduct we shall be forced, before we are through, to appeal back to perception, which we have condemned as inherently contradictory, both for data and for verification.

However, the insistence that perception must be ambiguous to, or for, something beyond itself is well grounded. And this was recognized in the statement that it is equivocal as a stimulus in conduct. There need be no mystery as to how such equivocation arises. That there is such a thing as a conduct at all means that there are certain beings who have acquired definite ways of responding to one another. It is important to observe that these forms of interaction—instinct and habit, perception, memory, etc.—are not to be located in either of the interacting beings but are functions of both. The conception of these operations as the private functions of an organism is the forerunner of the epistemological predicament. It results in a conception of knowing as wholly the act of a knower apart from the known. This is the beginning of epistemology.

But to whatever extent interacting beings have acquired definite and specific ways of behavior toward one another it is equally plain—the theory of external relations notwithstanding—that in this process of interaction these ways of behavior, of stimulus and response, undergo modification. If the world consisted of two interacting beings, it is conceivable that the modifications of behavior might occur in such close continuity of relation to each of the interacting beings that the adjustment would be very continuous, and there might be little or no ambiguity and conflict. But in a world where any two interacting beings have innumerable interactions with innumerable other beings and in all these interactions modifications are effected, it is to be expected that changes in the behavior of each or both will occur, so marked that they are bound to result in breaks in the continuity of stimulus and response—even to the point of tragedy. However, the tragedy is seldom so great that the ambiguity extends to the whole field of conduct. Except in extreme pathological cases (and in epistemology), complete skepticism and aboulia do not occur. Ambiguity always falls within a field or direction of conduct, and though it may extend much further, and must extend some further than the point at which equivocation occurs, yet it is never ubiquitous. An ambiguity concerning the action of gravitation is no less specific than one regarding color or sound; indeed, the one may be found to involve the other.

Logical conduct is, then, conduct which aims to remove ambiguity and inhibition in unreflective conduct. The instruments of its operation are forged from the processes of unreflective conduct by such modification and adaptation as is required to enable them to accomplish this end. Since these logical operations sometimes fail and sometimes succeed they become the subject-matter of logical theory. But the technique of this second involution of reflection is not supplied by some new and unique entity. It also is derived from modifications of previous operations of both reflective and non-reflective conduct.

While emphasizing the continuity between non-logical and logical operations, we must keep in mind that their distinction is of equal importance. Confusion at this point is fatal. A case in point is the confusion between non-logical and logical observation. The results of non-logical observation, e.g., looking and listening, are direct stimuli to further conduct. But the purpose and result of logical observation are to secure data, not as direct stimuli to immediate conduct but as stimuli to the construction or verification of hypotheses which are the responses of the logical operation of imagination to the data. Hypotheses are anticipatory. But they differ from non-logical anticipation in that they are tentatively, experimentally, i.e., logically anticipatory. The non-logical operations of memory and anticipation lack just this tentative, experimental character. When we confuse the logical and non-logical operations of these processes the result is either that logical processes will merely repeat non-logical operations in which case we have inference that is tautologous and trifling; or the non-logical will attempt to perform logical operations, and our inference is miraculous. If we seek to escape by an appeal to habit, as in empiricism, or to an objective universal, as in idealism and neo-realism, we are merely disguising, not removing the miracle.

It may be thought that this confusion would be most likely to occur in a theory which teaches that non-logical processes are carried over into logical operations. But this overlooks the fact that the theory recognizes at the same time that these non-logical operations undergo modification and adaptation to the demands of the logical enterprise. On the other hand, those who make all perceptions, memory, and anticipation, not to speak of habit and instinct, logical, have no basis for the distinction between logical and non-logical results; while those who refuse to give the operations of perception, memory, etc., any place in logic can make no connections between logical and non-logical conduct. Nor are they able to distinguish in a specific case truth from error.

In all logics that fail to make this connection and distinction between logical and non-logical operations there is no criterion for data. If ultimate simplicity is demanded of the data, there is no standard for simplicity except the minimum sensibile or the minimum intelligibile which have recently been resurrected. On the other hand, where simplicity is waived, as in the logic of objective idealism, there is still no criterion of logical adequacy. But if we understand by logical data not anything that happens to be given, but something sought as material for an hypothesis, i.e., a proposed solution (proposition) of an ambiguous object of conduct and affection, then whatever results of observation meet this requirement are logical data. And whenever data are found from which an hypothesis is constructed that succeeds in abolishing the ambiguity, they are simple, adequate, and true data.

No scientist, not even the mathematician, in the specific investigations of his field, seeks for ultimate and irreducible data at large. And if he found them he could not use them. It is only in his metaphysical personality that he longs for such data. The data which the scientist in any specific inquiry seeks are the data which suggest a solution of the question in which the investigation starts. When these data are found they are the "irreducibles" of that problem. But they are relative to the question and answer of the investigation. Their simplicity consists in the fact that they are the data from which a conclusion can be made. The term "simple data" is tautologous. That one is in need of data more "simple" means that one is in need of new data from which an hypothesis can be formed.

It is true that the actual working elements with which the scientist operates are always complex in the sense that they are always something more than elements in any specific investigation. They have other connections and alliances. And this complexity is at once the despair and the hope of the scientist; his despair, because he cannot be sure when these other connections will interfere with the allegiance of his elements to his particular undertaking; his hope, because when these alliances are revealed they often make the elements more efficient or exhibit capacities which will make them elements in some other undertaking for which elements have not been found. A general resolves his army into so many marching, eating, shooting units; but these elements are something more than marching, shooting units. They are husbands and fathers, brothers and lovers, protestants and catholics, artists and artisans, etc. And the militarist can never be sure at what point these other activities—I do not say merely external relationships—may upset his calculations. If he could find units whose whole and sole nature is to march and shoot, his problem would be, in some respects, simpler, though in others more complex. As it is, he is constantly required to ask how far these other functions will support and at what point they will rebel at the marching and shooting.

Such, in principle, is the situation in every scientific inquiry. When the failure of the old elements occurs it is common to say that "simpler" elements are needed. And doubtless in his perplexity the scientist may long for elements which have no entangling alliances, whose sole nature and character is to be elements. But what in fact he actually seeks in every specific investigation are elements whose nature and functions will not interfere with their serving as units in the enterprise in hand. But from some other standpoint these new elements may be vastly more complex than the old, as is the case with the modern as compared with the ancient atom. When the elements are secured which operate successfully, the non-interfering connections can be ignored and the elements can be treated as if they did not have them,—as if they were metaphysically simple. But there is no criterion for metaphysical simplicity except operative simplicity. To be simple is to serve as an element, and to serve as an element is to be simple.

It is scarcely necessary in view of the foregoing to add that the data of science are not "sense-data," if by sense-data be meant data which are the result of the operations of sense organs alone. Data are as much or more the result of operations, first, of the motor system of the scientist's own organism, and second, of all of the machinery of his laboratory which he calls to his aid. Whether named after the way they are obtained, or after the way they are used, data are quite as much "motor" as "sense." Nor, on the other hand, are there any purely intellectual data—not even for the mathematician. Some mathematicians may insist that their symbols and diagrams are merely stimuli to the platonic operation of pure and given universals. But until mathematics can get on without these symbols or any substitutes the intuitionist in mathematics will continue to have his say.

Wherever the discontinuity between logical operations and their acts persists, all the difficulties with data have their correlative difficulties with hypotheses. In Mill's logic the account of the origin of hypotheses oscillates between the view that they are happy guesses of a mind composed of states of consciousness, and the view that they are "found in the facts" or are "impressed on the mind by the facts." The miracle of relevancy required in the first position drives the theory to the second. And the tautologous, useless nature of the hypothesis in the second forces the theory back to the first view. In this predicament, little wonder Mill finds that the easiest way out is to make hypotheses "auxiliary" and not indigenous to inference. But this exclusion of hypotheses as essential leaves his account of inference to oscillate between the association of particulars of nominalism and scholastic formalism, from both of which Mill, with the dignified zeal of a prophet, set out to rescue logic.

Mill's rejection of hypotheses formed by a mind whose operations have no discoverable continuity with the operations of things, or by things whose actions are independent of the operations of ideas, is forever sound. But his acceptance of the discontinuity between the acts of knowing and the operation of things, and the conclusion that these two conceptions of the origin and nature of hypotheses are the only alternatives, were the source of most of his difficulties.

III

The efforts of classic empiricism at the reform of logic have long been an easy mark for idealistic reformers. But it is interesting to observe that the idealistic logic from the beginning finds itself in precisely the same predicament regarding hypotheses;—they are trifling or false. And in the end they are made, as in Mill, "accidents" of inference.

The part played by Kant's sense-material and the categories is almost the reverse of those of data and hypothesis in science. Sense material and the categories are the given elements from which objects are somehow made; in scientific procedure data and hypothesis are derived through logical observation and imagination from the content and operations of immediate experience. In Kant's account of the process by which objects are constructed we are nowhere in sight of any experimental procedure. Indeed, the real act of knowing, the selection and application of the category to the sense matter, is, as Kant in the end had to confess, "hidden away in the depths of the soul." Made in the presence of the elaborate machinery of knowing which Kant had constructed, this confession is almost tragic; and the tragic aspect grows when we find that the result of the "hidden" operation is merely a phenomenal object. That this should be the case, however, is not strange. A phenomenal object is the inevitable correlate of the "hidden" act of knowing whether in a "transcendental" or in an "empirical" logic. In vain do we call the act of knowing "constructive" and "synthetic" if its method of synthesis is hidden. A transcendental unity whose method is indefinable has no advantage over empirical association.

It was the dream of Kant as of Mill to replace the logics of sensationalism and rationalism with a "logic of things" and of "truth." But as Mill's things turned to states of consciousness, so Kant's are phenomenal. Their common fate proclaims their common failure—the failure to reëstablish continuity between the conduct of intelligence and other conduct.

One of the chief counts in Hegel's indictment of Kant's logic is that "it had no influence on the methods of science."[15] Hegel's explanation is that Kant's categories have no genesis; they are not constructed in and as part of logical operations. As given, ready-made, their relevance is a miracle. But if categories be "generated" in the process of knowing, says Hegel, they are indigenous, and their fitness is inevitable. In such statements Hegel raises expectations that we are at last to have a logic which squares with the procedure of science. But when we discover that instead of being "generated" out of all the material involved in the scientific problem Hegel's categories are derived from each other, misgivings arise. And when we further learn that this "genesis" is timeless, which means that, after all, the categories stand related to each other in a closed, eternal system of implication, we abandon hope of a scientific—i.e., experimental—logic.

Hegel also says it is the business of philosophy "to substitute categories or in more precise language adequate notions for the several modes of feeling, perception, desire, and will." The word "substitute" reveals the point at issue. If "to substitute" means that philosophy is a complete exchange of the modes of feeling, perception, desire, and will for a world of categories or notions, then, saying nothing of the range of values in such a world, the problem of the meaning of "adequate" is on our hands. What is the notion to be adequate to? But if "to substitute" means that the modes of feeling, perception, desire, and will, when in a specific situation of ambiguity and inhibition, go over into, take on, the modes of data and hypothesis in the effort to get rid of inhibiting conflict that is quite another matter. Here the "notion," as the scientific hypothesis, has a criterion for its adequacy. But if the notion usurps the place of feeling, perception, desire, and will, as many find, in the end, it does in Hegel's logic, it thereby loses all tests for the adequacy of its function and character as a notion.

In the development of the logical doctrines of Kant and Hegel by Lotze, Green, Sigwart, Bradley, Bosanquet, Royce, and others, there are indeed differences. But these differences only throw their common ground into bolder relief. This common ground is that, procedure by hypotheses, by induction, is, in the language of Professor Bosanquet, "a transient and external characteristic of inference."[16] And the ground of this verdict is essentially the same as Mill's, when he rejects hypotheses "made by the mind," namely, that such hypotheses are too subjective in their origin and nature to have objective validity. "Objective" idealism is trying, like Mill, to escape the subjectivism of the purely individual and "psychical" knower. But, being unable to reconstruct the finite knower, and being too sophisticated to make what it regards as Mill's naïve appeal to "hypotheses found in things," it transfers the real process of inference to the "objective universal," and the process of all thought, including inference, is now defined as "the reproduction, by a universal presented in a content, of contents distinguished from the presented content which also are differences of the same universal."[17]

It need scarcely be said that in inference thus defined there is scant room for hypotheses. There is nothing "hypothetical," "experimental," or "tentative" in this process of reproduction by the objective universal as such. As little is there any possibility of error. If there is anything hypothetical, or any possibility of error, in inference, it is due to the temporal, finite human being in which, paradoxically enough, this process of "reproduction" goes on and to whom, at times, is given an "infinitesimal" part in the operation, while at other times he is said merely to "witness" it. But the real inference does not "proceed by hypotheses"; it is only the finite mind in witnessing the real logical spectacle or in its "infinitesimal" contribution to it that lamely proceeds in this manner.

Here, again, we have the same break in continuity between the finite, human act of knowing and the operations that constitute the real world. When the logic of the objective universal rejects imputations of harboring a despoiled psychical knower it has in mind, of course, the objective universal as knower, not the finite, human act. But, if the participations of the latter are all accidents of inference, as they are said to be, its advantage over a purely psychical knower, or "states of consciousness," is difficult to see. The rejection of metaphysical dualism is of no consequence if the logical operations of the finite, human being are only "accidents" of the real logical process. As already remarked, the metaphysical disjunction is merely a schematism of the more fundamental, logical disjunction.

As for tautology and miracle, the follower of Mill might well ask: how an association of particulars, whether mental states or things, could be more tautologous than a universal reproducing its own differences? And if the transition from particular to particular is a miracle in which the grace of God is disguised as "habit," why is not habit as good a disguise for Providence as universals? Moreover, by what miracle does the one all-inclusive universal become a universal? And since perception always presents a number of universals, what determines which one shall perform the reproduction? Finally, since there are infinite differences of the universal that might be reproduced, what determines just which differences shall be reproduced? In this wise the controversy has gone on ever since the challenge of the old rationalistic logic by the nominalists launched the issue of empiricism and rationalism. All the charges which each makes against the other are easily retorted upon itself. Each side is resistless in attack, but helpless in defense.

In a conception of inference in which both data and hypothesis are regarded as the tentative, experimental results of the processes of perception, memory, and constructive imagination engaged in the special task of removing conflict, ambiguity, and inhibition, and in which these processes are not conceived as the functions of a private mind nor of an equally private brain and nervous system, but as functions of interacting beings,—in such a conception there is no ground for anxiety concerning the simplicity of data, nor the objectivity of hypotheses. Simplicity and objectivity do not have to be secured through elaborate and labored metaphysical construction. The data are simple and the hypothesis objective in so far as they accomplish the work where unto they are called—the removal of conflict, ambiguity, and inhibition in conduct and affection.

In the experimental conception of inference it is clear that the principles of formal logic must play their rôle wholly inside the course of logical operations. They do not apply to relations between these operations and "reality"; nor to "reality" itself. Formal identity and non-contradiction signify, in experimental logic, the complete correlativity of data and hypothesis. They mean that in the logical procedure data must not be shifted without a corresponding change in the hypothesis and conversely. The doctrine that "theoretically" there may be any number of hypotheses for "the same facts" is, when these multiple hypotheses are anything more than different names or symbols, nothing less than the very essence of formal contradiction. It doubtless makes little difference whether a disease be attributed to big or little, black or red, demons or whether the cause be represented by a, b, or c, etc. But where data and hypotheses are such as are capable of verification, i.e., of mutually checking up each other, a change in one without a corresponding modification of the other is the principle of all formal fallacies.[18]

With this conception of the origin, nature, and functions of logical operations little remains to be said of their truth and falsity. If the whole enterprise of logical operation, of the construction and verification of hypothesis, is in the interest of the removal of ambiguity, and inhibition in conduct, the only relevant truth or falsity they can possess must be determined by their success or failure in that undertaking. The acceptance of this view of truth and error, be it said again, depends on holding steadfastly to the conception of the operations of knowing as real acts, which, though having a distinct character and function, are yet in closest continuity with other acts of which indeed they are but modifications and adaptations in order to meet the logical demand.

Here, perhaps, is the place for a word on truth and satisfaction. The satisfaction which marks the truth of logical operations—"intellectual satisfaction"—is the satisfaction which attends the accomplishment of their task, viz., the removal of ambiguity in conduct, i.e., in our interaction with other beings. It does not mean that this satisfaction is bound to be followed by wholly blissful consequences. All our troubles are not over when the distress of ambiguity is removed. It may be indeed that the verdict of the logical operation is that we must face certain death. Very well, we must have felt it to be "good to know the worst," or no inquiry would have been started. We should have deemed ignorance bliss and sat with closed eyes waiting for fate to overtake us instead of going forward to meet it and in some measure determine it. Death anticipated and accepted is realiter very different from death that falls upon us unawares, however we may estimate that difference. If this distinction in the foci of satisfaction is kept clear it must do away with a large amount of the hedonistic interpretations of satisfaction in which many critics have indulged.

But hereupon some one may exclaim, as did a colleague recently: "Welcome to the ranks of the intellectualists!" If so, the experimentalist is bound to reply that he is as willing, and as unwilling, to be welcomed to the ranks of intellectualism as to those of anti-intellectualism. He wonders, however, how long the welcome would last in either. Among the intellectualists the welcome would begin to cool as soon as it should be discovered that the ambiguity to which logical operations are the response is not regarded by the experimentalist as a purely intellectual affair. It is an ambiguity in conduct with all the attendant affectional values that may be at stake.[19] It is, to be sure, the fact of ambiguity, and the effort to resolve it, that adds the intellectual, logical character to conduct and to affectional values. But if the logical interest attempts entirely to detach itself it will soon be without either subject-matter or criterion. And if it sets itself up as supreme, we shall be forced to say that our quandaries of affection, our problems of life and death are merely to furnish occasions and material for logical operations.

On the other hand, the welcome of the anti-intellectualists is equally sure to wane when the experimentalist asserts that the doctrine that logical operations mutilate the wholeness of immediate experience overlooks the palpable fact that it is precisely these immediate experiences—the experiences of intuition and instinct—that get into conflict and inhibit and mutilate one another, and as a consequence are obliged to go into logical session to patch up the mutilation and provide new and better methods of coöperation.

At this point the weakness in Bergson's view of logical operations appears. Bergson, too, is impressed by the break in continuity between logical operations and the rest of experience. But with Mr. Bradley he believes this breach to be essentially incurable, because the mutilations and disjunctions are due to and introduced by logical operations. Just why the latter are introduced remains in the end a mystery. Both, to be sure, believe that logical operations are valuable for "practical" purposes,—for action. But, aside from the question of how operations essentially mutilative can be valuable for action, immediate intuitional experience being already in unity with Reality, why should there be any practical need for logical operations—least of all such as introduce disjunction and mutilation?

The admission of a demand for logical operations, whether charged to matter, the devil, or any other metaphysical adversary, is, of course, a confession that conflict and ambiguity are as fundamental in experience as unity and immediacy and that logical operations are therefore no less indigenous. The failure to see this implication is responsible for the paradox that in the logic of Creative Evolution the operations of intelligence are neither creative nor evolutional. They not only have no constructive part but are positively destructive and devolutional.

Since, moreover, these logical operations, like those of the objective universal, and like Mill's association of particulars, can only reproduce in fragmentary form what has already been done, it is difficult to see how they can meet the demands of action. For here no more than in Mill, or in the logic of idealism, is there any place for constructive hypotheses or any technique by which they can become effective. Whatever "Creative Evolution" may be, there is no place in its logic for "Creative Intelligence."

IV

The prominence in current discussion of the logical reforms proposed by the "analytic logic" of the neo-realistic movement and the enthusiastic optimism of its representatives over the prospective results of these reforms for logic, science, and practical life are the warrant for devoting a special section to their discussion.

There are indeed some marked differences of opinion among the expounders of the "new logic" concerning the results which it is expected to achieve. Some find that it clears away incredible accumulations of metaphysical lumber; others rejoice that it is to restore metaphysics, "once the queen of the sciences, to her ancient throne."

But whatever the difference among the representatives of analytical logic all seem agreed at the outset on two fundamental reforms which the "new logic" makes. These are: first, that analytic logic gets rid entirely of the act of knowing, the retention of which has been the bane of all other logics; second, in its discovery of "terms and relations," "sense-data and universals" as the simple elements not only of logic but of the world, it furnishes science at last with the simple neutral elements at large which it is supposed science so long has sought, and "mourned because it found them not."

Taking these in order, we are told that "realism frees logic as a study of objective fact from all accounts of the states and operations of mind." ... "Logic and mathematics are sciences which can be pursued quite independently of the study of knowing."[20] "The new logic believes that it deals with no such entities as thoughts, ideas, or minds, but with entities that merely are."[20]

The motive for the banishment of the act of knowing from logic is that as an act knowing is "mental," "psychological," and "subjective."[21] All other logics have indeed realized this subjective character of the act of knowing, but have neither dared completely to discard it nor been able sufficiently to counteract its effects even with such agencies as the objective universal to prevent it from infecting logic with its subjectivity. Because logic has tolerated and attempted to compromise with this subjective act of knowing, say these reformers, it has been forced constantly into epistemology and has become a hybrid science. Had logic possessed the courage long ago to throw overboard this subjective Jonah it would have been spared the storms of epistemology and the reefs of metaphysics.

Analytic logic is the first attempt in the history of modern logical theory at a deliberate, sophisticated exclusion of the act of knowing from logic. Other logics, to be sure, have tried to neutralize the effects of its presence, but none has had the temerity to cast it bodily overboard. The experiment, therefore, is highly interesting.

We should note at the outset that in regarding the act of knowing as incurably "psychical" and "subjective" analytic logic accepts a fundamental premise of the logics of rationalism, empiricism, and idealism which it seeks to reform. It is true that it is the bold proposal of analytic logic to keep logic out of the pit of epistemology by excluding the act of knowing from logic. Nevertheless analytic logic still accepts the subjective character of this act; and if it excludes it from its logic it welcomes it in its psychology. This is a dangerous situation. Can the analytic logician prevent all osmosis between his logic and his psychology?[22] If not, and if the psychological act is subjective, woe then to his logic. Had the new logic begun with a bold challenge of the psychical character of the act of knowing, the prospect of a logic free from epistemology would have been much brighter.

With the desire to rid logic of the epistemological taint the "experimental logic" of the pragmatic movement has the strongest sympathy. But the proposal to effect this by the excision of the act of knowing appears to experimental logic to be a case of heroic but fatal surgery. Prima facie a logic with no act of knowing presents an uncanny appearance. What sort of logical operations are possible in such a logic and of what kind of truth and falsity are they capable?

Before taking up these questions in detail it is worth while to note the character of the entities that "merely are" with which analytic logic proposes exclusively to deal. In their general form they are "terms" and "propositions," "sense-data" and universals. We are struck at once by the fact that these entities bear the names of logical operations. They are, to be sure, disguised as entities and have been baptised in a highly dilute solution of objectivity called "subsistence." But this does not conceal their origin, nor does it obscure the fact that if it is possible for any entities that "merely are" to have logical character those made from hypostatized processes of logical operations should be the most promising. They might be expected to retain some vestiges of logical character even after they have been torn from the process of inquiry and converted into "entities that merely are." Also it is not surprising that having stripped the act of knowing of its constituent operations analytic logic should feel that it can well dispense with the empty shell called "mind" and, as Professor Dewey says, "wish it on psychology." But if the analytic logician be also a philosopher and perchance a lover of his fellow-man, it is hard to see how he can have a good conscience over this disposition of the case.

Turning now to the character of inference and of truth and falsity which are possible in a logic which excludes the operation of knowing and deals only with "entities that are," all the expounders seem to agree that in such a logic inference must be purely deductive. All alleged induction is either disguised deduction or a lucky guess. This raises apprehension at the start concerning the value of analytic logic for other sciences. But let us observe what deduction in analytic logic is.

We begin at once with a distinction which involves the whole issue.[23] We are asked to carefully distinguish "logical" deduction from "psychological" deduction. The latter is the vulgar meaning of the term, and is "the thinker's name for his own act of conforming his thought" to the objective and independent processes that constitute the real logical process. This act of conforming the mind is a purely "psychological" affair. It has no logical function whatever. In what the "conforming" consists is not clear. It seems to be merely the act of turning the "psychological" eye on the objective logical process. "One beholds it (the logical process) as one beholds a star, a river, a character in a play.... The novelist and the dramatist, like the mathematician and logician, are onlookers at the logical spectacle."[24] On the other hand, the term "conforming" suggests a task, with the possibilities of success and failure. Have we, then, two wholly independent possibilities of error—one merely "psychological," the other "logical"? The same point may be made even more obviously with reference to the term "beholding." The term is used as if beholding were a perfectly simple act, having no problems and no possibilities of mistakes—as if there could be no mis-beholding.[25]

But fixing our psychological eye on the "logical spectacle," what does it behold? A universal generating an infinite series of identical instances of itself—i.e., instances which differ only in "logical position." If in a world of entities that "merely are" the term "generation" causes perplexity, the tension is soon relieved; for this turns out to be a merely subsistential non-temporal generation which, like Hegel's generation of the categories, in no way compromises a world of entities that "merely are."

Steering clear of the thicket of metaphysical problems that we here encounter, let us keep to the logical trail. First it is clear that logical operations are of the same reproductive repetitive type that we have found in the associational logic of empiricism, and in the logic of the objective universal. Indeed, after objective idealism has conceded that the finite mind merely "witnesses" or at most contributes only in an "infinitesimal" degree to the logical activity of the objective universal, what remains of the supposed gulf between absolute idealism and analytic realism?

It follows, of course, that there can be no place in analytic logic for "procedure by hypotheses." However, it is to the credit of some analytic logicians that they see this and frankly accept the situation instead of attempting to retain hypotheses by making them "accidents" or mere "auxiliaries" of inference. On the other hand, others find that the chief glory of analytic logic is precisely that it "gives thought wings"[26] for the free construction of hypotheses. In his lectures on "Scientific Methods in Philosophy" Mr. Russell calls some of the most elemental and sacred entities of analytic logic "convenient fictions." This retention of hypotheses at the cost of cogency is of course in order to avoid a break with science. Those who see that there is no place in analytic logic for hypotheses are equally anxious to preserve their connections with science. Hence they boldly challenge the "superstition" that science has anything to do with hypotheses. Newton's "Hypotheses non fingo" should be the motto of every conscientious scientist who dares "trust his own perceptions and disregard the ukase of idealism." "The theory of mental construction is the child of idealism, now put out to service for the support of its parents." "Theory is no longer regarded in science as an hypothesis added to the observed facts," but a law which is "found in the facts."[27] The identity of this with Mill's doctrine of hypotheses as "found in things" is obvious.

As against the conception of hypotheses as "free," "winged," constructions of a psychical, beholding, gossiping mind we may well take our stand with those who would exclude such hypotheses from science. And this doubtless was the sort of mind and sort of hypotheses Newton meant when he said "Hypotheses non fingo."[28] But had Newton's mind really been of the character which he, as a physicist, had learned from philosophers to suppose it to be, and had he really waited to find his hypotheses ready-made in the facts, there never would have been any dispute about who discovered the calculus, and we should never have been interested in what Newton said about hypotheses or anything else. What Newton did is a much better source of information on the part hypotheses play in scientific method than what he said about them. The former speaks for itself; the latter is the pious repetition of a metaphysical creed made necessary by the very separation of mind from things expressed in the statement quoted.

Logically there is little to choose between hypotheses found ready-made in the facts and those which are the "winged" constructions of a purely psychical mind. Both are equally useless in logic and in science. One makes logic and science "trifling," the other makes them "miraculous." But if hypotheses be conceived not as the output of a cloistered psychical entity but as the joint product of all the beings and operations involved in the specific situation in which logical inquiry originates, and more particularly in all those involved in the operations of the inquiry itself (including all the experimental material and apparatus which the inquiry may require), we shall have sufficient continuity between hypotheses and things to do away with miracle, and sufficient reconstruction to avoid inference that is trifling.

It is, however, the second contribution of analytic logic that is the basis of the enthusiasm over its prospective value for other sciences. This is the discovery that terms and propositions, sense-data, and universals, are not only elements of logical operation but are the simple, neutral elements at large which science is supposed to have been seeking. "As the botanist analyzes the structures of the vegetable organism and finds chemical compounds of which they are built so the ordinary chemist analyzes these compounds into their elements, but does not analyze these. The physical chemist analyzes these elemental atoms, as now appears, into minuter components which he in turn must leave to the mathematicians and logicians further to analyze."[29]

Again it is worth noting that this mutation of logical into ontological elements seems to differ only "in position" from the universal logicism of absolute idealism.

What are these simple elements into which the mathematician and logician are to analyze the crude elements of the laboratory? And how are these elements to be put into operation in the laboratory? Let us picture an analytic logician meeting a physical scientist at a moment when the latter is distressed over the unmanageable complexity of his elements. Will the logician say to the scientist: "Your difficulty is that you are trusting too much to your mundane apparatus. The kingdom of truth cometh not with such things. Forsake your microscopes, test tubes, refractors and resonators, and follow me, and you shall behold the truly simple elements of which you have dreamed."? And when the moment of revelation arrives and the expectant scientist is solemnly told that the "simple elements" which he has sought so long are "terms and propositions," sense-data and universals, is it surprising that he does not seem impressed? Will he not ask: "What am I to do with these in the specific difficulties of my laboratory? Shall I say to the crude and complex elements of my laboratory operations: 'Be ye resolved into terms and propositions, sense-data and universals'; and will they forthwith obey this incantation and fall apart so that I may locate and remove the hidden source of my difficulty? Are you not mocking me and deceiving yourself with the old ontological argument? Your 'simple' elements—are they anything but the hypostatized process by which elements may be found?"[30]

The expounders as well as the critics of analytic logic have agreed that it reaches its most critical junction when it faces the problem of truth and error. There is no doubt that the logic of objective idealism, in other respects so similar to analytic logic, has at this point an advantage; for it retains just enough of the finite operation of knowing—an "infinitesimal" part will answer—to furnish the culture germs of error. But analytic logic having completely sterilized itself against this source of infection is in serious difficulty.

Here again it is Professor Holt who has the courage to follow—or shall we say "behold"?—his theory as it "generates" the doctrine that error is a given objective opposition of forces entirely independent of any such thing as a process of inquiry and all that such a process presupposes. "All collisions between bodies, all inference between energies, all process of warming and cooling, of starting and stopping, of combining and separating, all counterbalancings, as in cantilevers and gothic vaultings, are contradictory forces which can be stated only in propositions that manifestly contradict each other."[31] But the argument proves too much. For in the world of forces to which we have here appealed there is no force which is not opposed by others and no particle which is not the center of opposing forces. Hence error is ubiquitous. In making error objective we have made all objectivity erroneous. We find ourselves obliged to say that the choir of Westminster Abbey, the Brooklyn bridge, the heads on our shoulders are all supported by logical errors!

Following these illustrations of ontological contradictions there is indeed this interesting statement: "Nature is so full of these mutually negative processes that we are moved to admiration when a few forces coöperate long enough to form what we call an organism."[32] The implication is, apparently, that as an "opposition" of forces is error, "coöperation" of forces is truth. But what is to distinguish "opposition" from "coöperation"? In the illustration it is clear that opposing forces—error—do not interfere with coöperative forces—truth. Where should we find more counterbalancing, more starting and stopping, warming and cooling, combining and separating than in an organism? And if these processes can be stated only in propositions that are "manifestly contradictory," are we to understand that truth has errors for its constituent elements? Such paradoxes have always delighted the soul of absolute idealism. But, as we have seen, only the veil of an infinitesimal finitude intervenes between the logic of the objective universal of absolute idealism and the objective logic of analytic realism.

It is, of course, this predicament regarding objective truth and error that has driven most analytic logicians to recall the exiled psychological, "mental" act of knowing. It had to be recalled to provide some basis of distinction between truth and error, but, this act having already been conceived as incurably "subjective," the result is only an exchange of dilemmas. For the reinstatement of this act ipso facto reinstates the epistemological predicament to get rid of which it was first banished from logic.

Earnest efforts to escape this outcome have been made by attaching the act of knowing to the nervous system, and this is a move in the right direction. But so far the effort has been fruitless because no connection has been made between the knowing function of the nervous system and its other functions. The result is that the cognitive operation of the nervous system, as of the "psychical" mind, is that of a mere spectator; and the epistemological problem abides. An onlooking nervous system has no advantage over an "onlooking" mind. Onlooking, beholding may indeed be a part of a genuine act of knowing. But in that act it is always a stimulus or response to other acts. It is one of them;—never a mere spectator of them. It is when the act of knowing is cut off from its connection with other acts and finds itself adrift that it seeks metaphysical lodgings. And this it may find either in an empty psychical mind or in an equally empty body.[33]

If, in reinstating the act of knowing as a function of the nervous system, neo-realism had recognized the logical significance of the fact that the nervous system of which knowing is a function is the same nervous system of which loving and hating, desiring and striving are functions and that the transition from these to the operations of inquiry and knowing is not a capricious jump but a transition motived by the loving and hating, desiring and striving—if this had been recognized the logic of neo-realism would have been spared its embarrassments over the distinction of truth and error. It would have seen that the passage from loving and hating, desiring and striving to inquiry and knowing is made in order to renew and reform specific desires and strivings which, through conflict and consequent equivocation, have become fruitless and vain; and it must have seen that the results of the inquiry are true or false as they succeed or fail in this reformation and renewal.

But once more, it must steadily be kept in view that while the loving and hating, desiring and striving, which the logical operations are reforming and renewing, are functions of the nervous system, they are not functions of the nervous system alone, else the door of subjectivism again closes upon us. Loving and hating, desiring and striving have their "objects." Hence any reformation of these functions involves no less a reformation of their objects. When therefore we say that truth and error are relevant to desires and strivings, this means relevant to them as including their objects, not as entitized processes (such are the pitfalls of language) inclosed in a nervous system or mind. With this before us the relevance of truth and error to desires and strivings can never be made the basis for the charge of subjectivism. The conception of desires as peculiarly individual and subjective is a survival of the very isolation which is the source of the difficulty with truth and error. Hence the appeal to this isolation, made alike by idealism and realism, in charging instrumental logic with subjectivism is an elementary petitio.

Doubtless it will be urged again that the act of knowing is motived by an independent desire and striving of its own. This is of course consonant with the neo-realistic atomism, however inconsonant it may be with the conception of implication which it employs. If we take a small enough, isolated segment of experience we can find meaning for this notion, as we may for the idea that the earth is flat and that the sun moves around the earth. But as consequences accrue we find as great difficulties with the one as with the other. If the course of events did not bring us to book, if we could get off with a mere definition of truth and error we might go on piling up subsistential definitional logics world without end. But sublime adventurers, logically unregenerate and uninitiated, will go on sailing westward to the confusion and confounding of all definitional systems that leave them out of account.

The conclusion is plain. If logic is to have room in its household for both truth and error, if it is to avoid the old predicament of knowledge that is trifling or miraculous, tautologous or false, if it is to have no fear of the challenge of other sciences or of practical life, it must be content to take for its subject-matter the operations of intelligence conceived as real acts on the same metaphysical plane and in strictest continuity with other acts. Such a logic will not fear the challenge of science, for it is precisely this continuity that makes possible experimentation, which is the fundamental characteristic of scientific procedure. Science without experiment is indeed a strange apparition. It is a λόγος with no λέγειν, a science with no scire; and this spells dogmatism. How necessary such continuity is to experimentation is apparent when we recall that there is no limit to the range of operations of every sort which scientific experiment calls into play; and that unless there be thoroughgoing continuity between the logical demand of the experiment and all the materials and devices employed in the process of the experiment, the operations of the latter in the experiment will be either miraculous or ruinous.

Finally, if this continuity of the operations of intelligence with other operations be essential to science, its relation to "practical" life is ipso facto established. For science is "practical" life aware of its problems and aware of the part that experimental—i.e., creative—intelligence plays in the solution of those problems.

INTELLIGENCE AND MATHEMATICS

HAROLD CHAPMAN BROWN

Herbart is said to have given the deathblow to faculty psychology. Man no longer appears endowed with volition, passion, desire, and reason; and logic, deprived of its hereditary right to elucidate the operations of inherent intelligence, has the new problem of investigating forms of intelligence in the making. This is no inconsequential task. "If man originally possesses only capacities which after a given amount of education will produce ideas and judgments" (Thorndike, Educational Psychology, Vol. I, p. 198), and if these ideas and judgments are to be substituted for a mythical intelligence it follows that tracing their development and observing their functioning renders clearer our conception of their nature and value and brings us nearer that exact knowledge of what we are talking about in which the philosopher at least aspires to equal the scientist, however much he may fall below his ideal.

For contemporary thought concerning the mathematical sciences this altered point of view generates peculiarly pressing problems. Mathematicians have weighed the old logic and found it wanting. They have builded themselves a new logic more adequate to their ends. But they have not whole-heartedly recognized the change that has come about in psychology; hence they have retained the faculty of intelligence knit into certain indefinables such as implication, relation, class, term, and the like, and have transported the faculty from the human soul to a mysterious realm of subsistence whence it radiates its ghostly light upon the realm of existence below. But while they reproach the old logic, often bitterly, their new logic merely furnishes a more adequate show-case in which already attained knowledge may be arranged to set off its charms for the observer in the same way that specimens in a museum are displayed before an admiring world. This statement is not a sweeping condemnation, however, for such a setting forth is not useless. It resembles the classificatory stage of science which, although not itself in the highest sense creative, often leads to higher stages by bringing under observation relations and facts that might otherwise have escaped notice. And in the realm of pure mathematics, the new logic has undoubtedly contributed in this manner to such discoveries. Danger appears when the logician attains Cartesian intoxication with the beauty of logico-mathematical form and tries to infer from the form itself the real nature of the formed material. The realm of subsistence too often has armed Indefinables with metaphysical myths whose attack is valiant when the doors of reflection are opened. It may be possible, however, to arrive at an understanding of mathematics without entering the kingdom of these warriors.

It is the essence of science to make prediction possible. The value of prediction lies in the fact that through this function man can control his environment, or, at worst, fortify himself to meet its vagaries. To attain such predictions, however, the world need not be grasped in its full concreteness. Hence arise processes of abstraction. While all other symptoms remain unnoticed, the temperature and pulse may mark a disease, or a barometer-reading the weather. The physicist may work only in terms of quantity in a world which is equally truly qualitative. All that is necessary is to select the elements which are most effective for prediction and control. Such selection gives the principle that dominates all abstractions. Progress is movement from the less abstract to the more abstract, but it is progress only because the more abstract is as genuinely an aspect of the concrete starting-point as anything is. Moreover, the outcome of progress of this sort cannot be definitely foreseen at the beginnings. The simple activities of primitive men have to be spontaneously performed before their value becomes evident. Only afterwards can they be cultivated for the sake of their value, and then only can the self-conscious cultivation of a science begin. The process remains full not only of perplexities, but of surprises; men's activities lead to goals far other than those which appear at the start. These goals, however, never deny the method by which the start is made. Developed intelligence is nothing but skill in using a set of concepts generated in this manner. In this sense the histories of all human endeavors run parallel.

Where the empirical bases of a science are continually in the foreground, as in physics or chemistry, the foregoing formulation of procedure is intelligible and acceptable to most men. Mathematics seem, however, to stand peculiarly apart. Many, with Descartes, have delighted in them "on account of the certitude and evidence of their reasonings" and recognized their contribution to the advancement of mechanical arts. But since the days of Kant even this value has become a problem, and many a young philosophic student has the question laid before him as to why it is that mathematics, "a purely conceptual science," can tell us anything about the character of a world which is, apparently at least, free from the idiosyncrasies of individual mind. It may be that mathematics began in empirical practice, such philosophers admit, but they add that, somehow, in its later career, it has escaped its lowly origin. Now it moves in the higher circles of postulated relations and arbitrarily defined entities to which its humble progenitors and relatives are denied the entrée. Parvenus, however, usually bear with them the mark of history, and in the case of this one, at least, we may hope that the history will be sufficient to drag it from the affectations of its newly acquired set and reinstate it in its proper place in the workaday world. For the sake of this hope, we shall take the risk of being tedious by citing certain striking moments of mathematical progress; and then we shall try to interpret its genuine status in the world of working truths.

I

Beginnings of Arithmetic and Geometry

The most primitive mathematical activity of man is counting, but here his first efforts are lost in the obscurity of the past. The lower races, however, yield us evidence that is not without value. Although the savage mind is not identical with the mind of primitive man, there is much in the activities of undeveloped races that can throw light upon the behavior of peoples more advanced. We must be careful in our inferences, however. Among the Australians and South Americans there are peoples whose numerical systems go little, or not at all, beyond the first two or three numbers. "It has been inferred from this," writes Professor Boas (Mind of Primitive Man, pp. 152-53), "that the people speaking these languages are not capable of forming the concept of higher numbers.... People like the South American Indians, ... or like the Esquimo ... are presumably not in need of higher numerical expressions, because there are not many objects that they have to count. On the other hand, just as soon as these same people find themselves in contact with civilization, and when they acquire standards of value that have to be counted, they adopt with perfect ease higher numerals from other languages, and develop a more or less perfect system of counting.... It must be borne in mind that counting does not become necessary until objects are considered in such generalized form that their individualities are entirely lost sight of. For this reason it is possible that even a person who owns a herd of domesticated animals may know them by name and by their characteristics, without even desiring to count them."

And there is one other false interpretation to be avoided. Man does not feel the need of counting and then develop a system of numerals to meet the need. Such an assumption is as ridiculous as to assume prehistoric man thinking to himself: "I must speak," and then inventing voice culture and grammar to make speaking pleasant and possible. Rather, when powers of communication are once attained, presumably in their beginnings also without forethought, man being still more animal than man, there were gradually dissociated communications of a kind approaching what numbers mean to us. But the number is not yet a symbol apart from that of the things numbered. Picture writing, re-representing the things meant, preceded developmentally any kind of symbolization representing the number by mere one-one correspondence with non-particularized symbols. It is plausible, although I have no anthropological authority for the statement, that the prevalence of finger words as number symbols (cf. infra) is originally a consequence of the fact that our organization makes the hand the natural instrument of pointing.

The difficulty of passing from concrete representations to abstract symbols has been keenly stated by Conant (The Number Concept, pp. 72-73), although his terminology is that of an old psychology and the limitations implied for the primitive mind are limitations of practice rather than of capacity as Mr. Conant seems to believe. "An abstract conception is something quite foreign to the essentially primitive mind, as missionaries and explorers have found to their chagrin. The savage can form no mental concept of what civilized man means by such a word as soul; nor would his idea of the abstract number 5 be much clearer. When he says five, he uses, in many cases at least, the same word that serves him when he wishes to say hand; and his mental concept when he says five is a hand. The concrete idea of a closed fist, of an open hand with outstretched fingers, is what is uppermost in his mind. He knows no more and cares no more about the pure number 5 than he does about the law of conservation of energy. He sees in his mental picture only the real, material image, and his only comprehension of the number is, "these objects are as many as the fingers on my hand." Then, in the lapse of the long interval of centuries which intervene between lowest barbarism and highest civilization, the abstract and concrete become slowly dissociated, the one from the other. First the actual hand picture fades away, and the number is recognized without the original assistance furnished by the derivation of the word. But the number is still for a long time a certain number of objects, and not an independent concept."

An excellent fur trader's story, reported to me by Mr. Dewey, suggests a further impulse to count besides that given by the need of keeping a tally, namely, the need of making one thing correspond to another in a business transaction. The Indian laid down one skin and the trader two dollars; if he proposed to count several skins at once and pay for all together, the former replied "too much cheatem." The result, however, demanded a tally either by the fingers, a pebble, or a mark made in the sand, and as the magnitude of such transactions grows the need of a specific number symbol becomes ever more acute.

The first obstacle, then, to overcome—and it has already been successfully passed by many primitive peoples—is the need of fortuitous attainment of a numerical symbol, which is not the mere repeated symbol of the things numbered. Significantly, this symbol is usually derived from the hand, suggesting gestures of tallying, and not from the words of already developed language. Consequently, number words relate themselves for the most part to the hand, and written number symbols, which are among the earliest writings of most peoples, tend to depict it as soon as they have passed beyond the stage mentioned above of merely repeating the symbol of the things numbered. W. C. Eells, in writing of the Number Systems of the North American Indians (Am. Math. Mo., Nov., 1913; pp. 263-72), finds clear linguistic evidence for a digital origin in about 40% of the languages examined. Of the non-digital instances, 1 was sometimes connected with the first personal pronoun, 2 with roots meaning separation, 3, rarely, meaning more, or plural as distinguished from the dual, just as the Greek uses a plural as well as a dual in nouns and verbs, 4 is often the perfect, complete right. It is often a sacred number and the base of a quarternary system. Conant (loc. cit. p. 98) also gives a classification of the meanings of simple number words for more advanced languages; and even in them the hand is constantly in evidence, as in 5, the hand; 10, two hands, half a man, when fingers and toes are both considered, or a man, when the hands alone are considered; 20, one man, two feet. The other meanings hang upon the ideas of existence, piece, group, beginning, for 1; and repetition, division, and collection for higher numerals.

A peculiar difficulty lies in the fact that when once numbering has become a self-conscious effort, the collection of things to be numbered frequently tends to exceed the number of names that have become available. Sometimes the difficulty is met by using a second man when the fingers and toes of the first are used up, sometimes by a method of repetition with the record of the number of the repetition itself added to the numerical significance of the whole process. Hence arise the various systems of bases that occur in developed mathematics. But the inertia to be overcome in the recognition of the base idea is nowhere more obvious than in the retention by the comparatively developed Babylonian system of a second base of 60 to supplement the decimal one for smaller numbers. Among the American Indians (Eells, loc. cit.) the system of bases used varies from the cumbersome binary scale, that exercised such a fascination over Leibniz (Opera, III, p. 346), through the rare ternary, and the more common quarternary to the "natural" quinary, decimal, and vigesimal systems derived from the use of the fingers and toes in counting. The achievement of a number base and number words, however, does not always open the way to further mathematical development. Only too often a complexity of expression is involved that almost immediately cuts off further progress. Thus the Youcos of the Amazon cannot get beyond the number three, for the simplest expression for the idea in their language is "pzettarrarorincoaroac" (Conant, loc. cit., pp. 145, 83, 53). Such names as "99, tongo solo manani nun solo manani" (i.e., 10, understood, 5 plus 4 times, and 5 plus 4) of the Soussous of Sierra Leone; "399, caxtolli onnauh poalli ipan caxtolli onnaui" (15 plus 4 times 20 plus 15 plus 4) of the Aztec; "29, wick a chimen ne nompah sam pah nep e chu wink a" (Sioux), make it easy to understand the proverb of the Yorubas of Abeokuta, "You may be very clever, but you can't tell 9 times 9."

Almost contemporaneously with the beginnings of counting various auxiliary devices were introduced to help out the difficult task. In place of many men, notched sticks, knotted strings, pebbles, or finger pantomime were used. In the best form, these devices resulted in the abacus; indeed, it was not until after the introduction of arabic numerals and well into the Renaissance period that instrumental arithmetic gave way to graphical in Europe (D. E. Smith, Rara Arithmetica, under "Counters"). "In eastern Europe," say Smith and Mikami (Japanese Mathematics, pp. 18-19), "it"—the abacus—"has never been replaced, for the tschotü is used everywhere in Russia to-day, and when one passes over into Persia the same type of abacus is common in all the bazaars. In China the swan-pan is universally used for the purposes of computation, and in Japan the soroban is as strongly entrenched as it was before the invasion of western ideas."

Given, then, the idea of counting, and a mechanical device to aid computation, it still remains necessary to obtain some notation in which to record results. At the early dawn of history the Egyptians seem to have been already possessed of number signs (cf. Cantor, Gesch. de. Math., p. 44) and the Phœnicians either wrote out their number words or used a few simple signs, vertical, horizontal, and oblique lines, a process which the Arabians perpetuated up to the beginning of the eleventh century (Fink, p. 15); the Greeks, as early as 600 B. C., used the initial letters of words for numbers. But speaking generally, historical beginnings of European number signs are too obscure to furnish us good material.

Our Indians have few number symbols other than words, but when they occur (cf. Eells, loc. cit.) they usually take the form of pictorial presentation of some counting device such as strokes, lines dotted to suggest a knotted cord, etc. Indeed, the smaller Roman numerals were probably but a pictorial representation of finger symbols. However, a beautiful concrete instance is furnished us in the Japanese mathematics (cf. Smith and Mikami, Ch. III). The earliest instrument of reckoning in Japan seems to have been the rod, Ch'eou, adapted from the Chinese under the name of Chikusaku (bamboo rods) about 600 A. D. At first relatively large (measuring rods?), they became reduced to about 12 cm., but from their tendency to roll were quickly replaced by the sangi (square prisms, about 7 mm. thick and 5 cm. long) and the number symbols were evidently derived from the use of these rods:

For the sake of clearness, tens, hundreds, etc., were expressed in the even place by horizontal instead of vertical lines and vice versa; thus 1267 would be formed

The rods were arranged on a sort of chessboard called the swan-pan. Much later the lines were transferred to paper, and a circle used to denote the vacant square. The use of squares, however, rendered it unnecessary to arrange the even places differently from the odd, so numbers like 38057 came to be written

instead of

as in the earlier notation.

Somewhere in the course of these early mathematical activities the process has changed from the more or less spontaneous operating that led primitive man to the first enunciation of arithmetical ideas, and has become a self-conscious striving for the solution of problems. This change had already taken place before the historical origins of arithmetic are met. Thus, the treatise of Ahmes (2000 B. C.) contains the curious problem: 7 persons each have 7 cats; each cat eats 7 mice; each mouse eats 7 ears of barley; from each ear 7 measures of corn may grow; how much grain has been saved? Such problems are, however, half play, as appears in a Leonardo of Pisa version some 3000 years later: 7 old women go to Rome; each woman has 7 mules; each mule, 7 sacks; each sack contains 7 loaves; with each loaf are 7 knives; each knife is in 7 sheaths. Similarly in Diophantus' epitaph (330 A. D.): "Diophantus passed 1/6 of his life in childhood, 1/12 in youth, and 1/7 more as a bachelor; 5 years after his marriage, was born a son who died 4 years before his father at 1/2 his age." Often among peoples such puzzles were a favorite social amusement. Thus Braymagupta (628 A. D.) reads, "These problems are proposed simply for pleasure; the wise man can invent a thousand others, or he can solve the problems of others by the rules given here. As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them" (Cajori, Hist. of Math., p. 92).

The limitation of these early methods is that the notation merely records and does not aid computation. And this is true even of such a highly developed system as was in use among the Romans. If the reader is unconvinced, let him attempt some such problem as the multiplication of CCCXVI by CCCCLXVIII, expressing it and carrying it through in Roman numerals, and he will long for the abacus to assist his labors. It was the positional arithmetic of the Arabians, of which the origins are obscure, that made possible the development of modern technique. Of this discovery, or rediscovery from the Hindoos, together with the zero symbol, Cajori (Hist. of Math., p. 11) has said "of all mathematical discoveries, no one has contributed more to the general progress of intelligence than this." The notation no longer merely records results, but now assists in performing operations.

The origins of geometry are even more obscure than those of arithmetic. Not only is geometry as highly developed as arithmetic when it first appears in occidental civilization, but, in addition, the problems of primitive peoples seem to have been such that they have developed no geometrical formulæ striking enough to be recorded by investigators, so far as I have been able to discover. But just as the commercial life of the Phœnicians early forced them self-consciously to develop arithmetical calculation, so environmental conditions seem to have forced upon the Egyptians a need for geometrical considerations.

It is almost platitudinous to quote Herodotus' remark that the invention of geometry was necessary because of the floods of the Nile, which washed away the boundaries and changed the contours of the fields. And as Proclus Diadochus adds (Procli Diadochi, in primum Euclidis elementorum librum commentarii—quoted Cantor, I, p. 125): "It is not surprising that the discovery of this as well as other sciences has sprung from need, because everything in the process of beginning proceeds from the incomplete to the complete. There takes place a suitable transition from sensible perception to thoughtful consideration and rational knowledge. Just as with the Phœnicians, for the sake of business and commerce, an exact knowledge of numbers had its beginning, so with the Egyptians, for the above-mentioned reasons, was geometry contrived."

The earliest Egyptian mathematical writing that we know is that of Ahmes (2000 B. C.), but long before this the mural decorations of the temple wall involved many figures, the construction of which involved a certain amount of working knowledge of such operations as may be performed with the aid of a ruler and compass. The fact that these operations did not earlier lead to geometry, as ruler and compass work seems to have done in Japan in the nineteenth century (Smith and Mikami, index, "Geometry"), is probably due to the stage at which the development of Egyptian intelligence had arrived, feebly advanced on the road to higher abstract thinking. It is everywhere characteristic of Egyptian genius that little purely intellectual curiosity is shown. Even astronomical knowledge was limited to those determinations which had religious or magically practical significance, and its arithmetic and geometry never escaped these bounds as with the more imaginative Pythagoreans, where mystical interpretation seems to have been a consequence of rather than a stimulus to investigation. An old Egyptian treatise reads (Cantor, p. 63): "I hold the wooden pin (Nebi) and the handle of the mallet (semes), I hold the line in concurrence with the Goddess Sạfech. My glance follows the course of the stars. When my eye comes to the constellation of the great bear and the time of the number of the hour determined by me is fulfilled, I place the corner of the temple." This incantation method could hardly advance intelligence; but the methods of practical measuring were more effective. Here the rather happy device of using knotted cords, carried about by the Harpedonapts, or cord stretchers, was of some moment. Especially, the fact that the lengths 3, 4, and 5, brought into triangular form, served for an interesting connection between arithmetic and the right triangle, was not a little gain, later making possible the discovery of the Pythagorean theorem, although in Egypt the theoretical properties of the triangle were never developed. The triangle obviously must have been practically considered by the decorators of the temple and its builders, but the cord stretchers rendered clear its arithmetical significance. However, Ahmes' "Rules for attaining the knowledge of all dark things ... all secrets that are contained in objects" (Cantor, loc. cit., p. 22) contains merely a mixture of all sorts of mathematical information of a practical nature,—"rules for making a round fruit house," "rules for measuring fields," "rules for making an ornament," etc., but hardly a word of arithmetical and geometrical processes in themselves, unless it be certain devices for writing fractions and the like.

II

The Progress of Self-conscious Theory

A characteristic of Greek social life is responsible both for the next phase of the development of mathematical thought and for the misapprehension of its nature by so many moderns. "When Archytas and Menaechmus employed mechanical instruments for solving certain geometrical problems, 'Plato,' says Plutarch, 'inveighed against them with great indignation and persistence as destroying and perverting all the good that there is in geometry; for the method absconds from incorporeal and intellectual or sensible things, and besides employs again such bodies as require much vulgar handicraft: in this way mechanics was dissimilated and expelled from geometry, and being for a long time looked down upon by philosophy, became one of the arts of war.' In fact, manual labor was looked down upon by the Greeks, and a sharp distinction was drawn between the slaves who performed bodily work and really observed nature, and the leisured upper classes who speculated, and often only knew nature by hearsay. This explains much of the naïve dreamy and hazy character of ancient natural science. Only seldom did the impulse to make experiments for oneself break through; but when it did, a great progress resulted, as was the case of Archytas and Archimedes. Archimedes, like Plato, held that it was undesirable for a philosopher to seek to apply the results of science to any practical use; but, whatever might have been his view of what ought to be in the case, he did actually introduce a large number of new inventions" (Jourdain, The Nature of Mathematics, pp. 18-19). Following the Greek lead, certain empirically minded modern thinkers construe geometry wholly from an intellectual point of view. History is read by them as establishing indubitably the proposition that mathematics is a matter of purely intellectual operations. But by so construing it, they have, in geometry, remembered solely the measuring and forgotten the land, and, in arithmetic, remembered the counting and forgotten the things counted.

Arithmetic experienced little immediate gain from its new association with geometry, which was destined to be of momentous import in its latter history, beyond the discovery of irrationals (which, however, were for centuries not accepted as numbers), and the establishment of the problem of root-taking by its association with the square, and interest in negative numbers.

The Greeks had only subtracted smaller numbers from larger, but the Arabs began to generalize the process and had some acquaintance with negative results, but it was difficult for them to see that these results might really have significance. N. Chuquet, in the fifteenth century, seems to have been the first to interpret the negative numbers, but he remained a long time without imitators. Michael Stifel, in the sixteenth century, still calls them "Numeri absurdi" as over against the "Numeri veri." However, their geometrical interpretation was not difficult, and they soon won their way into good standing. But the case of the imaginary is more striking. The need for it was first felt when it was seen that negative numbers have no square roots. Chuquet had dealt with second-degree equations involving the roots of negative numbers in 1484, but says these numbers are "impossible," and Descartes (Geom., 1637) first uses the word "imaginary" to denote them. Their introduction is due to the Italian algebrists of the sixteenth century. They knew that the real roots of certain algebraic equations of the third degree are represented as results of operations effected upon "impossible" numbers of the form a + b√-1 (where a and b are real numbers) without it being possible in general to find an algebraic expression for the roots containing only real numbers. Cardan calculated with these "impossibles," using them to get real results [(5 + √-15) (5 - √-15) = 25 - (-15) = 40], but adds that it is a "quantitas quae vere est sophistica" and that the calculus itself "adeo est subtilis ut est inutilis." In 1629, Girard announced the theorem that every complete algebraic equation admits of as many roots, real or imaginary, as there are units in its degree, but Gauss first proved this in 1799, and finally, in his Theory of Complex Quantity, in 1831.

Geometry, however, among the Greeks passed into a stage of abstraction in which lines, planes, etc., in the sense in which they are understood in our elementary texts, took the place of actually measured surfaces, and also took on the deductive form of presentation that has served as a model for all mathematical presentation since Euclid. Mensuration smacked too much of the exchange, and before the time of Archimedes is practically wholly absent. Even such theorems as "that the area of a triangle equals half the product of its base and its altitude" is foreign to Euclid (cf. Cajori, p. 39). Lines were merely directions, and points limitations from which one worked. But there was still dependence upon the things that one measures. Euclid's elements, "when examined in the light of strict mathematical logic, ... has been pronounced by C. S. Peirce to be 'Riddled with fallacies'" (Cajori, p. 37). Not logic, but observation of the figures drawn, that is, concrete symbolization of the processes indicated, saves Euclid from error.

Roman practical geometry seems to have come from the Etruscans, but the Roman here is as little inventive as in his arithmetical ventures, although the latter were stimulated somewhat by problems of inheritance and interest reckoning. Indeed, before the entrance of Arabic learning into Europe and the translation of Euclid from the Arabic in 1120, there is little or no advance over the Egyptian geometry of 600 B. C. Even the universities neglected mathematics. At Paris "in 1336 a rule was introduced that no student should take a degree without attending lectures on mathematics, and from a commentary on the first six books of Euclid, dated 1536, it appears that candidates for the degree of A. M. had to give an oath that they had attended lectures on these books. Examinations, when held at all, probably did not extend beyond the first book, as is shown by the nickname 'magister matheseos' applied to the Theorem of Pythagoras, the last in the first book.... At Oxford, in the middle of the fifteenth century, the first two books of Euclid were read" (Cajori, loc. cit., p. 136). But later geometry dropped out and not till 1619 was a professorship of geometry instituted at Oxford. Roger Bacon speaks of Euclid's fifth proposition as "elefuga," and it also gets the name of "pons asinorum" from its point of transition to higher learning. As late as the fourteenth century an English manuscript begins "Nowe sues here a Tretis of Geometri whereby you may knowe the hegte, depnes, and the brede of most what erthely thynges."

The first significant turning-point lies in the geometry of Descartes. Viete (1540-1603) and others had already applied algebra to geometry, but Descartes, by means of coördinate representation, established the idea of motion in geometry in a fashion destined to react most fruitfully on algebra, and through this, on arithmetic, as well as enormously to increase the scope of geometry. These discoveries are not, however, of first moment for our problem, for the ideas of mathematical entities remain throughout them the generalized processes that had appeared in Greece. It is worth noting, however, that in England mechanics has always been taught as an experimental science, while on the Continent it has been expanded deductively, as a development of a priori principles.

III

Contemporary Thought in Arithmetic and Geometry

To develop the complete history of arithmetic and geometry would be a task quite beyond the limits of this paper, and of the writer's knowledge. In arithmetic we were able to observe a stage in which spontaneous behavior led to the invention of number names and methods of counting. Then, by certain speculative and "play" impulses, there arose elementary arithmetical problems which began to be of interest in themselves. Geometry here also comes into consideration, and, in connection with positional number symbols, begin those interactions between arithmetic and geometry that result in the forms of our contemporary mathematics. The complex quantities represented by number symbols are no longer merely the necessary results of analyzing commercial relations or practical measurements, and geometry is no longer directly based upon the intuitively given line, point, and plane. If number relations are to be expressed in terms of empirical spatial positions, it is necessary to construct many imaginary surfaces, as is done by Riemann in his theory of functions, a construction representing the type of imagination which Poincaré has called the intuitional in contradistinction to the logical (Value of Science, Ch. I). And geometry has not only been led to the construction of many non-Euclidian spaces, but has even, with Peano and his school, been freed from the bonds of any necessary spatial interpretation whatsoever.

To trace in concrete detail the attainment of modern refinements of number theory would likewise exhibit nothing new in the building up of mathematical intelligence. We should find, here, a process carried out without thought of the consequences, there, an analogy suggesting an operation that might lead us beyond a difficulty that had blocked progress; here, a play interest leading to a combination of symbols out of which a new idea has sprung; there, a painstaking and methodical effort to overcome a difficulty recognized from the start. It is rather for us now to ask what it is that has been attained by these means, to inquire finally what are those things called "number" and "line" in the broad sense in which the terms are now used.

In so far as the cardinal number at least is concerned, the answer generally accepted by Dedekind, Peano, Russell, and such writers is this: the number is a "class of similar classes" (Whitehead and Russell, Prin. Math., Vol. II, p. 4). To the interpretation of this answer, Mr. Russell, the most self-consciously philosophical of these mathematicians, has devoted his full dialectic skill. The definition has at least the merit of being free from certain arbitrary psychologizing that has vitiated many earlier attempts at the problem. Mr. Russell claims for it "(1) that the formal properties which we expect cardinal numbers to have result from it; (2) that unless we adopt this definition or some more complicated and practically equivalent definition, it is necessary to regard the cardinal number of a class as indefinable" (loc. cit., p. 4). That the definition's terms, however, are not without obscurity appears in Mr. Russell's struggles with the zigzag theory, the no-class theory, etc., and finally in his taking refuge in the theory of "logical types" (loc. cit., Vol. III, Part V. E.), whereby the contradiction that subverted Frege and drove Mr. Russell from the standpoint of the Principles of Mathematics is finally overcome.

The second of Mr. Russell's claims for his definition adds nothing to the first, for it merely asserts that unless we adopt some definition of the cardinal number from which its formal properties result, number is undefined. Any such definition would be, ipso facto, a practical equivalent of the first. We need only consider whether or not the formal properties of numbers clearly follow from this definition.

Mr. Russell's own experience makes us hesitate. When he first adopted this definition from Frege, he was led to make the inference that the class of all possible classes might furnish a type for a greatest cardinal number. But this led to nothing but paradox and contradiction. The obvious conclusion was that something was wrong with the concept of class, and the obvious way out was to deny the possibility of any such all-inclusive class. Just why there should be such limitation, except that it enables one to escape the contradiction, is not clear from Mr. Russell's analysis (cf. Brown, "The Logic of Mr. Russell," Journ. of Phil., Psych., and Sci. Meth., Vol. VIII, No. 4, pp. 85-89). Furthermore, to pass to the theory of types on this ground is to give up the value of the first claim for the definition (quoted above), since the formal properties of numbers now merely follow from the definition because the terms of the definition are reinterpreted from the properties of number, so that these properties will follow from it. The definition has become circular.

The real difficulty lies in the concept of the class. Dogmatic realism is prone to find here an entity for which, as it is obviously not a physical thing, a home must be provided in some region of "being." Hence arises the realm of subsistence, as for Plato the world of facts duplicated itself in a world of ideas. But the subsistent realm of the mathematician is even more astounding than the ideal realm of Plato, for the latter world is a prototype of the world of things, while the world of the mathematician is peopled by all sorts of entities that never were on land or sea. The transfinite numbers of Cantor have, without doubt, a definite mathematical meaning, but they have no known representatives in the world of things, nor in the imagination of man, and in spite of the efforts of philosophers it may even be doubted whether an entity correlative to the mathematical infinite has ever been or can ever be specified.

Mr. Russell now teaches that "classes are merely symbolic" (Sci. Meth. in Phil., p. 208), but this expression still needs elucidation. It does, to be sure, avoid the earlier difficulty of admitting "new and mysterious metaphysical entities" (loc. cit., p. 204), but the "feeling of oddity" that accompanies it seems not without significance. What can be meant by a merely symbolic class of similar classes themselves merely symbolical? I do not know, unless it is that we are to throw overboard the effort aimed at arbitrary and creative definition and proceed in simple inductive and interpretative fashion. With classes as entities abandoned, we are left, until we have passed to a new point of view as to arithmetical entities, in the position of the intelligent ignoramus who defined a stock market operation as buying what you can't get with money you never had, and selling what you never owned for more than it was ever worth.

The situation seems to be that we are now face to face with new generalizations. Just as number symbols arose to denote operations gone through in counting things when attention is diverted from the particular characteristics of the things counted, and remained a symbol for those operations with things, so now we are becoming self-conscious of the character of the operations we have been performing and are developing new symbols to express possible operations with operations. The infinity of the number series expresses the fact that it is possible to continue the enumerating process indefinitely, and when we are asked by certain mathematicians to practise ourselves in such thoughts as that for infinite series a proper part can be the equal of the whole, where equality is defined through the establishment of one-one correspondence, we are really merely informed that among the group of symbols used to denote the concrete steps of an ever open counting process are groups of symbols that can be used to indicate operations that are of the same type as the given one in so far as the characteristic of being an open series is concerned. If there were anywhere an infinity of things to count, an unintelligible supposition, it would by no means be true that any selection of things from that series would be the equivalent of all things in the series, except in so far as equivalence meant that they could be arranged in the same type of series as that from which they were drawn.

Similarly the mathematical conception of the continuum is nothing but a formulation of the manner in which the cuts of a line or the numbers of a continuous series must be chosen so that there shall remain no possible cut or number of which the choice is not indicated. Correspondence is reached between elements of such series when the corresponding elements can be reached by an identical process. It seems to me, however, a mistake to identify the number continuum with the linear continuum, for the latter must include the irrational numbers, whereas the irrational number can never represent a spatial position in a series. For example, the √2 is by nature a decimal involving an infinite, i.e., an ever increasing, number of digits to express it and, by virtue of the infinity of these digits, they can never be looked upon as all given. It is then truly a number, for it expresses a genuine numerical operation, but it is not a position, for it cannot be a determinate magnitude but merely a quantity approaching a determinate magnitude as closely as one may please. That is, without its complete expression, which would be analogous to the self-contradictory task of finding a greatest cardinal number, there can be no cut in the line which is symbolized by it. But the operations of translating algebraic expressions into geometrical ones and vice versa (operations which are so important in physical investigations) are facilitated by the notion of a one to one correspondence between number and space.

When we pass to the transfinite numbers, we have nothing in the Alephs but the symbols of certain groupings of operations expressible in ordinary number series. And the many forms of numbers are all simply the result of recognizing value in naming definite groups of operations of a lower level, which may itself be a complication of processes indicated by the simple numerical signs. To create such symbols is by no means illegitimate and no paradox results in any forms as long as we remember that our numbers are not things but are signs of operations that may be performed directly upon things or upon other operations.

For example, let us consider such a symbol as √-5. -5 signifies the totality of a counting process carried on in an opposite sense from that denoted by +5. To take the square root is to symbolize a number, the totality of an operation, such that when the operation denoted by multiplying it by itself is performed the result is 5. Consequently the √-5 is merely the symbol of these processes combined in such a way that the whole operation is to be considered as opposite in some sense to that denoted by √5. Hence, an easy method for the representation of such imaginaries is based on the principle of analytic geometry and a system of co-ordinates.

The nature of this last generalization of mathematics is well shown by Mr. Whitehead in his monumental Universal Algebra. The work begins with the definition of a calculus as "The art of manipulating substitutive signs according to fixed rules, and the deduction therefrom of true propositions" (loc. cit., p. 4). The deduction itself is really a manipulation according to rules, and the truth consists essentially in the results being actually derived from the premises according to rule. Following Stout, substitutive signs are characterized thus: "a word is an instrument for thinking about the meaning which it expresses; a substitutive sign is a means of not thinking about the meaning which it symbolizes." Mathematical symbols have, then, become substitutive signs. But this is only possible because they were at an early stage of their history expressive signs, and the laws which connected them were derived from the relations of the things for which they stood. First it became possible to forget the things in their concreteness, and now they have become mere terms for the relations that had been generalized between them. Consequently, the things forgotten and the terms treated as mere elements of a relational complex, it is possible to state such relational complexes with the utmost freedom. But this does not mean that mathematics can be created in a purely arbitrary fashion. The mark of its origin is upon it in the need of exhibiting some existing situation through which the non-contradictory character of its postulates can be verified. The real advantage of the generalization is that of all generalizations in science, namely, that by looking away from practical applications (as appears in a historical survey) results are frequently obtained that would never have been attained if our labor had been consciously limited merely to those problems where the advantages of a solution were obvious. So the most fantastic forms of mathematics, which themselves seem to bear no relation to actual phenomena, just because the relations involved in them are the relations that have been derived from dealing with an actual world, may contribute to the solutions of problems in other forms of calculus, or even to the creation of new forms of mathematics. And these new forms may stand in a more intimate connection with aspects of the real world than the original mathematics.

In 1836-39 there appeared in the Gelehrte Schriften der Universität Kasan, Lobatchewsky's epoch-making "New Elements of Geometry, with a Complete Theory of Parallels." After proving that "if a straight line falling on two other straight lines make the alternate angles equal to one another, the two straight lines shall be parallel to one another," Euclid, finding himself unable to prove that in every other case they were not parallel, assumed it in an axiom. But it had never seemed obvious. Lobatchewsky's system amounted merely to developing a geometry on the basis of the contradictory axiom, that through a point outside a line an indefinite number of lines can be drawn, no one of which shall cut a given line in that plane. In 1832-33, similar results were attained by Johann Bolyai in an appendix to his father's "Tentamen juventutem studiosam in elementa matheseosos puræ ... introducendi" entitled "The Science of Absolute Space." In 1824 the dissertation of Riemann, under Gauss, introduced the idea of an n-ply extended magnitude, or a study of n-dimensional manifolds and a new road was opened for mathematical intelligence.

At first this new knowledge suggested all sorts of metaphysical hypotheses. If it is possible to build geometries of n-dimensions or geometries in which the axiom of parallels is no longer true, why may it not be that the space in which we make our measurements and on which we base our mechanics is some one of these "non-Euclidian" spaces? And indeed many experiments were conducted in search of some clue that this might be the case. Such experiments in relation to "curved spaces" seemed particularly alluring, but all have turned out to be fruitless in results. Failure leads to investigation of the causes of failure. If our space had been some one of these spaces how would it have been possible for us to know this fact? The traditional definition of a straight line has never been satisfactory from a physical point of view. To define it as the shortest distance between two points is to introduce the idea of distance, and the idea of distance itself has no meaning without the idea of straight line, and so the definition moves in a vicious circle. On the metaphysical side, Lotze (Metaphysik, p. 249) and others (Merz, History of European Thought in the Nineteenth Century, Vol. II, p. 716) criticized these attempts, on the whole justly, but the best interpretation of the situation has been given by Poincaré.

Two lines of thought now lead to a recasting of our conceptions of the fundamental notions of geometry. On the one hand, that very investigation of postulates that had led to the discovery of the apparently strange non-Euclidian geometries was easily continued to an investigation of the simplest basis on which a geometry could be founded. Then by reaction it was continued with similar methods in dealing with algebra, and other forms of analysis, with the result that conceptions of mathematical entities have gradually emerged that represent a new stage of abstraction in the evolution of mathematics, soon to be discussed as the dominating conceptions in contemporary thought. On the other hand, there also developed the problem of the relations of these geometrical worlds to one another, which has been primarily significant in helping to clear up the relations of mathematics in its "pure" and "applied" forms.

Geometry passed through a stage of abstraction like that examined in connection with arithmetic. Beginning with the discovery of non-Euclidian geometry, it has been becoming more and more evident that a line need not be a name for an aspect of a physical object such as the ridge-pole line of a house and the like, nor even for the more abstract mechanical characteristic of direction of movement;—although the persistency with which intuitionally minded geometers have sought to adapt such illustrations to their needs has somewhat obscured this fact. However, even a cursory examination of a modern treatise on geometry makes clear what has taken place. For example, Professor Hilbert begins his Grundlagen der Geometrie, not with definition of points, lines, and planes, but with the assumption of three different systems of things (Dinge) of which the first, called points, are denoted A, B, C, etc., second, called straight lines (Gerade), are denoted a, b, c, etc., and the third, called planes, are denoted by α, β, γ, etc. The relations between these things then receive "genaue und vollständige Beschreibung" through the axioms of the geometry. And the fact that these "things" are called points, lines, and planes is not to give to them any of the connotations ordinarily associated with these words further than are determined by the axiom groups that follow. Indeed, other geometers are even more explicit on this point. Thus for Peano (I Principii di Geometria, 1889) the line is a mere class of entities, the relations amongst which are no longer concrete relations but types of relations. The plane is a class of classes of entities, etc. And an almost unlimited number of examples, about which the theorems of the geometry will express truths, can be exhibited, not one of which has any close resemblance to spatial facts in the ordinary sense.

Philosophers, it seems to me, have been slow to recognize the significance of the step involved in this last phase of mathematical thought. We have been so schooled in an arbitrary distinction between relations and concepts, that while long familiar with general ideas of concepts, we are not familiar with generalized ideas of relations. Yet this is exactly what mathematics is everywhere presenting. A transition has been made from relations to types of relations, so that instead of speaking in terms of quantitative, spatial and temporal relations, mathematicians can now talk in terms of symmetrical, asymmetrical, transitive, intransitive relational types and the like. These present, however, nothing but the empirical character that is common to such relations as that of father and son; debtor and creditor; master and servant; a is to the left of b, b of c; c of d; a is older than b, b than c, c than d, etc. Hence this is not abandonment of experience but a generalization of it, which results in a calculus potentially applicable not only to it but also to other subject-matter of thought. Indeed, if it were not for the possibility of this generalization, the almost unlimited applicability of diagrams, so useful in the classroom, to illustrate everything from the nature of reality to the categorical imperative, as well as to the more technical usages of the psychological and social sciences, would not be understandable.

It would be a paradox, however, if starting out from processes of counting and measuring, generalizations had been attained that no longer had significance for counting or measuring, and the non-Euclidian hyper-dimensional geometries seem at first to present this paradox. But, as the outcome of our second line of thought proves, this is not the case. The investigation of the relations of different geometrical systems to each other has shown (cf. Brown, "The Work of H. Poincaré," Journ. of Phil., Psy., and Sci. Meth., Vol. XI, No. 9, p. 229) that these different systems have a correspondence with one another so that for any theorem stated in one of them there is a corresponding theorem that can be stated in another. In other words, given any factual situation that can be stated in Euclidian geometry, the aspect treated as a straight line in the Euclidian exposition will be treated as a curve in the non-Euclidian, and a situation treated as three-dimensional by Euclid's methods can be treated as of any number of dimensions when the proper fundamental element is chosen, and vice versa, although of course the element will not be the line or plane in our empirical usage of the term. This is what Poincaré means by saying that our geometry is a free choice, but not arbitrary (The Value of Science, Pt. III, Ch. X, Sec. 3), for there are many limitations imposed by fact upon the choice, and usually there is some clear indication of convenience as to the system chosen, based on the fundamental ideal of simplicity.

It is evident, then, that geometry and arithmetic have been drawing closer together, and that to-day the distinction between them is somewhat hard to maintain. The older arithmetic had limited itself largely to the study of the relations involved in serial orders as suggested by counting, whereas geometry had concerned itself primarily with the relations of groups of such series to each other when the series, or groups of series, are represented as lines or planes. But partly by interaction in analytic geometry, and partly in the generalization of their own methods, both have come to recognize the fundamental character of the relations involved in their thought, and arithmetic, through the complex number and the algebraic unknown quantities, has come to consider more complex serial types, while geometry has approached the analysis of its series through interaction with number theory. For both, the content of their entities and the relations involved have been brought to a minimum. And this is true even of such apparently essentially intuitional fields as projective geometry, where entities can be substituted for directional lines and the axioms be turned into relational postulates governing their configurations.

Nevertheless, geometry like arithmetic, has remained true to the need that gave it initial impulse. As in the beginning it was only a method of dealing with a concrete situation, so in the end it is nothing but such a method, although, as in the case of arithmetic, from ever closer contact with the situation in question, it has been led, by refinements that thoughtful and continual contact bring, to dissect that situation and give heed to aspects of it which were undreamed of at the initial moment. In a sense, then, there are no such things as mathematical entities, as scholastic realism would conceive them. And yet, mathematics is not dealing with unrealities, for it is everywhere concerned with real rational types and systems where such types may be exemplified. Or we can say in a purely practical way that mathematical entities are constituted by their relations, but this phrase cannot here be interpreted in the Hegelian ontological sense in which it has played so great and so pernicious a part in contemporary philosophy. Such metaphysical interpretation and its consequences are the basis of paradoxical absolutisms, such as that arrived at by Professor Royce (World and the Individual, Vol. II, Supplementary Essay). The peculiar character of abstract or pure mathematics seems to be that its own operations on a lower level constitute material which serves for the subject-matter with which its later investigations deal. But mathematics is, after all, not fundamentally different from the other sciences. The concepts of all sciences alike constitute a special language peculiarly adapted for dealing with certain experience adjustments, and the differences in the development of the different sciences merely express different degrees of success with which such languages have been formulated with respect to making it possible to predict concerning not yet realized situations. Some sciences are still seeking their terms and fundamental concepts, others are formulating their first "grammar," and mathematics, still inadequate, yearly gains both in vocabulary and flexibility.

But if we are to conceive mathematical entities as mere terminal points in a relational system, it is necessary that we should become clear as to just what is meant by relation, and what is the connection between relations and quantities. Modern thought has shown a strong tendency to insist, somewhat arbitrarily, on the "internal" or "external" character of relations. The former emphasis has been primarily associated with idealistic ontology, and has often brought with it complex dialectic questions as to the identity of an individual thing in passing from one relational situation to another. The latter insistence has meant primarily that things do not change with changing relations to other things. It has, however, often implied the independent existence, in some curiously metaphysical state, of relations that are not relating anything, and is hardly less paradoxical than the older view. In the field of physical phenomena, it seems to triumph, while the facts of social life, on the other hand, lend some countenance to the view of the "internalists." Like many such discussions, the best way around them is to forget their arguments, and turn to a fresh and independent investigation of the facts in question.

IV

Things, Relations, and Quantities

As I write, the way is paved for me by Professor Cohen (Journ. of Phil., Psy., and Sci. Meth., Vol. XI, No. 23, Nov. 5, 1914, pp. 623-24), who outlines a theory of relations closely allied to that which I have in mind. Professor Cohen writes: "Like the distinction between primary and secondary qualities, the distinction between qualities and relations seems to me a shifting one because the 'nature' of a thing changes as the thing shifts from one context to another.... To Professors Montague and Lovejoy the 'thing' is like an old-fashioned landowner and the qualities are its immemorial private possessions. A thing may enter into commercial relations with others, but these relations are extrinsic. It never parts with its patrimony. To me, the 'nature' of a thing seems not to be so private or fixed. It may consist entirely of bonds, stocks, franchises, and other ways in which public credit or the right to certain transactions is represented.... At any rate, relations or transactions may be regarded as wider or more primary than qualities or possessions. The latter may be defined as internal relations, that is, relations within the system that constitutes the 'thing.' The nature of a thing contains an essence, i.e., a group of characteristics which, in any given system or context, remain invariant, so that if these are changed the things drop out of our system ... but the same thing may present different essences in different contexts. As a thing shifts from one context to another, it acquires new relations and drops old ones, and in all transformations there is a change or readjustment of the line between the internal relations which constitute the essence and the external relations which are outside the inner circle...."

Before continuing, however, I wish to make certain interpretations of these statements for which, of course, Professor Cohen is not responsible, and with which he would not be wholly in agreement. My general attitude will be shown by the first comment. Concepts are only means of denoting fragments of experience directly or indirectly given. If we then try to speak of a "nature of a thing" two interpretations of this expression are possible. The "thing" as such is only a bit of reality which some motive, that without undue extension of the term can be called practical, has led us to treat as more or less isolable from the rest of reality. Its nature, then, may consist of either its relations to other practically isolated realities or things, its actual effective value in its environment (and hence shift with the environment as Professor Cohen points out), or may consist of its essence, the "relations within the system," considered from the point of view of the potentialities implied by these for various environments. In the first sense the nature may easily change with change in environment, but if it changes in the second sense, as Professor Cohen remarks, it "drops out of our system." This I should interpret as meaning that we no longer have that thing, but some other thing selected from reality by a different purpose and point of view. I should not say with Professor Cohen that "the same thing may present different essences in different contexts." Every reality is more than one thing—man is an aggregate of atoms, a living being, an animal, and a thinker, and all of these are different things in essence, although having certain common characteristics. All attribution of "thingship" is abstraction, and all particular things may be said to participate in higher, i.e., more abstract, levels of thingship. Hence the effort to retain a thingship through a changing of essence seems to me but the echo of the motive that has so long deduced ontological monism from the logical fact that to conceive any two things is at least to throw them into a common universe of discourse. Consequently I should part company from Professor Cohen on this one point (which is perhaps largely a matter of definition, though here not unimportant) and distinguish merely the nature of a thing as actual and as potential. Of these the former alone changes with the environment, while the latter changes only as the thing ceases to be by passing into some other thing. In other words, if the example does not do violence to Professor Cohen's thought, I can quite understand this paper as a stimulator of criticism, or as a means of kindling a fire. Professor Cohen would, I suspect, take this to mean that the same thing—this paper—must be looked upon as having two different essences in two different contexts, for "the same thing may possess two different essences in different contexts," whereas I should prefer to interpret the situation as meaning that there are before me three (and as many more as may be) different things having three different essences: first, the paper as a physical object having a considerable number of definite properties; second, written words, which are undoubtedly in one sense mere structural modifications of the physical object paper (i.e., coloring on it by ink, etc.), but whose reality for my purpose lies in the power of evoking ideas acquired by things as symbols (things, indeed, but things whose essence lies in the effects they produce upon a reader rather than in their physical character); and third, the chemical and combustion producing properties of the paper. Now it is simpler for me to consider the situation as one in which three things have a common point in thingship, i.e., an abstract element in common, than to think of "a thing" shifting contexts and thereby changing its essence.

But now my divergence from Professor Cohen becomes more marked. He continues with the following example (p. 622): "Our neighbor M. is tall, modest, cheerful, and we understand a banker. His tallness, modesty, cheerfulness, and the fact that he is a banker we usually regard as his qualities; the fact that he is our neighbor is a relation which he seems to bear to us. He may move his residence, cease to be our neighbor, and yet remain the same person with the same qualities. If, however, I become his tailor, his tallness becomes translated into certain relations of measurement; if I become his social companion, his modesty means that he will stand in certain social relations with me, etc." In other words, we are illustrating the doctrine that "qualities are reducible to relations" (cf. p. 623). This doctrine I cannot quite accept without modification, for I cannot tell what it means. Without any presuppositions as to subjectivity or consciousness (cf. p. 623, (a).) there are in the world as I know it certain colored objects—let the expression be taken naïvely to avoid idealistico-realistic discussion which is here irrelevant. Now it is as unintelligible to me that the red flowers and green leaves of the geraniums before my windows should be reducible to mere relations in any existential sense, as it would be to ask for the square root of their odor, though of course it is quite intelligible that the physical theory and predictions concerning green and red surfaces (or odors) should be stated in terms of atomic distances and ether vibrations of specific lengths. The scientific conception is, after all, nothing more than an indication of how to take hold of things and manipulate them to get foreseen results, and its entities are real things only in the sense that they are the practically effective keynotes of the complex reality. Accordingly, instead of reducing qualities to relations, it seems to me a much more intelligible view to consider relations as abstract ways of taking qualities in general, as qualities thought of in their function of bridging a gap or making a transition between two bits of reality that have previously been taken as separate things. Indeed, it is just because things are not ontologically independent beings (but rather selections from genuinely concatenated existence) that relations become important as indications of the practical significance of qualitative continuities which have been neglected in the prior isolation of the thing. Thus, instead of an existential world that is "a network of relations whose intersections are called terms" (p. 622), I find more intelligible a qualitatively heterogeneous reality that can be variously partitioned into things, and that can he abstractly replaced by systems of terms and relations that are adequate to symbolize their effective nature in particular respects. There is a tendency for certain attributes to maintain their concreteness (qualitativeness) in things, and for others to suggest the connection of things with other things, and so to emphasize a more abstract aspect of experience. Thus then arises a temporary and practical distinction that tends to be taken as opposition between qualities and relations. As spatial and temporal characteristics possess their chief practical value in the connection of things, so they, like Professor Cohen's neighbor-character, are ordinarily assumed abstractly as mere relations, while shapes, colors, etc., and Professor Cohen's "modesty, tallness, cheerfulness," may be thought of more easily without emphasis on other things and so tend to be accepted in their concreteness as qualities, but how slender is the dividing-line Professor Cohen's easy translation of these things into relations makes clear.

Taken purely intellectualistically, there would be first a fiction of separation in what is really already continuous and then another fiction to bridge the gap thus made. This would, of course, be the falsification against which Bergson inveighs. But this interpretation is to misunderstand the nature of abstraction. Abstraction does not substitute an unreal for a real, but selects from reality a genuine characteristic of it which is adequate for a particular purpose. Thus to conceive time as a succession of moments is not to falsify time, but to select from processes going on in time a characteristic of them through which predictions can be made, which may be verified and turned into an instrument for the control of life or environment. A similar misunderstanding of abstraction, coupled with a fuller appreciation than Bergson evinces of the value of its results, has led to the neo-realistic insistence on turning abstractions into existent entities of which the real world is taken to be an organized composite aggregate.

The practice of turning qualities into merely conscious entities has done much to obscure the status of scientific knowing, for it has left mere quantity as the only real character of the actual world. But once take a realistic standpoint, and quantity is no more real than quality. For primitive man, the qualitative aspect of reality is probably the first to which he gives heed, and it is only through efforts to get along with the world in its qualitative character that its quantitative side is forced upon the attention. Then so-called "exact" science is born, but it does not follow that qualities henceforth become insignificant. They are still the basis of all relations, even of those that are most directly construed as quantitative. Quality and quantity are only different aspects of the world which the status of our practical life leads us to take separately or abstractly. "Thing" is no less an abstraction, in which we disregard certain continuities with the rest of the world because we are so constituted that the demands of living make it expedient to do so. Things once given, further abstractions become possible, among which are those leading to mathematical thinking, in which higher abstractions are made, guided always by the "generating problem" (cf. Karl Schmidt, Jour. of Phil., Psy., and Sci. Meth., Vol. X, No. 3, 1913, pp. 64-75).

V

The Function of Theory in Science

The controlling factors for the progress of scientific thought are inventions that lead the scientist into closer contact with his data, and direct attention to complexities which would otherwise have escaped observation. This end is best fulfilled by conceiving entities that under some point of view are practically isolable from the context in which they occur. Only too often philosophic thought has confused this practical segregation with ontological separation, and so been obliged to introduce metaphysical and external relations to bring these entities together again in a real world, when in reality they have never been separated from one another and hence not from the real world. Furthermore, the conceptual model, built on the lines of a calculus of mathematics, is often considered the truth par excellence after the analogy of a camera's portrait. Progress in science, however, shows that these models have to be continually rebuilt. Each seems to lead to further knowledge that necessitates its reconstruction, so that truth takes on an ideal value as an ultimate but unattained, if not unattainable, goal, while existing science becomes reduced to working hypotheses. From a positivistic point of view, however, the goal is not only practically unattainable, but it is irrational, for there seems to be every evidence that it expresses something contrary to the nature of the real. Yet scientific theory is not wholly arbitrary. We cannot construe nature as constituted of any sorts of entities that may suit our whim. And this is because science itself recognizes that its entities are not really isolated, but are endowed with all sorts of properties that serve to connect them with other entities. They are only symbols of critical points of reality which, conceived in a certain way, make the behavior of the whole intelligible. Indeed, the only significant sense in which they are true for the scientist is that they indicate real connections that might otherwise have been overlooked, and this is only possible from the fact that reality has the characteristics that they present and that, with their relations, they give an approximate presentation of what is actually presented just as a successful portrait painter considers the individuality of the eyes, nose, mouth, etc., although he does not imply that a face is compounded of these separate features as a house is built of boards.

The atomic theory, for example, has undoubtedly been of the greatest service to chemistry, and atoms undoubtedly denote a significant resting-place in the analysis of the physical world. Yet in the light of electron theories, it is becoming more and more evident that atoms are not ultimate particles, and are not even all alike (Becker, "Isostasy and Radioactivity," Sci., Jan. 29, 1915) when they represent a single substance. Again, while there is as yet no evidence to suggest that the electron must itself be considered as divisible (unless it be the distinction between the positive and negative electron), there are suggestions that electrons may themselves arise and pass away (cf. Moore, Origin, and Nature of Life, p. 39). "A wisely positivistic mind," writes Enriques (Problems of Science, p. 34), "can see in the atomic hypothesis only a subjective representation,"[34] and, we might add, "in any other hypothesis." He continues (pp. 34-36): "robbing the atom of the concrete attributes inherent in its image, we find ourselves regarding it as a mere symbol. The logical value of the atomic theory depends, then, upon the establishment of a proper correspondence between the symbols which it contains and the reality which we are trying to represent.

"Now, if we go back to the time when the atomic theory was accepted by modern chemistry, we see that the plain atomic formulæ contain only the representation of the invariable relations in the combination of simple bodies, in weight and volume; these last being taken in relation to a well-defined gaseous state.

"But, once introduced into science, the atomic phraseology suggested the extension of the meaning of the symbols, and the search in reality for facts in correspondence with its more extended conception.

"The theory advances, urged on, as it were, by its metaphysical nature, or, if you wish, by the association of ideas which the concrete image of the atom carries with it.

"Thus for the plain formulæ we have substituted, in the chemistry of carbon compounds, structural formulæ, which come to represent, thanks to the disposition or grouping of atoms in a molecule, structural relations of the second degree, that is to say, relations inherent in certain chemical transformations with respect to which some groups of elements have in some way an invariant character. And here, because the image of a simple molecule upon a plane does not suffice to explain, for example, the facts of isomerism, we must resort to the stereo-chemical representation of Van't Hoff.