BY PROFESSOR ALFRED EDWARD TAYLOR

[Alfred Edward Taylor, Frothingham Professor of Philosophy, McGill University, Montreal, Canada. b. Oundle, England, December 22, 1869. M.A. Oxford. Fellow, Merton College, Oxford, 1891-98, 1902-; Lecturer in Greek and Philosophy, Owens College, Manchester, 1896-1903; Assistant Examiner to University of Wales, 1899-1903; Green Moral Philosophy Prizeman, Oxford, 1899; Frothingham Professor of Philosophy, McGill University, 1903-; Member Philosophical Society, Owens College, American Philosophical Association. Author of The Problem of Conduct; Elements of Metaphysics.]

When we seek to determine the place of metaphysics in the general scheme of human knowledge, we are at once confronted by an initial difficulty of some magnitude. There seems, in fact, to be no one universally accepted definition of our study, and even no very general consensus among its votaries as to the problems with which the metaphysician ought to concern himself. This difficulty, serious as it is, does not, however, justify the suspicion that our science is, like alchemy or astrology, an illusion, and its high-sounding title a mere "idol of the market-place," one of those nomina rerum quae non sunt against which the Chancellor Bacon has so eloquently warned mankind. If it is hard to determine precisely the scope of metaphysics, it is no less difficult to do the same thing for the undoubtedly legitimate sciences of logic and mathematics. And in all three cases the absence of definition merely shows that we are dealing with branches of knowledge which are, so to say, still in the making. It is not until the first principles of science are already firmly laid beyond the possibility of cavil that we must look for general agreement as to its boundary lines, though excellent work may be done, long before this point has been reached, in the establishment of individual principles and deduction of consequences from them. To revert to the parallel cases I have just cited, many mathematical principles of the highest importance are formulated in the Elements of Euclid, and many logical principles in the Organon of Aristotle; yet it is only in our own time that it has become possible to offer a general definition either of logic or of mathematics, and even now it would probably be true to say that the majority of logicians and mathematicians trouble themselves very little about the precise definition of their respective studies.

The state of our science then compels me to begin this address with a more or less arbitrary, because provisional, definition of the term metaphysics, for which I claim no more than that it may serve to indicate with approximate accuracy the class of problems which I shall have in view in my subsequent use of the word. By metaphysics, then, I propose to understand the inquiry which used formerly to be known as ontology, that is, the investigation into the general character which belongs to real Being as such, the science, in Aristotelian phraseology, of ὄντα ᾗ ὄντα. Or, if the term "real" be objected against as ambiguous, I would suggest as an alternative account the statement that metaphysics is the inquiry into the general character by which the content of true assertions is distinguished from that of false assertions. The two definitions here offered will, I think, be found equivalent when it is borne in mind that what the second of them speaks of is exclusively the content which is asserted as true in a true proposition, not the process of true assertion, which, like all other processes in the highest cerebral centres, falls under the consideration of the vastly different sciences of psychology and cerebral physiology. Of the two equivalent forms of statement, the former has perhaps the advantage of making it most clear that it is ultimately upon the objective distinction between the reality and the unreality of that which is asserted for truth, and not upon any psychological peculiarity in the process of assertion itself that the distinction between true and untrue rests, while the second may be useful in guarding against misconceptions that might be suggested by too narrow an interpretation of the term "reality," such as, e. g., the identification of the "real" with what is revealed by sensuous perception.

From the acceptance of such a definition two important consequences would follow. (1) The first is that metaphysics is at once sharply discriminated from any study of the psychical process of knowledge, if indeed, there can be any such study distinct from the psychology of conception and belief, which is clearly not itself the science we have in view. For the psychological laws of the formation of concepts and beliefs are exemplified equally in the discovery and propagation of truth and of error. And thus it is in vain to look to them for any explanation of the difference between the two. Nor does the otherwise promising extension of Darwinian conceptions of the "struggle for existence" and the "survival of the fittest" to the field of opinions and convictions appear to affect this conclusion. Such considerations may indeed assist us to understand how true convictions in virtue of their "usefulness" gradually come to be established and extended, but they require to presume the truth of these convictions as an antecedent condition of their "usefulness" and consequent establishment. I should infer, then, that it is a mistake in principle to seek to replace ontology by a "theory of knowledge," and should even be inclined to question the very possibility of such a theory as distinct from metaphysics on the one hand and empirical psychology on the other. (2) The second consequence is of even greater importance. The inquiry into the general character by which the contents of true assertions are discriminated from the contents of false assertions must be carefully distinguished from any investigation into the truth or falsehood of special assertions. To ask how in the end truth differs from falsehood is to raise an entirely different problem from that created by asking whether a given statement is to be regarded as true or false. The distinction becomes particularly important when we have to deal with what Locke would call assertions of "real existence," i. e., assertions as to the occurrence of particular events in the temporal order. All such assertions depend, in part at least, upon the admission of what we may style "empirical" evidence, the immediate unanalyzed witness of simple apprehension to the occurrence of an alleged matter of fact. Thus it would follow from our proposed conception of metaphysics that metaphysics is in principle incapable either of establishing or refuting any assertion as to the details of our immediate experience of empirical fact, though it may have important bearings upon any theory of the general nature of true Being which we may seek to found upon our alleged experiences. In a word, if our conception be the correct one, the functions of a science of metaphysics in respect of our knowledge of the temporal sequence of events psychical and physical must be purely critical, never constructive,—a point to which I shall presently have to recur.

One more general reflection, and we may pass to the consideration of the relation of metaphysics to the various already organized branches of human knowledge more in detail. The admission that there is, or may be, such a study as we have described, seems of itself to involve the recognition that definite knowledge about the character of what really "is," is attainable, and thus to commit us to a position of sharp opposition both to consistent and thorough-going agnosticism and also to the latent agnosticism of Kantian and neo-Kantian "critical philosophy." In recognizing ontology as a legitimate investigation, we revert in principle to the "dogmatist" position common, e. g., to Plato, to Spinoza and to Leibniz, that there is genuine truth which can be known, and that this genuine truth is not confined to statements about the process of knowing itself. In fact, the "critical" view that the only certain truth is truth about the process of knowing seems to be inherently self-contradictory. For the knowledge that such a proposition as, e. g., "I know only the laws of my own apprehending activity," is true, would itself be knowledge not about the process of knowing but about the content known. Thus metaphysics, conceived as the science of the general character which distinguishes truth from falsehood, presupposes throughout all knowledge the presence of what we may call a "transcendent object," that is, a content which is never identical with the process by which it is apprehended, though it may no doubt be maintained that the two, the process and its content, if distinct, are yet not ultimately separable. That they are in point of fact not ultimately separable would seem to be the doctrine which, under various forms of statement, is common to and characteristic of all the "idealistic" systems of metaphysics. So much then in defense of a metaphysical point of view which seems to be closely akin to that of Mr. Bradley and of Professor Royce, to mention only two names of contemporary philosophers, and which might, I think, for the purpose of putting it in sharp opposition to the "neo-Kantian" view, not unfairly be called, if it is held to need a name, "neo-Leibnizian."

In passing on to discuss in brief the nature of the boundary lines which divide metaphysics from other branches of study, it seems necessary to start with a clear distinction between the "pure" or "formal" and the "applied" or "empirical" sciences, the more so as in the loose current employment of language the name "science" is frequently given exclusively to the latter. In every-day life, when we are told that a certain person is a "man of science," or as the detestable jargon of our time likes to say, a "scientist," we expect to find that he is, e. g., a geologist, a chemist, a biologist, or an electrician. We should be a little surprised to find on inquiry that our "man of science" was a pure mathematician, and probably more than a little to learn that he was a formal logician. The distinction between the pure and the empirical sciences may be roughly indicated by saying that the latter class comprises all those sciences which yield information about the particular details of the temporal order of events physical and psychical, whereas the pure sciences deal solely with the general characteristics either of all truths, or of all truths of some well-defined class. More exactly we may say that the marks by which an empirical is distinguished from a pure science are two. (1) The empirical sciences one and all imply the presence among their premises of empirical propositions, that is, propositions which assert the actual occurrence of some temporal fact, and depend upon the witness of immediate apprehension, either in the form of senseperception or in that of what is commonly called self-consciousness. In the vague language made current by Kant, they involve an appeal to some form of unanalyzed "intuition." The pure sciences, on the other hand, contain no empirical propositions either among their premises or their conclusions. The principles which form their premises are self-evidently true propositions, containing no reference to the actual occurrence of any event in the temporal order, and thus involving no appeal to any form of "intuition." And the conclusions established in a pure science are all rigidly logical deductions from such self-evident premises. That the universality of this distinction is still often overlooked even by professed writers on scientific method seems explicable by two simple considerations. On the one hand, it is easy to overlook the important distinction between a principle which is self-evident, that is, which cannot be denied without explicit falsehood, and a proposition affirmed on the warrant of the senses, because, though its denial cannot be seen to be obviously false, the senses appear on each fresh appeal to substantiate the assertion. Thus the Euclidean postulate about parallels was long falsely supposed to possess exactly the same kind of self-evidence as the dictum de omni and the principle of identity which are part of the foundations of all logic. And further Kant, writing under the influence of this very confusion, has given wide popularity to the view that the best known of the pure sciences, that of mathematics, depends upon the admission of empirical premises in the form of an appeal to intuition of the kind just described. Fortunately the recent developments of arithmetic at the hands of such men as Weierstrass, Cantor, and Dedekind seem to have definitely refuted the Kantian view as far as general arithmetic, the pure science of number, is concerned, by proving that one and all of its propositions are analytic in the strict sense of the word, that is, that they are capable of rigid deduction from self-evident premises, so that, in what regards arithmetic, we may say with Schröder that the famous Kantian question "how are synthetic judgments a priori possible?" is now known to be meaningless. As regards geometry, the case appears to a non-mathematician like myself more doubtful. Those who hold with Schröder that geometry essentially involves, as Kant thought it did, an appeal to principles not self-evident and dependent upon an appeal to sensuous "intuition," are logically bound to conclude with him that geometry is an "empirical," or as W. K. Clifford called it, a "physical" science, different in no way from mechanics except in the relative paucity of the empirical premises presupposed, and to class it with the applied sciences. On the other hand, if Mr. Bertrand Russell should be successful in his promised demonstration that all the principles of geometry are deducible from a few premises which include nothing of the nature of an appeal to sensuous diagrams, geometry too would take its place among the pure sciences, but only on condition of our recognizing that its truths, like those of arithmetic, are one and all, as Leibniz held, strictly analytical. Thus we obtain as a first distinction between the pure and the empirical sciences the principle that the propositions of the former class are all analytical, those of the latter all synthetic. It is not the least of the services which France is now rendering to the study of philosophy that we are at last being placed by the labors of M. Couturat in a position to appreciate at their full worth the views of the first and greatest of German philosophers on this distinction, and to understand how marvelously they have been confirmed by the subsequent history of mathematics and of logic.

(2) A consequence of this distinction is that only the pure or formal sciences can be matter of rigid logical demonstration. Since the empirical or applied sciences one and all contain empirical premises, i. e., premises which we admit as true only because they have always appeared to be confirmed by the appeal to "intuition," and not because the denial of them can be shown to lead to falsehood, the conclusions to which they conduct us must one and all depend, in part at least, upon induction from actual observation of particular temporal sequences. This is as much as to say that all propositions in the applied sciences involve somewhere in the course of the reasoning by which they are established the appeal to the calculus of Probabilities, which is our one method of eliciting general results from the statistics supplied by observation or experiment. That this is the case with the more concrete among such applied sciences has long been universally acknowledged. That it is no less true of sciences of such wide range as mechanics may be said, I think, to have been definitely established in our own day by the work of such eminent physicists as Kirchhoff and Mach. In fact, the recent developments of the science of pure number, to which reference has been made in a preceding paragraph, combined with the creation of the "descriptive" theory of mechanics, may fairly be said to have finally vindicated the distinction drawn by Leibniz long ago between the truths of reason and the truths of empirical fact, a distinction which the Kantian trend of philosophical speculation tended during the greater part of the nineteenth century to obscure, while it was absolutely ignored by the empiricist opponents of metaphysics both in England and in Germany. The philosophical consequences of a revival of the distinction are, I conceive, of far-reaching importance. On the one side, recognition of the empirical and contingent character of all general propositions established by induction appears absolutely fatal to the current mechanistic conception of the universe as a realm of purposeless sequences unequivocally determined by unalterable "laws of nature," a result which has in recent years been admirably illustrated for the English-speaking world by Professor Ward's well-known Gifford lectures on "Naturalism and Agnosticism." Laws of physical nature, on the empiristic view of applied science, can mean no more than observed regularities, obtained by the application of the doctrine of chances,—regularities which we are indeed justified in accepting with confidence as the basis for calculation of the future course of temporal sequence, but which we have no logical warrant for treating as ultimate truths about the final constitution of things. Thus, for example, take the common assumption that our physical environment is composed of a multitude of particles each in every respect the exact counterpart of every other. Reflection upon the nature of the evidence by which this conclusion, if supported at all, has to be supported, should convince us that at most all that the statement ought to mean is that individual differences between the elementary constituents of the physical world need not be allowed for in devising practical formulae for the intelligent anticipation of events. When the proposition is put forward as an absolute truth and treated as a reason for denying the ultimate spirituality of the world, we are well within our rights in declining the consequence on the logical ground that conclusions from an empirical premise must in their own nature be themselves empirical and contingent.

On the other hand, the extreme empiricism which treats all knowledge whatsoever as merely relative to the total psychical state of the knower, and therefore in the end problematic, must, I apprehend, go down before any serious investigation into the nature of the analytic truths of arithmetic, a consequence which seems to be of some relevance in connection with the philosophic view popularly known as Pragmatism. Thus I should look to the coming regeneration of metaphysics, of which there are so many signs at the moment, on the one hand, for emphatic insistence on the right, e. g., of physics and biology and psychology to be treated as purely empirical sciences, and as such freed from the last vestiges of any domination by metaphysical presuppositions and foregone conclusions, and on the other, for an equally salutary purgation of formal studies like logic and arithmetic from the taint of corruption by the irrelevant intrusion of considerations of empirical psychology.

We cannot too persistently bear in mind that there is, corresponding to the logical distinction between the analytic and the synthetic proposition, a deep and broad general difference between the wants of our nature ministered to by the formal and the applied sciences respectively. The formal sciences, incapable of adding anything to our detailed knowledge of the course of events, as we have seen, enlighten us solely as to the general laws of interconnection by which all conceivable systems of true assertions are permeated and bound together. In a different connection it would be interesting to develop further the reflection that the necessity of appealing to such formal principles in all reasoning about empirical matters of fact contains the explanation of the famous Platonic assertion that the "Idea of Good" or supreme principle of organization and order in the universe, is itself not an existent, but something ἔτι ἐπέκεινα τῆς οὐσίας, "transcending even existence," and the very similar declaration of Hegel that the question whether "God"—in the sense of such a supreme principle—exists is frivolous, inasmuch as existence (Dasein) is a category entirely inadequate to express the Divine nature. For my present purpose it is enough to remark that the need to which the formal sciences minister is the demand for that purely speculative satisfaction which arises from insight into the order of interconnection between the various truths which compose the totality of true knowledge. Hence it seems a mistake to say, as some theorists have done, that were we born with a complete knowledge of the course of temporal sequences throughout the universe, and a faultless memory, we should have no need of logic or metaphysics, or in fact of inference. For even a mind already in possession of all true propositions concerning the course of events, would still lack one of the requisites for complete intellectual satisfaction unless it were also aware, not only of the individual truths, but of the order of their interdependence. What Aristotle said long ago with reference to a particular instance may be equally said universally of all our empirical knowledge; "even if we stood on the moon and saw the earth intercepting the light of the sun, we should still have to ask for the reason why." The purposes ministered to by the empirical sciences, on the other hand, always include some reference to the actual manipulation in advance by human agency of the stream of events. We study mechanics, for instance, not merely that we may perceive the interdependence of truths, but that we may learn how to maintain a system of bodies in equilibrium, or how to move masses in a given direction with a given momentum. Hence it is true of applied science, though untrue of science as a whole, that it would become useless if the whole past and future course of events were from the first familiar to us. And, incidentally it may be observed, it is for the same reason untrue of inference, though true of inductive inference, that it is essentially a passage from the known to the unknown.