BY PROFESSOR ALFRED EDWARD TAYLOR

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 sense perception 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.

In dealing with the relation of metaphysics to the formal sciences generally, the great difficulty which confronts us is that of determining exactly the boundaries which separate one from another. Among such pure sciences we have by universal admission to include at least two, pure formal logic and pure mathematics, as distinguished from the special applications of logic and mathematics to an empirical material. Whether we ought also to recognize ethics and æsthetics, in the sense of the general determination of the nature of the good and the beautiful, as non-empirical sciences, seems to be a more difficult question. It seems clear, for instance, that ethical discussions, such as bulk so largely in our contemporary literature, as to what is the right course of conduct under various conditions, are concerned throughout with an empirical material, namely, the existing peculiarities of human nature as we find it, and must therefore be regarded as capable only of an empirical and therefore problematic solution. Accordingly I was at one time myself tempted to regard ethics as a purely empirical science, and even published a lengthy treatise in defense of that point of view and in opposition to the whole Kantian conception of the possibility of a constructive Metaphysik der Sitten. It seems, however, possible to hold that in the question "What do we mean by good?" as distinguished from the question "What in particular is it right to do?" there is no more of a reference to the empirical facts of human psychology than in the question "What do we mean by truth?" and that there must therefore be a non-empirical answer to the problem. The same would of course hold equally true of the question "What is beauty?" If there are, however, such a pure science of ethics and again of æsthetics, it must at least be allowed that for the most part these sciences are still undiscovered, and that the ethical and æsthetical results hitherto established are in the main of an empirical nature, and this must be my excuse for confining the remarks of the next two paragraphs to the two great pure sciences of which the general principles may be taken to be now in large measure known.

That metaphysics and logic should sometimes have been absolutely identified, as for instance by Hegel, will not surprise us when we consider how hard it becomes on the view here defended to draw any hard and fast boundary line between them. For metaphysics, according to this conception of its scope, deals with the formulation of the self-evident principles implied, in there being such a thing as truth and the deductions which these principles warrant us in drawing. Thus it might be fairly said to be the supreme science of order, and it would not be hard to show that all the special questions commonly included in its range, as to the nature of space, time, causation, continuity, and so forth, are all branches of the general question, how many types of order among concepts are there, and what is their nature. A completed metaphysics would thus appear as the realization of Plato's splendid conception of dialectic as the ultimate reduction of the contents of knowledge to order by their continuous deduction from a supreme principle (or, we may add, principles). Now such a view seems to make it almost impossible to draw any ultimate distinction between logic and metaphysics. For logic is strictly the science of the mutual implication of propositions, as we see as soon as we carefully exclude from it all psychological accretions. In the question what are the conditions under which one proposition or group of propositions imply another, we exhaust the whole scope of logic pure and proper, as distinguished from its various empirical applications. This is the important point which is so commonly forgotten when logic is defined as being in some way a study of "psychical processes," or when the reference to the presence of "minds" in which propositions exist, is intended into logical science. We cannot too strongly insist that for logic the question so constantly raised in a multitude of text-books, what processes actually take place when we pass from the assertion of the premises to the assertion of the conclusion, is an irrelevant one, and that the only logical problem raised by inference is whether the assertion of the premises as true warrants the further assertion of the conclusion, supposing it to be made. (At the risk of a little digression I cannot help pointing out that the confusion between a logical and a psychological problem is committed whenever we attempt, as is so often done, to make the self-evidence of a principle identical with our psychological inability to believe the contradictory. From the strictly logical point of view, all that is to be said about the two sides of such an ultimate contradiction is that the one is true and the other is false. Whether it is or is not possible, as a matter of psychical fact for me to affirm with equal conviction, both sides of a contradiction, knowing that I am doing so, is a question of empirical psychology which is possibly insoluble, and at any rate seems not to have received from the psychologists the attention it deserves. But the logician, so far as I can see, has no interest as a logician in its solution. For him it would still be the case even though all mankind should actually and consciously affirm both sides of a given contradiction, that one of the affirmations would be true, and the other untrue.) Logic thus seems to become either the whole or an integral part of the science of order, and there remain only two possible ways of distinguishing it from metaphysics. It might be suggested that logical order, the order of implication between truths, is only one species of a wider genus, order in general by the side, for example, of spatial, temporal, and numerical order, and thus that logic is one subordinate branch of the wider science of metaphysics. Such a view, of course, implies that there are a plurality of ultimately independent forms of order irreducible to a single type. Whether this is the case, I must confess myself at present incompetent to decide, though the signal success with which the principles of number have already been deduced from the fundamental definitions and axioms of symbolic logic, and number itself defined, as by Mr. Russell, in terms of the purely logical concept of class-relation, seems to afford some presumption to the contrary. Or it may be held that the difference is purely one of the degree of completeness with which the inquiry into order is pursued. Thus the ordinary symbolic logic of what Schröder has called the "identical calculus," or "calculus of domains," consists of a series of deductions from the fundamental concepts of class and number, identical equality, totality or the "logical 1," zero or the null-class, and the three principles of identity, subsumption, and negation. The moment you cease to accept these data in their totality as the given material for your science, and to inquire into their mutual coherence, by asking for instance whether any one of them could be denied, and yet a body of consistent results deduced from the rest, your inquiry, it might be said, becomes metaphysics. So, again, the discussion of the well-known contradictions which arise when we try to apply these principles in their entirety and without modification to classes of classes instead of classes of individuals, or of the problem raised by Peano and Russell, whether the assertions "Socrates is a man" and "the Greeks are men" affirm the same or a different relation between their subject and predicate (which seems indeed to be the same question differently stated), would generally be allowed to be metaphysical. And the same thing seems to be equally true of the introduction of time relations into the interpretation of our symbols for predication employed by Boole in his treatment of hypotheticals, and subsequently adopted by his successors as the foundation of the "calculus of equivalent statements."

However we may decide such questions, we seem at least driven by their existence to the recognition of two important conclusions. (1) The relation between logical and metaphysical problems is so close that you cannot in consistency deny the possibility of a science of metaphysics unless you are prepared with the absolute skeptic to go the length of denying the possibility of logic also, and reducing the first principles of inference to the level of formulae which have happened hitherto to prove useful but are, for all we know, just as likely to fail us in future application as not. (Any appeal to the doctrine of chances would be out of place here, as that doctrine is itself based on the very principles at stake.) (2) The existence of fundamental problems of this kind which remained almost or wholly unsuspected until revealed in our own time by the creation of a science of symbolic logic should console us if ever we are tempted to suspect that metaphysics is at any rate a science in which all the main constructive work has already been accomplished by the great thinkers of the past. To me it appears, on the contrary, that the recent enormous developments in the purely formal sciences of logic and mathematics, with the host of fundamental problems they open up, give promise of an approaching era of fresh speculative construction which bids fair to be no less rich in results than any of the great "golden" periods in the past history of our science. Indeed, but that I would avoid the slightest suspicion of a desire to advertise personal friends, I fancy I might even venture to name some of those to whom we may reasonably look for the work to be done.

Of the relation of metaphysics to pure mathematics it would be impertinent for any but a trained mathematician to say very much. I must therefore be content to point out that the same difficulty in drawing boundary lines meets us here as in the case of logic. Not so long ago this difficulty might have been ignored, as it still is by too many writers on the philosophy of science. Until recently mathematics would have been thought to be adequately defined as the science of numerical and quantitative relations, and adequately distinguished from metaphysics by the non-quantitative and non-numerical character of the latter, though it would probably have been admitted that the problem of the definition of quantity and number themselves is a metaphysical one. But in the present state of our knowledge such an account seems doubly unsatisfactory. On the one hand, we have to recognize the existence of branches of mathematics, such as the so-called descriptive geometry, which are neither quantitative nor numerical, and, on the other, quantity as distinct from number appears to play no part in mathematical science, while number itself, thanks to the labors of such men as Cantor and Dedekind, seems, as I have said before, to be known now to be only a special type of order in a series. Thus there appears to be ground for regarding serial order as the fundamental category of mathematics, and we are thrown back once more upon the difficult task of deciding how many ultimately irreducible types of order there may be before we can undertake any precise discrimination between mathematical and metaphysical science. However we may regard the problem, it is at least certain that the recent researches of mathematicians into the meaning of such concepts as continuity and infinity have, besides opening up new metaphysical problems, done much to transfigure the familiar ones, as all readers of Professor Royce must be aware. For instance I imagine all of us here present, even the youngest, were brought up on the Aristotelian doctrine that there is and can be no such thing as an actually existing infinite collection, but which of us would care to defend that time-honored position to-day? Similarly with continuity all of us were probably once on a time instructed that whereas "quantity" is continuous, number is essentially "discrete," and is indeed the typical instance of what we mean by the non-continuous. To-day we know that it is in the number series that we have our one certain and familiar instance of a perfect continuum. Still a third illustration of the transforming light which is thrown upon old standing metaphysical puzzles by the increasing formal development of mathematics may be found in the difficulties attendant upon the conception of the "infinitely little," once regarded as the logical foundation of the so-called Differential Calculus. With the demonstration, which maybe found in Mr. Russell's important work, that "infinitesimal," unlike "infinite," is a purely relative term, and that there are no infinitesimal real numbers, the supposed logical significance of the concept seems simply to disappear. Instances of this kind could easily be multiplied almost indefinitely, but those already cited should be sufficient to show how important are the metaphysical results which may be anticipated from contemporary mathematical research, and how grave a mistake it would be to regard existing metaphysical construction, e. g., that of the Hegelian system, as adequate in principle to the present state of our organized knowledge. In fact, all the materials for a new Kategorienlehre, which may be to the knowledge of our day what Hegel's Logic was to that of eighty years ago, appear to lie ready to hand when it may please Providence to send us the metaphysician who knows how to avail himself of them. The proof, given since this address was delivered, by E. Zermelo, that every assemblage can be well ordered, is an even more startling illustration of the remarks in the text.

It remains to say something of the relation of metaphysical speculation to the various sciences which make use of empirical premises. On this topic I maybe allowed to be all the more brief, as I have quite recently expressed my views at fair length in an extended treatise (Elements of Metaphysics, Bks. 3 and 4), and have nothing of consequence to add to what has been there said. The empirical sciences, as previously defined, appear to fall into two main classes, distinguished by a difference which corresponds to that often taken in the past as the criterion by which science is to be separated from philosophy. We may study the facts of temporal sequence either with a view to the actual control of future sequences or with a view to detecting under the sequence some coherent purpose. It is in the former way that we deal with facts in mechanics, for instance, or in chemistry, in the latter that we treat them when we study history for the purpose of gaining insight into national aims and character. We may, if we please, with Professor Royce, distinguish the two attitudes toward fact as the attitude respectively of description and of appreciation or evaluation. Now as regards the descriptive sciences, the position to which, as I believe, metaphysicians are more and more tending is that here metaphysics has, strictly speaking, no right at all to interfere. Just because of the absence from metaphysics itself of all empirical premises, it can be no business of the metaphysician to determine what the course of events will be or to prescribe to the sciences what methods and hypotheses they shall employ in the work of such determination. Within these sciences any and every hypothesis is sufficiently justified, whatever its nature, so long as it enables us more efficiently than any other to perform the actual task of calculation and prediction. And it was owing to neglect of this caution that the Naturphilosophie of the early nineteenth century speedily fell into a disrepute fully merited by its ignorant presumption. As regards the physical sciences, the metaphysician has indeed by this time probably learned his lesson. We are not likely to-day to repeat the mistake of supposing that it is for us as metaphysicians to dictate what shall be the physicist's or chemist's definition of matter or mass or elementary substance or energy, or how he shall formulate the laws of motion or of chemical composition. Here, at any rate, we can see that the metaphysician's work is done when his analysis has made it clear that we are dealing with no self-evident truths such as the laws of number, but with inductive, and therefore problematic and provisional results of empirical assumptions as to the course of facts, assumptions made not because of their inherent necessity, but because of their practical utility for the special task of calculation. It is only when such empirical assumptions are treated as self-evident axioms, in fact when mechanical science gives itself out as a mechanistic philosophy, that the metaphysician obtains a right to speak, and then only for the purpose of showing by analysis that the presence of the empirical postulates which is characteristic of the natural sciences of itself excludes their erection into a philosophy of first principles.

What is important in this connection is that we should recognize quite clearly that psychology stands in this respect on precisely the same logical footing as physics or chemistry. It is tempting to suppose that in psychology, at any rate, we are dealing throughout with absolute certainties, realities which "consciousness" apprehends just as they are without any of that artificial selection and construction which, as we are beginning to see, is imposed upon the study of physical nature by the limitations of our purpose of submitting the course of events to calculation and manipulation. And it is a natural consequence of this point of view to infer that since psychology deals directly with realities, it must be taken as the foundation of the metaphysical constructions which aim at understanding the general character of the real as such. The consequence, indeed, disappears at once if the views maintained in this address as to the intimate relation of metaphysics and logic, and the radical expulsion from logic of all discussion of mental processes as such, be admitted. But it is still important to note that the premises from which the conclusion in question was drawn are themselves false. We must never allow ourselves to forget that, as the ever-increasing domination of psychology by the highly artificial methods of observation and experiment introduced by Fechner and Wundt is daily making more apparent, psychology itself, like physics, deals not directly with the concrete realities of individual experience, but with an abstract selected from that experience, or rather a set of artificial symbols only partially corresponding with the realities symbolized, and devised for the special object of submitting the realm of mental sequences to mathematical calculation. We might, in fact, have based this inference upon the single reflection that every psychological "law" is obtained, like physical laws, by the statistical method of elimination of individual peculiarities, and the taking of an average from an extended series of measurements. For this very reason, no psychological law can possibly describe the unique realities of individual experience. We have in psychology, as in the physical sciences, the duty of suspecting exact correspondence between the single case and the general "law" to be of itself proof of error somewhere in the course of our computation. These views, which I suppose I learned in the first instance from Mr. F. H. Bradley's paper called A Defence of Phenomenalism in Psychology, may now, I think, be taken as finally established beyond doubt by the exhaustive analysis of Professor Münsterberg's Grundzüge der Psychologie. They possess the double advantage of freeing the psychologist once for all from any interference by the metaphysician in the prosecution of his proper study, and delivering metaphysics from the danger of having assumptions whose sole justification lies in their utility for the purpose of statistical computation thrust upon it as self-evident principles. For their full discussion I may perhaps be allowed to refer to the first three chapters of the concluding book of my Elements of Metaphysics.

When we turn to the sciences which aim at the appreciation or evaluation of empirical fact, the case seems rather different. It may fairly be regarded as incumbent on the metaphysician to consider how far the general conception he has formed of the character of reality can be substantiated and filled in by our empirical knowledge of the actual course of temporal sequence. And thus the way seems to lie open to the construction of what may fairly be called a Philosophy of Nature and History. For instance, a metaphysician who has rightly or wrongly convinced himself that the universe can only be coherently conceived as a society of souls or wills may reasonably go on to ask what views seem best in accord with our knowledge of human character and animal intelligence as to the varying degrees of organized intelligence manifested by the members of such a hierarchy of souls, and the nature and amount of mutual intercourse between them. And again, he may fairly ask what general way of conceiving what we loosely call the inanimate world would at once be true to fundamental metaphysical principles and free from disagreement with the actual state of our physical hypotheses. Only he will need to bear in mind that since conclusions on these points involve appeal to the present results of the inductive sciences, and thus to purely empirical postulates, any views he may adopt must of necessity share in the problematic and provisional character of the empirical sciences themselves, and can have no claim to be regarded as definitely demonstrated in respect of their details. I will here only indicate very briefly two lines of inquiry to which these reflections appear applicable. The growth of evolutionary science, with the new light it has thrown upon the processes by which useful variations may be established without the need for presupposing conscious preëxisting design, naturally gives rise to the question whether such unconscious factors are of themselves sufficient to account for the actual course of development so far as it can be traced, or whether the actual history of the world offers instances of results which, so far as we can see, can only have issued from deliberate design. And thus we seem justified in regarding the problem of the presence of ends in Nature as an intelligible and legitimate one for the philosophy of the future. I would only suggest that such an inquiry must be prosecuted throughout by the same empirical methods, and with the same consciousness of the provisional character of any conclusions we may reach which would be recognized as in place if we were called on to decide whether some peculiar characteristic of an animal group or some singular social practice in a recently discovered tribe does or does not indicate definite purpose on the part of breeders or legislators.

The same remarks, in my opinion, apply to the familiar problems of Natural Theology relative to the existence and activity of such non-human intelligences as are commonly understood by the names "God" or "gods." Hume and Kant, as it seems to me, have definitely shown between them that the old-fashioned attempts to demonstrate from self-evident principles the existence of a supreme personal intelligence as a condition of the very being of truth all involve unavoidable logical paralogisms. I should myself, indeed, be prepared to go further, and to say that the conception of a single personality as the ground of truth and reality can be demonstrated to involve contradiction, but this I know is a question upon which some philosophers for whom I entertain the profoundest respect hold a contrary opinion. The more modest question, however, whether the actual course of human history affords probable ground for believing in the activity of one or more non-human personalities as agents in the development of our species I cannot but think a perfectly proper subject for empirical investigation, if only it be borne in mind that any conclusion upon such a point is inevitably affected by the provisional character of our information as to empirical facts themselves, and can claim in consequence nothing more than a certain grade of probability. With this proviso, I cannot but regard the question as to the existence of a God or of gods as one upon which we may reasonably hope for greater certainty as our knowledge of the empirical facts of the world's history increases. And I should be inclined only to object to any attempt to foreclose examination by forcing a conclusion either in the theistic or in the atheistic sense on alleged grounds of a priori metaphysics. In a word, I would maintain not only with Kant that the "physico-theological" argument is specially deserving of our regard, but with Boole that it is with it that Natural Theology must stand or fall.

NOTE ON EXTENSION AND INTENSION OF TERMS

Among the numerous difficulties which beset the teaching of the elements of formal logic to beginners, one of the earliest is that of deciding whether all names shall be considered to have meaning both in extension and intension. As we all know, the problem arises in connection with two classes of names, (1) proper names of individuals, (2) abstract terms. I should like to indicate what seems to me the true solution of the difficulty, though I do not remember to have seen it advocated anywhere in just the form I should prefer.

(1) As to proper names. It seems clear that those who regard the true proper name as a meaningless label are nearer the truth than those who assert with Jevons that a proper name has for its intension all the predicates which can be truly ascribed to the object named. As has often been observed, it is a sufficient proof that, for example, John does not mean "a human being of the male sex," to note that he who names his daughter, his dog, or his canoe John, makes no false assertion, though he may commit a solecism. So far the followers of Mill seem to have a satisfactory answer to Jevons, when they say, for example, that he confuses the intension of a term with its accidental or acquired associations. (So, again, we can see that Socrates cannot mean "the wisest of the Greek philosophers," by considering that I may perfectly well understand the statement "there goes Socrates" without being aware that Socrates is wise or a Greek or a philosopher.) And if we objected that no proper name actually in use is ever without some associations which in part determine its meaning by restricting its applicability, it would be a valid rejoinder that in pure logic we have to consider not the actual usages of language, but those that would prevail in an ideal language purged of all elements of irrelevancy. In such an ideal scientific language, it might be said, the proper name would be reduced to the level of a mere mark serviceable for identification, but conveying no implication whatever as to the special nature of the thing identified. Thus it would be indifferent what mark we attach to any particular individual, just as in mathematics it is indifferent what alphabetical symbol we appropriate to stand for a given class or number. I think, however, that even in such an ideal scientific language the proper name would have a certain intension. In the first place, the use of proper name seems to inform us that the thing named is not unique, is not the only member of a class. To a monotheist, for instance, the name "God" is no true proper name, nor can he consistently give a proper name to his Deity. It is only where one member of a class has to be distinguished from others that the bestowal of a proper name has a meaning. And, further, to give a thing a proper name seems to imply that the thing is itself not a class. In logic we have, of course, occasion to form the concept of classes which have other classes for their individual members. But the classes which compose such classes of classes could not themselves be identified by means of proper names. Thus the employment of a proper name seems to indicate that the thing named is not the only member of its class, and further that it is not itself a class of individuals. Beyond this it seems to be a mere question of linguistic convention what information the use of a proper name shall convey. Hence it ought to be said, not that the proper name has no intension, but that it represents a limiting case in which intension is at a minimum.

(2) As to abstract terms. Ought we to say, with so many English formal logicians, that an abstract term is always singular and non-intensional? The case for asserting that such terms are all singular, I own, seems unanswerable. For it is clear that if the name of an attribute or relation is equally the name of another attribute or relation, it is ambiguous and thus not properly one term at all. To say, for example, that whiteness means two or more distinct qualities seems to amount to saying that it has no one definite meaning. Of course, it is true that milk is white, paper is white, and snow is white, and yet the color-tones of the three are distinct. But what we assert here is, not that there are different whitenesses, but only that there are different degrees of approximation to a single ideal standard or type of whiteness. It is just because the whiteness we have in view is one and not many that we can intelligibly assert, for example, that newly fallen snow is whiter than any paper. All the instances produced by Mill to show that abstract terms may be general seem to me either to involve confusion between difference of kind and difference in degree of approximation to type, or else to depend upon treating as abstract a term which is really concrete. Thus when we say red, blue, green, are different kinds of color, surely what we mean is different kinds of colored surface. Quà colored, they are not different; I mean just as much and no more when I say "a red thing is colored," or "has color," as when I say "a green thing is colored." If Mill were right, the proposition "red is a color" ought to mean exactly the same as "red is red." Or, to put it in another way, it would become impossible to form in thought any concept of a single class of colored things.

But need we infer because abstract terms are singular that therefore they have no intension and are mere meaningless marks? Commonly as this inference is made, it seems to me clearly mistaken. It seems, in fact, to rest upon the vague and ill-defined principle that an attribute can have no attributes of its own. That it is false is shown, I think, by the simple reflection that scientific definitions are one and all statements as to the meaning of abstract names of attributes and relations. For example, the definition of a circle is a statement as to the meaning of circularity, the legal definition of responsible persons a statement as to the meaning of the abstraction "responsibility," and so on. (We only evade the point if we argue that abstract terms when used as the subjects of propositions are really being employed concretely. For "cruelty is odious," for instance, does not merely mean that cruel acts are odious acts, but that they are odious because they are cruel.) In fact, the doctrine that abstract terms have no intension would seem, if thought out, to lead to the view that there are only classes of individuals, but no classes of classes. Thus to say "cruel acts are odious because cruel" implies, not only that I can form the concept of a class of cruel acts, but also that of classes of odious acts of which the class of cruel acts in its turn is a member. And to admit as much as this is to admit that the class of cruel acts, considered as a member of the class of odious acts, shares the common predicate of odiousness with the other classes of acts composing the higher class. Hence the true account of abstract terms seems to me to be that we have in them another limiting case, a case in which the extension and the intension are coincident. Incidentally, by illustrating the ambiguity of the principle that attributes have no attributes of their own, our discussion seems to indicate the advantage of taking the purely extensional view is opposed to the predicative view of the import of propositions as the basis of an elementary treatment of logical doctrine.

BY ALEXANDER T. ORMOND