Chapter XXXVI: Section D: RELIGIOUS WORK. (Hall 1, September 24, 3 p. m.) (9)

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.

THE PRESENT PROBLEMS OF METAPHYSICS

BY ALEXANDER T. ORMOND

[Alexander Thomas Ormond, McCosh Professor of Philosophy,
Princeton University, since 1897. b. 1847, Punxsutawney,
Pennsylvania. Mental Science Fellow, Princeton, 1877-78;
Post-grad. Bonn and Berlin, 1884-85; Ph.D. Princeton, 1880;
A.B. _ibid._ 1877; LL.D. Miami, 1899. Professor of
Philosophy and History, University of Minnesota, 1880-83;
Professor of Mental Science and Logic, Princeton University,
1883-97. Member American Philosophical Association, American
Psychological Association.]

I

THE PRELIMINARY QUESTION

The living problems of any science arise out of two sources: (1) out of what men may think of it, in view of its nature and claims, and (2) the problems that at any period are vital to it, and in the solution of which it realizes the purpose of its existence. Now if we distinguish the body of the sciences which deal with aspects of the world's phenomena--and here I would include both the psychic and the physical--from metaphysics, which professes to go behind the phenomenon and determine the world in terms of its inner, and, therefore, _ultimate_ reality, it may be truly said of the body of the sciences that they are in a position to disregard in a great measure questions that arise out of the first source, inasmuch as the data from which they make their departure are obvious to common observation. Our world is all around us, and its phenomena either press upon us or are patent to our observation. Lying thus within the field of observation, it does not occur to the average mind to question either the legitimacy or the possibility of that effort of reflection which is devoted to their investigation and interpretation. Metaphysics, however, enjoys no such immunity as this, but its claims are liable to be met with skepticism or denial at the outset, and this is due partly to the nature of its initial claims, and partly to the fact that its real data are less open to observation than are those of the sciences. I say partly to the nature of the initial claims of metaphysics, for it is characteristic of metaphysics that it refuses to regard the distinction between phenomena and ground or inner nature, on which the sciences rest, as final, and is committed from the outset to the claim that the real is in its inner nature one and to be interpreted in the light of, or in terms of, its inner unity; whereas, science has so indoctrinated the modern mind with the supposition that only the outer movements of things are open to knowledge, while their inner and real nature must forever remain inaccessible to our powers; I say that the modern mind has been so imbued with this pretension as to have almost completely forgotten the fact that the distinction of phenomenon and ground is one of science's own making. Neither the plain man nor the cultured man, if he happens not to be tinctured with science, finds his world a duality. The things he deals with are the realities, and it is only when his naïve realism begins to break down before the complex demands of his growing life, that the thought occurs to him that his world may be more complex than he has dreamed. It is clear, then, that the distinction of our world into phenomena and ground, on which science so largely rests, is a first product of reflection, and not a fact of observation at all.

If this be the case, it may be possible and even necessary for reflection at some stage to transcend this distinction. At least, there can be no reason except an arbitrary one for taking this first step of reflection to be a finality. And there would be the same justification for a second step that would transcend this dualism, as for the initial step out of which the distinction arose; provided, it should be found that the initial distinction does not supply an adequate basis for a rational interpretation of the world that can be taken as final. Now, it is precisely because the dualistic distinction of the sciences does fail in this regard, that a further demand for a reflective transformation of the data arises. Let us bear in mind that the data of the sciences are not the simple facts of observation, but rather those facts transformed by an act of reflection by virtue of which they become phenomena distinguished from a more fundamental nature on which they depend and which itself is not open to observation. The real data of science are found only when the world of observation has been thus transformed by an act of reflection. If then at some stage in our effort to interpret our world it should become clear that the sciences of phenomena, whatever value their results may possess, are not giving us an interpretation in terms that can be taken as final, and that in order to ground such an interpretation a further transformation of our data becomes necessary, I do not see why any of the sciences should feel that they have cause to demur. In truth, it is out of just such a situation as this that the metaphysical interpretation arises (as I propose very briefly here to show), a situation that supplies a genuine demand in the light of which the effort of metaphysics to understand its world seems to possess as high a claim to legitimacy as that of the sciences of phenomena. Let us take our stand with the plain man or the child, within the world of unmodified observation. The things of observation, in this world, are the realities, and at first we may suppose have undergone little reflective transformation. The first reflective effort to change this world in any way will, no doubt, be an effort to _number_ or _count_ the things that present themselves to observation, and out of this effort will arise the transformation of the world that results from considering it under the concepts and categories of number. In short, to mathematical reflection of this simple sort, the things of observation will resolve themselves into a plurality of countable things, which the numbering reflection becoming explicit in its ordinal and cardinal moments will translate into a system that will be regarded as a whole made up of the sum of its parts. The very first step, then, in the reflective transformation of things resolves them into a dual system, the world conceived as a cardinal whole that is made up of its ordinal parts, and exactly equal to them. This mathematical conception is moreover purely quantitative; involving the exact and stable equivalence of its parts or units and that of the sum of the parts with the whole. Now it is with this purely quantitative transformation that mathematics and the mathematical sciences begin. We may ask, then, why should there be any other than mathematical science,[1] and what ground can non-mathematical science point to as substantiating its claims? I confess I can see no other final reason than this, that mathematical science does not meet the whole demand we feel obliged to make on our world. If mathematics were asked to vindicate itself, it no doubt would do so by claiming that things present quantitative aspects on which it founds its procedure. In like manner non-mathematical, or, as we may call it, physical or natural science, will seek to substantiate its claims by pointing to certain ultra-quantitative or qualitative aspects of things. It is true that, so far as things are merely _numerable_, they are purely quantitative; but mathematics abstracts from the content and character of its units and aggregates, which may and do change, so that a relation of stable equivalence is not maintained among them. In fact, the basis of these sciences is found in the tendency of things to be always changing and becoming different from what they were before. The problem of these sciences is how to ground a rational scheme of knowledge in connection with a fickle world like that of qualitative change. It is here that reflection finds its problem, and noticing that the tendency of this world of change is for _a_ to pass into _b_ and thus to lose its own identity, the act of reflection that rationalizes the situation is one that connects _a_ and _b_ by relating them to a common ground _x_ of which they stand as successive manifestations or symbols. _X_ thus supplies the thread of identity that binds the two changes _a_ and _b_ into a relation to which the name causation may be applied. And just as quantitative equivalence is the principle of relationship among the parts of the simple mathematical world, so here in the world of the dynamic or natural sciences, the principle of relation is natural causation.[2] We find, then, that the non-mathematical sciences rest on a basis that is constituted by a _second act of reflection_; one that translates our world into a system of phenomena causally inter-related and connected with their underlying grounds.

[Footnote 1: I do not raise the question of qualitative
mathematics at all. It is clear that the first mathematical
reflection will be quantitative.]

[Footnote 2: By natural causation I mean such a relationship
between _a_ and _b_ in a phenomenal system as enables _a_
through its connection with its ground to determine _b_.]

We have now reached a point where it will be possible in a few sentences to indicate the rise of the metaphysical reflection and the ground on which it rests. If we consider both the mathematical and the physical ways of looking at things, we will find that they possess this feature in common,--they are purely external, having nothing to say respecting the _inner_ and, therefore, _real_ nature of the things with which they deal. Or, if we concede the latest claims of some of the physical speculators and agree that the aim of physics is an ultimate physical explanation of reality, it will still be true that the whole standpoint of this explanation will be external. Let me explain briefly what I mean substantially by the term _external_ as I use it here. Every interpretation of a world is a function of some knowing consciousness, and consequently of some knowing self. This is too obvious to need proof. A system will be _external_ to such a knower just to the extent that the knower finds it dominated and determined by categories that are different from those of its own determination. A world physically interpreted is one that is brought completely under the rubrics of physics and mathematics; whose movements yield themselves completely, therefore, to a mechanical calculus that gives rise to purely descriptive formulæ; _or_ to the control of a dynamic principle; that of natural causation, by virtue of which everything is determined without thought of its own, by the impulse of another, which impulse itself is not directly traceable to any thought or purpose. Now, the occasion for the metaphysical reflection arises when this situation that brings us face to face, with, nay, makes us part and parcel of, an alien system of things, becomes intolerable, and the knower begins to demand a closer kinship with his world. The knower finds the categories of his own central and characteristic activity in experience. Here he is conscious of being an agent going out in forms of activity for the realization of his world. The determining categories of the activity he is most fully conscious of, are interest, idea, prevision, purpose, and that selective activity which goes to its termination in some achieved end. The metaphysical interpretation arises out of the demand that the world shall be brought into bonds of kinship with the knower. And this is effected by generalizing the categories of consciousness and applying them as principles of interpretation to the world. The act of reflection on which the metaphysical interpretation proceeds is one, then, in which the world of science is further transformed by bringing the inner nature of things out of its isolation and translating the world-movements into process the terms of which are no longer _phenomena and hidden ground_, but rather inception and realization, or, more specifically, _Idea_ and _Reality_. And the point to be noted here is the fact that these metaphysical categories are led up to positivity by an act of reflection that has for its guiding aim an interpretation of the world that will be more ultimately satisfactory to the knower than that of the physical or natural sciences; while negatively, it is led up to by the refusal of the knowing consciousness to rest in a world alien to its own nature and in which it is subordinated to the physical and made a mere epiphenomenon.

II

QUESTIONS OF POINT OF VIEW, PRINCIPLE AND METHOD OF METAPHYSICS

It is clear from what has been said that the metaphysical interpretation proceeds on a presupposition radically different from that of mathematical and physical science. The presumption of these sciences is that the world is physical, that the physical categories supply the norms of reality, and that consciousness and the psychic, in general, are subordinate and phenomenal to the physical. On the contrary, metaphysics arises out of a revolt from these presumptions toward the opposite presumption, namely, that _consciousness itself is the great reality_, and that the norms of an ultimate interpretation of things are to be sought in its categories. This is the great transformation that conditions the possibility and value of all metaphysics. It is the Copernican revolution which the mind must pass through, a revolution in which matter and the physical world yields the primacy to mind; a revolution in which consciousness becomes central, its categories and analogies supplying the principles of final world-interpretation. Let us consider then, in the light of this great Copernican revolution, the questions of the _point of view_, _principle_, and _method_ of metaphysics. And here the utmost brevity must be observed. If consciousness be the great reality, then its own central activity, that effort by which it realizes its world, will determine for us the _point of view_ or departure of which we are in quest. This will be _inner_ rather than _outer_; it will be motived by _interest_, will shape itself into interest-directed effort. This effort will be cognitive; dominated by an _idea_ which will be an anticipation of the _goal_ of the effort. It will, therefore, become _directive_, _selective_, and will stand as the _end_ or _aim_ of the completed effort. The whole movement will thus take the form, genetically, of a developing _purpose informed by an idea_, or _teleologically_, of a _purpose going on to its fulfillment_ in some _aim_ which is also its _motive_. Now, metaphysics determines its point of view in the following reasoning: if in consciousness we find the type of the inner nature of things, then the point of view for the interpretation of this inner nature will be to seek by generalizing the standpoint of consciously determined effort and asserting that this is the true point of view from which the _meaning_ of the world is to be sought.

Having determined the metaphysical point of view, the next question of vital importance is that of its _principle_. And we may cut matters short here by saying at once that the principle we are seeking is that of _sufficient reason_, and we may say that a reason will be sufficient when it adequately expresses the world-view or concept under which an investigation is being prosecuted. Let us suppose that this world-view is that of simple mathematics, the principle of sufficient reason here will be that of _quantitative equivalence_ of parts; or, from the standpoint of the whole, that of _infinite divisibility_. Whereas, if we take the world of the ultra-mathematical science, which is determined by the notion of _phenomena depending on underlying ground_, we will find that the sufficient reason in this sphere takes the form of _adequate cause or condition_. The determining condition or causes of any physical phenomenon supply, from that point of view, the _ratio sufficiens_ of its existence. We have seen that the sufficiency of a reason in the above cases has been determined in view of that notion which defines the kind of world the investigation is dealing with. Let us apply this insight to the problem of the principle of metaphysics, and we will soon conclude that no reason can be metaphysically sufficient that does not satisfy the requirements of a world conceived under the notion of _inception_ and _realization_; or, more specifically, _idea_ and _reality_. In short, the _reason_ of metaphysics will refuse to regard its world as a mechanism that is devoid of thought and intention; that lacks, in short, the motives of internal determination and movement, and will in all cases insist that an explanation or interpretation can be metaphysically adequate only when its ultimate reference is to an idea that is in the process of _purposive_ fulfillment. Such an explanation we call _teleological_ or _rational_, rather than merely mechanical, and such a principle is alone adequate to embody the _ratio sufficiens_ of metaphysics.

Having determined the point of view and principle of metaphysics, the question of metaphysical _method_ will be divested of some of its greatest difficulties. It will be clear to any one who reflects that the very first problem in regard to the method of metaphysics will be that of its starting-point and the kind of results it is to look for. And little can be accomplished here until it has been settled that consciousness is to have the primacy, and that its prerogative is to supply both standpoint and principle of the investigation. We have gone a long way toward mastering our method when we have settled these points: (1) that the metaphysical world is a world of consciousness; (2) that the conscious form of effort rather than the mechanical is the species of activity or movement with which we have to deal; and, (3) that the world it is seeking to interpret is ultimately one of _idea_ and _reality_ in which the processes take the _purposive_ form. In view of this, the important steps of method (and we use the term method here in the most fundamental sense) will be (1) the question of the _form_ of metaphysical activity or agency as contrasted with that of the physical sciences. This may be brought out in the contrast of the two terms _finality_ and _mere efficiency_, in which by mere efficiency is meant an agency that is presumed to be thoughtless and purposeless, and consequently without _foresight_. All this is embodied in the term _force_ or physical energy, and less explicitly in that of _natural causation_. Contrasted with this, _finality_ is a term that involves the forward impulse of _idea_, _prevision_, and _purpose_. Anything that is capable of any sort of _foretaste_ has in it a principle of prevision, selection, choice, and purpose. The impulse that motives and runs it, that also stands out as the _end_ of its fulfillment, is a foretaste, an _Ahnung_, an anticipation, and the whole process or movement, as well as every part of it, will take on this character. (2) The second question of method will be that of the nature of this category of which _finality_ is the form. What is its content, pure idea or pure will, or a synthesis that includes both? We have here the three alternatives of _pure rationalism_, _voluntarism_, and a doctrine hard to characterize in a single word; that rests on a _synthesis_ of the norms of both rationalism and voluntarism. Without debating these alternatives, I propose here briefly to characterize the _synthetic_ concept as supplying what I conceive to be the most satisfactory doctrine. The principle of _pure rationalism_ is one of insight but is lacking in practical energy, whereas, that of _voluntarism_ supplies practical energy, but is lacking in insight. Pure voluntarism is _blind_, while pure rationalism is _powerless_. But the synthesis of _idea_ and _will_, provided we go a step further (as I think we must) and presuppose also a germ of _feeling_ as _interest_, supplies both _insight_ and _energy_. So that the spring out of which our world is to arise may be described as either the _idea informed with purposive energy_, or _purpose or will informed and guided by the idea_. It makes no difference which form of conception we use. In either case if we include feeling as interest we are able to conceive movements originating in some species of apprehension, taking the dynamic form of purpose, and motived and selected, so to speak, by interest; and in describing such activity we are simply describing these normal movements of consciousness with which our experience makes us most familiar. (3) The third question of method involves the relation or correlation of the metaphysical interpretation with that of the natural or physical science. Two points are fundamental here. In the first place, it must be borne in mind that it is the same world with which the plain man, the man of science, and the metaphysician are concerned. We cannot partition off the external world to the plain man, the atoms and ethers to the man of science, leaving the metaphysician in exclusive and solitary possession of the world of consciousness. It is the same world for all. The metaphysician cannot shift the physical world, with its oceans and icebergs, its vast planetary systems and milky ways, on to the shoulders of the physicist. This is the metaphysician's own recalcitrant world, which will doubtless task all his resources to explain. In the _second_ place, though it is the same world that is clamoring for interpretation, it is a world that passes through successive transformations, in order to adapt itself to progressive modes of interpretation. The plain man is called to pass through a species of Copernican revolution that subordinates the phenomenon to its ground, before he can become a man of science. In turn, the man of science must go through the Copernican process, and learn to subordinate his atoms and ethers to consciousness before he can become a metaphysician. And it is this transformation that marks one of the most fundamental steps in the method of metaphysics. The world must experience this transformation, and it must become habitual to the thinker to subordinate the physical to the mental before the metaphysical point of view can be other than foreign to him. If, then, it be the same content with which the sciences and metaphysics are called on to deal, it is clear that we have on our hands another problem on the answer to which the fate of metaphysics vitally depends; the question of the _correlation_ of its method with that of the sciences so that it may stand vindicated as the final interpretation of things.

III

QUESTION OF THE CORRELATION OF METAPHYSICS WITH THE SCIENCES