Читать книгу The Essential John Dewey: 20+ Books in One Edition - Джон Дьюи - Страница 23

Table of Contents

The third book of Locke’s Essay is upon words and language; and in the order of treatment this would be the next topic for discussion. But much of what is said in this connection both by Locke and by Leibniz is philological, rhetorical, and grammatical in character, and although not without interest in itself, is yet without any especial bearing upon the philosophical points in controversy. The only topics in this book demanding our attention are general and particular terms; but these fall most naturally into the discussion of general and particular knowledge. In fact, it is not the terms which Locke actually discusses, but the ideas for which the terms stand. We pass on accordingly, without further ceremony, to the fourth book, which is concerning knowledge in general. Locke defines knowledge as “nothing but the perception of the connection and agreement, or disagreement and repugnancy, of any of our ideas.” These agreements or disagreements may be reduced to four sorts,—Identity, or diversity; Relation; Co-existence, or necessary connection; Real existence. The statement of identity and diversity is implied in all knowledge whatsoever. By them “the mind clearly and infallibly perceives each idea to agree with itself and be what it is, and all distinct ideas to disagree; i. e., the one not to be the other.” The agreement of relation is such knowledge as the mind derives from the comparison of its ideas. It includes mathematical knowledge. The connection of co-existence “belongs particularly to substances.” Locke’s example is that “gold is fixed,”—by which we understand that the idea of fixedness goes along with that group of ideas which we call gold. All statements of fact coming under the natural sciences would fall into this class. The fourth sort is “that of actual and real existence agreeing to any idea.”

Leibniz’s criticism upon these statements of Locke is brief and to the point. He admits Locke’s definition of knowledge, qualifying it, however, by the statement that in much of our knowledge, perhaps in all that is merely empirical, we do not know the reason and connection of things and hence cannot be said to perceive the agreement or disagreement of ideas, but only to feel it confusedly. His most important remark, however, is to the effect that relation is not a special kind of knowledge, but that all Locke’s four kinds are varieties of relation. Locke’s “connection” of ideas which makes knowledge is nothing but relation. And there are two kinds of relation,—those of “comparison” and of “concourse.” That of comparison states the identity or distinction of ideas, either in whole or in part. That of concourse contains Locke’s two classes of co-existence and existence. “When we say that a thing really exists, this existence is the predicate,—that is to say, a notion connected with the idea which is the subject; and there is connection between these two notions. The existence of an object of an idea may be considered as the concourse of this object with me. Hence comparison, which marks identity or diversity, and concourse of an object with me (or with the ego) are the only forms of knowledge.”

Leibniz leaves the matter here; but he only needed to develop what is contained in this statement to anticipate Berkeley and Kant in some of the most important of their discoveries. The contradiction which lies concealed in Locke’s account is between his definition of knowledge in general, and knowledge of real existence in particular. One is the agreement or disagreement of ideas; the other is the agreement of an idea with an object. Berkeley’s work, in its simplest form, was to remove this inconsistency. He saw clearly that the “object” was an intruder here. If knowledge lies in the connection of ideas, it is impossible to get outside the ideas to find an object with which they agree. Either that object is entirely unknown, or it is an idea. It is impossible, therefore, to find the knowledge of reality in the comparison of an idea with an object. It must be in some property of the ideas themselves.

Kant developed more fully the nature of this property, which constitutes the “objectivity” of our ideas. It is their connection with one another according to certain necessary forms of perception and rules of conception. In other words, the reality of ideas lies in their being connected by the necessary and hence universal relations of synthetic intelligence, or, as Kant often states it, in their agreement with the conditions of self-consciousness. It is not, I believe, unduly stretching either the letter or the spirit of Leibniz to find in that “concourse of the object with the ego” which makes its reality, the analogue of this doctrine of Kant; it is at all events the recognition of the fact that reality is not to be found in the relating of ideas to unknown things, but in their relation to self-conscious intelligence. The points of similarity between Kant and Leibniz do not end here. Leibniz’s two relations of “comparison” and “concourse” are certainly the congeners of Kant’s “analytic” and “synthetic” judgments. But Leibniz, as we shall see hereafter, trusts too thoroughly to the merely formal relations of identity and contradiction to permit him such a development of these two kinds of relation as renders Kant’s treatment of them epoch-making.

The discussion then advances to the subject of degrees of knowledge, of which Locke recognizes three,—intuitive, demonstrative, and sensitive. Intuitive knowledge is immediate knowledge,—recognition of likeness or difference without the intervention of a third idea; it is the most certain and clear of all knowledge. In demonstrative knowledge the agreement or disagreement cannot be perceived directly, because the ideas cannot be put together so as to show it. Hence the mind has recourse to intermediaries. “And this is what we call reasoning.” Demonstrative rests on intuitive knowledge, because each intermediate idea used must be immediately perceived to be like or unlike its neighboring idea, or it would itself need intermediates for its proof. Besides these two degrees of knowledge there is “another perception of the mind employed about the particular existence of finite things without us, which, going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, passes under the name of knowledge.”

Leibniz’s comments are again brief. The primitive truths which are known by intuition are to be divided into two classes,—truths of reason and of fact. The primitive truths of reason are necessary, and may be called identical, because they seem only to repeat the same thing, without teaching us anything. A is A. A is not non-A. Such propositions are not frivolous or useless, because the conclusions of logic are demonstrated by means of identical propositions, and many of those of geometry by the principle of contradiction. All the intuitive truths of reason may be said to be made known through the “immediation” of ideas. The intuitive truths of fact, on the other hand, are contingent and are made known through the “immediation” of feeling. In this latter class come such truths as the Cartesian, “I think, therefore I am.” Neither class can be proved by anything more certain.

Demonstration is defined by Leibniz as by Locke. The former recognizes, however, two sorts,—analytic and synthetic. Synthesis goes from the simple to the complex. There are many cases, however, where this is not applicable; where it would be a task “equal to drinking up the sea to attempt to make all the necessary combinations. Here the method of exclusions should be employed, cutting off many of the useless combinations.” If this cannot be done, then it is analysis which gives the clew into the labyrinth. He is also of the opinion that besides demonstration, giving certainty, there should be admitted an art of calculating probabilities,—the lack of which is, he says, a great defect in our present logic, and which would be more useful than a large part of our demonstrative sciences. As to sensitive knowledge, he agrees with Locke that there is such a thing as real knowledge of objects without us, and that this variety does not have the same metaphysical certainty as the other two; but he disagrees regarding its criterion. According to Locke, the criterion is simply the greater degree of vividness and force that sensations have as compared with imaginations, and the actual pleasures or pains which accompany them. Leibniz points out that this criterion, which in reality is purely emotional, is of no great value, and states the principle of the reality of sensible phenomena which we have already given, repeating that it is found in the connection of phenomena, and that “this connection is verified by means of the truths of reason, just as the phenomena of optics are explained by geometry.”

The discussion regarding “primitive truths,” axioms, and maxims, as well as the distinction between truths of fact and of reason, has its most important bearing in Locke’s next chapter. This chapter has for its title the “Extent of Human Knowledge,” and in connection with the sixth chapter, upon universal propositions, and with the seventh, upon axioms, really contains the gist of the treatment of knowledge. It is here also that are to be considered chapters three and six of book third, having respectively as their titles, “Of General Terms,” and “Of the Names of Substances.”

To understand Locke’s views upon the extent and limitations of our knowledge, it is necessary to recur to his theory of its origin. If we compare what he says about the origin of ideas from sensations with what he says about the development of general knowledge from particular, we shall find that Locke unconsciously puts side by side two different, and even contradictory, theories upon this point. In the view already given when treating of sensation, knowledge originates from the combination, the addition, of the simple ideas furnished us by our senses. It begins with the simple, the unrelated, and advances to the complex. But according to the doctrine which he propounds in treating of general terms, knowledge begins with the individual, which is already qualified by definite relations, and hence complex, and proceeds, by abstracting some of these qualities, towards the simple. Or, in Locke’s own language, “ideas become general by separating from them the circumstances of time and place and any other ideas that may determine them to this and that particular existence.” And, still more definitely, he says that general ideas are framed by “leaving out of the complex idea of individuals that which is peculiar to each, and retaining only what is common to them all.” From this it follows that “general and universal belong not to the real existence of things, but are the inventions and creatures of the understanding.” “When we quit particulars, the generals that rest are only creatures of our own making. . . . The signification they have is nothing but a relation that by the mind of man is added to them.” And in language which reminds us of Kant, but with very different bearing, he says that relations are the workmanship of the understanding. The abstract idea of what is common to all the members of the class constitutes “nominal essence.” This nominal essence, not being a particular existence in nature, but the “workmanship of the understanding,” is to be carefully distinguished from the real essence, “which is the being of anything whereby it is what it is.” This real essence is evidently equivalent to the unknown “substance” of which we have heard before. “It is the real, internal, and unknown constitution of things.” In simple or unrelated ideas and in modes the real and the nominal essence is the same; and hence whatever is demonstrated of one is demonstrated of the other. But as to substance it is different, the one being natural, the other artificial. The nominal essence always relates to sorts, or classes, and is a pattern or standard by which we classify objects. In the individual there is nothing essential, in this sense. “Particular beings, considered barely in themselves, will be found to have all their qualities equally essential to them, or, which is more, nothing at all.” As for the “real essence” which things have, “we only suppose its being without precisely knowing what it is.”

Locke here presents us with the confusion which, in one form or another, is always found in empiricism, and which indeed is essential to it. Locke, like the ordinary empiricist, has no doubt of the existence of real things. His starting-point is the existence of two substances, mind and matter; while, further, there is a great number of substances of each kind. Each mind and every separate portion of matter is a distinct substance. This supposed deliverance of common sense Locke never called into question. Working on this line, all knowledge will consist in abstraction from the ready-made things presented to us in perception, “in leaving out from the complex idea of individuals” something belonging to them. But on the other hand, Locke never doubts that knowledge begins with sensation, and that, therefore, the process of knowledge is one of adding simple, unrelated elements. The two theories are absolutely opposed to each other, and yet one and the same philosophical inference may be drawn from each; namely, that only the particular is real, and that the universal (or relations) is an artificial product, manufactured in one case by abstraction from the real individual, in the other by compounding the real sensation.

The result is, that when he comes to a discussion of the extent of knowledge, he admits knowledge of self, of God, and of “things,” only by a denial of his very definition of knowledge, while knowledge of other conceptions, like those of mathematics, is not knowledge of reality, but only of ideas which we ourselves frame. All knowledge, that is to say, is obtained only either by contradicting his own fundamental notion, or by placing it in relations which are confessedly artificial and superinduced. It is to this point that we come.

The proposition which is fundamental to the discussion is that we have knowledge only where we perceive the agreement or disagreement of ideas. Locke then takes up each of his four classes of connection, in order to ascertain the extent of knowledge in it. Our knowledge of “identity and diversity extends as far as our ideas,” because we intuitively perceive every idea to be “what it is, and different from any other.” Locke afterwards states, however, that all purely identical propositions are “trifling,” that is, they contain no instruction; they teach us nothing. Thus the first class of relations cannot be said to be of much avail. If we consider the fourth kind of knowledge, that of real existence, we have an intuitive knowledge of self, a demonstrative knowledge of God, and a sensitive knowledge of other things. But sensitive knowledge, it must be noted, “does not extend beyond the objects actually present to our senses.” It can hardly be said, therefore, to assure us of the existence of objects at all. It only tells us what experiences are being at the time undergone. Furthermore, knowledge of all three (God, self, and matter), since of real being, and not of relations between ideas, contradicts his definition of knowledge. But perhaps we shall find knowledge more extended in the other classes. And indeed Locke tells us that knowledge of relations is the “largest field of our knowledge.” It includes morals and mathematics; but it is to be noticed that, according to Locke, in both of these branches our demonstrations are not regarding facts, but regarding either “modes” framed by ourselves, or relations that are the creatures of our minds,—“extraneous and superinduced” upon the facts, as he says. He thus anticipates in substance, though not in phraseology, Hume’s distinction between “matters of fact” and “connections of ideas,” in the latter of which we may have knowledge, but not going beyond the combinations that we ourselves make.

This leaves one class, that of co-existence, to be examined. Here, if anywhere, must knowledge, worthy of being termed scientific, be found. This class, it will be remembered, comprehends our knowledge concerning substances. But this extends, according to Locke, “a very little way.” The idea of a substance is a complex of various “simple ideas united in one subject and co-existing together.” When we would know anything further concerning a substance, we only inquire what other simple ideas, besides those already united, co-exist with them. Since there is no necessary connection, however, among these simple ideas, since each is, by its very simplicity, essentially distinct from every other, or, as we have already learned, since nothing is essential to an individual, we can never be sure that any idea really co-exists with others. Or, as Locke says, in physical matters we “can go no further than particular experience informs us of. . . . We can have no certain knowledge of universal truths concerning natural bodies.” And again, “universal propositions of whose truth and falsehood we have certain knowledge concern not existence;” while, on the other hand, “particular affirmations are only concerning existence, declaring only the accidental union or separation of ideas in things existing.” This particular knowledge, it must be recalled, is, in turn, only sensitive, and thus extends not beyond the time when the sensation is had.

We are not surprised then at learning from Locke that regarding bodies “we are not capable of scientific knowledge.” “Natural philosophy is not capable of being made a science;” or, as Locke elsewhere states it, knowledge regarding the nominal essence is “trifling” (Kant’s analytic judgment); regarding the real essence is impossible. For example, when we say that all gold is fusible, this means either simply that fusibility is one of the ideas which we combine to get the general idea of gold, so that in making the given judgment we only expand our own notion; or it means that the “real” substance gold is always fusible. But this is a statement we have no right to make, and for two reasons: we do not know what the real substance gold is; and even if we did, we should not know that fusibility always co-exists with it. The summary of the whole matter is that “general certainty is to be found only in our ideas. Whenever we go to seek it elsewhere, in experiment or observations without us, our knowledge goes not beyond particulars.”

It has been necessary to give an account of Locke’s views at this length because it is in his discussion of the limitations and extent of knowledge that his theory culminates. While not working out his sensationalism as consistently as did Hume, he yet reduces knowledge to that of the existence of God and ourselves (whose natures, however, are unknown), and to a knowledge of mathematical and moral relations, which, however, concerns only “the habitudes and relations of abstract ideas.” We have now to see by what means Leibniz finds a wider sphere for certain and general knowledge by his theory of intellectualism than Locke can by his sensationalism.

Leibniz’s theory of knowledge rests upon a distinction between truths of fact, which are a posteriori and contingent, and truths of reason, which are a priori and necessary. In discussing his views regarding experience, we learned that, according to him, all judgments which are empirical are also particular, not allowing any inference beyond the given cases experienced. Experience gives only instances, not principles. If we postpone for the present the discussions of truths of reason, by admitting that they may properly be said to be at once certain and universal, the question arises how in matters of fact there can be any knowledge beyond that which Locke admits; and the answer is, that so far as the mere existence and occurrence of these facts is concerned, there is neither demonstrative nor general knowledge. But the intelligence of man does not stop with the isolated fact; it proceeds to inquire into its cause, to ascertain its conditions, and thus to see into, not merely its actual existence, but its possibility. In Leibniz’s language: “The real existence of things that are not necessary is a point of fact or history; but the knowledge of possibilities or necessities (the necessary being that whose opposite is not possible) constitutes demonstrative science.” In other words, it is the principle of causality, which makes us see a fact not as a mere fact, but as a dependent consequence; which elevates knowledge, otherwise contingent and particular, into the realm of the universal and apodictic. Underlying all “accidental union” is the real synthesis of causation.

If we follow the discussion as it centres about the terms “nominal” and “real,” it stands as follows: Leibniz objects to the use of the term “essence” in this connection, but is willing to accept that of “definition;” for, as he says, a substance can have but one essence, while there may be several definitions, which, however, all express the same essence. The essence is the possibility of that which is under consideration; the definition is the statement of that which is supposed to be possible. The “nominal” definition, however, while it implies this possibility, does not expressly affirm it,—that is to say, it may always be doubted whether the nominal definition has any possibility (or reality) corresponding to it until experience comes to our aid and makes us know it a posteriori. A “real” definition, on the other hand, makes us know a priori the reality of the thing defined by showing us the mode of its production, “by exhibiting its cause or generation.” Even our knowledge of facts of experience cannot be said, therefore, to be arbitrary, for we do not combine ideas just as we please, but “our combinations may be justified by reason which shows them to be possible, or by experience which shows them to be actual, and consequently also possible.” To take Locke’s example about gold, “the essence of gold is that which constitutes it and gives it its sensible qualities, and these qualities, so far as they enable us to recognize it, constitute its nominal essence, while a real and causal definition would enable us to explain the contexture or internal disposition. The nominal definition, however, is also real in one sense,—not in itself, indeed, since it does not enable us to know a priori the possibility or production of the body, but empirically real.”

It is evident from these quotations that what Leibniz understands by “possibility” is the condition or cause of a given fact; and that, while Locke distinguishes between particular, accidental and demonstrative, general knowledge as two opposed kinds, concerned with two distinct and mutually exclusive spheres, with Leibniz they are distinctions in the aspect of the same sphere of fact. In reality there is no combination of qualities accidental, as Locke thought that by far the greater part were; in every empirical fact there is a cause or condition involved that is invariable, and that constitutes the reason of the fact. The “accidental” is only in the relation of our ideas to objects, not in the objects themselves. There may be accidental mental associations; there are no accidental relations. In empirical, or a posteriori, knowledge, so-called, the reason is there, but is not known. A priori knowledge, the real definition, discovers and explicitly states this reason. Contingent knowledge is therefore potentially rational; demonstrative knowledge is the actual development of the reasons implicitly contained in experience.

We may with advantage connect this discussion with the fundamental doctrine of Locke and Leibniz regarding intelligence and reality. To Locke, as we have seen, knowledge is essentially a matter of relations or connections; but relations are “superinduced” and “extraneous” as regards the facts. Every act of knowledge constitutes, therefore, in some way a departure from the reality to be known. Knowledge and fact are, by their very definition, opposed to one another. But in Leibniz’s view intelligence, or reason, enters into the constitution of reality; indeed, it is reality. The relations which are the “creatures of the understanding” are, therefore, not foreign to the material to be known, but are organic to it, forming its content. The process, then, in which the mind perceives the connections or relations of ideas or objects, is simply the process by which the mind comes to the consciousness of the real nature of these objects, not a process of “superinducing” unreal ideas upon them. The difficulty of Locke is the difficulty of every theory of knowledge that does not admit an organic unity of the knowing mind and the known universe. The theory is obliged to admit that all knowledge is in the form of relations which have their source in intelligence. But being tied to the view that reality is distinct from intelligence, it is obliged to draw the conclusion that these relations are not to be found in actual existence, and hence that all knowledge, whatever else it may be, is unreal in the sense that it does not and cannot conform to actual fact. But, in the theory of Leibniz, the process of relating which is the essence of knowledge is only the realization on the part of the individual mind of the relations or reasons that eternally constitute reality. Since reality is, and is what it is, through intelligence, whatever relations intelligence rightly perceives are not “extraneous” to reality, but are its “essence.” As Leibniz says, “Truth consists in the relations between the objects of our ideas. This does not depend upon language, but is common to us with God, so that when God manifests a truth to us, we acquire what is already in his understanding. For although there is an infinite difference between his ideas and ours as to their perfection and extent, yet it is always true that as to the same relation they are identical. And it is in this relation that truth exists.” To this may be added another statement, which throws still further light on this point: “Ideas are eternally in God, and are in us before we perceive them.”

We have now to consider somewhat more in detail the means by which the transformation of empirical into rational knowledge is carried on. Leibniz points out that the difficulty concerning scientific knowledge of sensible facts is not lack of data, but, in a certain sense, superfluity of data. It is not that we perceive no connections among objects, but that we perceive many which we cannot reduce to one another. “Our experiences,” says Leibniz, “are simple only in appearance, for they are always accompanied by circumstances connected with them, although these relations are not understood by us. These circumstances furnish material capable of explanation and analysis. There is thus a sort of pleonasm in our perceptions of sensible objects and qualities, since we have more than one idea of the same object. Gold can be nominally defined in many ways. Such definitions are only provisional.” This is to say, empirical knowledge will become rational when it is possible to view any subject-matter as a unity, instead of a multiplicity of varied aspects. And on this same subject he says, in another connection: “A great number of experiences can furnish us data more than sufficient for scientific knowledge, provided only we have the art of using these data.” The aim of science is therefore, to discover the dynamic unity which makes a whole of what appears to be a mere mass of accidentally connected circumstances. This unity of relations is the individual.

It is thus evident that to Leibniz the individual is not the beginning of knowledge, but its goal. The individual is the organic, the dynamic unity of the variety of phases or notions presented us in sense-experience. Individuality is not “simplicity” in the sense of Locke; that is, separation from all relations. It is complete connection of all relations. “It is impossible for us to have [complete] knowledge of individuals, and to find the means of determining exactly the individuality of anything; for in individuality all circumstances are combined. Individuality envelops the infinite. Only so far as we know the infinite do we know the individual, on account of the influence (if this word be correctly understood) that all things in the universe exercise upon one another.” Leibniz, in short, remains true to his conception of the monad as the ultimate reality; for the monad, though an individual, yet has the universe as its content. We shall be able, therefore, to render our sensible experiences rational just in the degree in which we can discover the underlying relations and dependencies which make them members of one individual.

For the process of transformation Leibniz relies especially upon two methods,—those of mathematics and of classification. Of the former he here says but little; but the entire progress of physical science since the time of Leibniz has been the justification of that little. In the passage already quoted regarding the need of method for using our sensible data, he goes on to say that the “infinitesimal analysis has given us the means of allying physics and geometry, and that dynamics has furnished us with the key to the general laws of nature.” It is certainly competent testimony to the truth of Leibniz’s fundamental principles that he foresaw also the course which the development of biological science would take. No classification based upon resemblances, says Leibniz in effect, can be regarded as wholly arbitrary, since resemblances are found in nature also. The only question is whether our classification is based upon superficial or fundamental identities; the superficial resemblances being such as are external, or the effects of some common cause, while the fundamental resemblances are such as are the cause of whatever other similarities are found. “It can be said that whatever we compare or distinguish with truth, nature differentiates, or makes agree, also; but that nature has differences and identities which are better than ours, which we do not know. . . . The more we discover the generation of species, and the more we follow in our classifications the conditions that are required for their production, the nearer we approach the natural order.” Our classifications, then, so far as they depend upon what is conditioned, are imperfect and provisional, although they cannot be said to be false (since “while nature may give us those more complete and convenient, it will not give the lie to those we have already”); while so far as they rest upon what is causal and conditioning, they are true, general, and necessary. In thus insisting that classification should be genetic, Leibniz anticipated the great service which the theory of evolution has done for biological science in enabling science to form classes which are “natural;” that is, based on identity of origin.

Leibniz culminates his discussion of classification as a method of translating the empirical into the rational, by pointing out that it rests upon the law of continuity; and that this law contains two factors,—one equivalent to the axiom of the Realists, that nature is nowhere empty; the other, to that of the Nominalists, that nature does nothing uselessly. “One of these principles seems to make nature a prodigal, the other a miser; and yet both are true if properly understood,” says Leibniz. “Nature is like a good manager, sparing where it is necessary, in order to be magnificent. It is magnificent in its effects, and economical in the causes used to produce them.” In other words, classification becomes science when it presents us with both unity and difference. The principle of unity is that of nature as a miser and economical; that of differentiation is the principle of nature as prodigal and magnificent. The thoroughly differentiated unity is nature as self-specifying, or as an organic, not an abstract, unity.

The gist of the whole matter is, then, that experience presents us with an infinity of ideas, which may appear at first sight arbitrary and accidental in their connections. This appearance, however, is not the fact. These ideas are the effects of certain causes; and in ascertaining these conditions, we reduce the apparently unrelated variety of experiences to underlying unities, and these unities, like all real unities or simple beings, are spiritual and rational in nature. Leibniz’s ordinary way of stating this is that the principle of truths of fact is that of sufficient reason. This principle Leibniz always treats as distinguished from that of identity (and contradiction) as the ruling category of truths of reason. And we shall follow him in discussing the two together.

“Our reasonings are based on two leading principles,—that of contradiction, in virtue of which we judge false all which contains contradiction, and true that which is opposed or contradictory to that which is false; and that of sufficient reason, in virtue of which we judge that no fact is true or actual, no proposition veritable, unless there is a sufficient reason why it is as it is, and not otherwise, although these reasons are generally unknown to us. Thus there are two sorts of truths,—those of reason, and those of fact. The truths of reason are necessary, and their opposites impossible; while those of fact are contingent, and their opposites possible. When a truth is necessary, its reason can be discovered by analysis, resolving it into ideas and truths that are simpler, until the primitive truths are arrived at. It is thus that the mathematicians proceed in reducing by analysis the theorems of speculation and the canons of practice into definitions, axioms, and postulates. Thus they come to simple ideas whose definition cannot be given; primitive truths that cannot be proved, and which do not need it, since they are identical propositions, whose opposite contains a manifest contradiction.”

“But in contingent truths—those of fact—the sufficient reason must be found; namely, in the succession of things which fill the created universe,—for otherwise the analysis into particular reasons would go into detail without limit, by reason of the immense variety of natural things, and of the infinite divisibility of bodies. There are an infinity of figures and of past and present movements which enter into the efficient cause of my present writing, and there are an infinity of minute inclinations and dispositions of my soul which enter into its final cause. And since all this detail contains only other contingent and particular antecedents, each of which has need of a similar analysis to account for it, we really make no progress by this analysis; and it is necessary that the final or sufficient reason be outside the endless succession or series of contingent particulars, that it consist in a necessary being, in which this series of changes is contained only eminenter, as in its source. This necessary being and source is what we call God.”

In other words, the tracing of empirical facts to their causes and conditions does not, after all, render them wholly rational. The series of causes is endless. Every condition is in turn conditioned. We are not so much solving the problem of the reason of a given fact, as we are stating the problem in other terms as we go on in this series. Every solution offers itself again as a problem, and this endlessly. If these truths of fact, then, are to be rendered wholly rational, it must be in something which lies outside of the series considered as a series; that is, something which is not an antecedent of any one of the series, but is equally related to each and to all as their ground and source. This, considered as an argument for the existence of God, we shall deal with hereafter; now we are concerned only with its bearing upon the relation of experience to the universality and necessity of knowledge. According to this, the ultimate meaning of facts is found in their relation to the divine intelligence; for Leibniz is emphatic in insisting that the relation of God to experience is not one of bare will to creatures produced by this will (as Descartes had supposed), but of a will governed wholly by Intelligence. As Leibniz states it in another connection, not only matters of fact, but mathematical truths, have the same final basis in the divine understanding.

“Such truths, strictly speaking, are only conditional, and say that in case their subject existed they would be found such and such. But if it is again asked in what consists this conditional connection in which there is necessary reality, the reply is that it is in the relation of ideas. And by the further question, Where would be the ideas if no spirit existed; and what would then become of the foundation of the certainty of such truths?—we are brought to the final foundation of truths; namely, that supreme and universal spirit, which must exist, and whose understanding is, in reality, the region of the eternal truths. And in order that it may not be thought that it is not necessary to have recourse to this region, we must consider that these necessary truths contain the determining reason and regulative principle of existence, and, in a word, of the laws of the universe. Thus these necessary truths, being anterior to the existences of contingent beings, must in turn be based upon the existence of a necessary substance.”

It is because facts are not mere facts, in short, but are the manifestation of a “determining reason and regulative principle” which finds its home in universal intelligence, that knowledge of them can become necessary and general.

The general nature of truths of reason and of their ruling principle, identity and contradiction, has already been given in the quotation regarding the principle of sufficient reason. It is Leibniz’s contention that only in truths whose opposite is seen to involve self-contradiction can we have absolute certainty, and that it is through connection with such eternal truths that the certainty of our other knowledge rests. It is thus evident why Leibniz insists, as against Locke, upon the great importance of axioms and maxims. They are important, not merely in themselves, but as the sole and indispensable bases of scientific truth regarding all matters. Leibniz at times, it is true, speaks as if demonstrative and contingent truths were of themselves, in principle, distinct, and even opposed. But he also corrects himself by showing that contingency is rather a subjective limitation than an objective quality. We, indeed, do not see that the truth “I exist,” for example, is necessary, because we cannot see how its opposite involves contradiction. But “God sees how the two terms ‘I’ and ‘exist’ are connected; that is, why I exist.” So far as we can see facts, then, from the standpoint of the divine intelligence, so far, it would appear, our knowledge is necessary.

Since these axioms, maxims, or first truths are “innate,” we are in a condition to complete (for the first time) the discussion of innate ideas. These ideas constitute, as we have learned, the essential content of the divine intelligence, and of ours so far as we have realized our identity with God’s understanding. The highest form of knowledge, therefore, is self-consciousness. This bears the same relation to necessary truths that the latter bear to experience. “Knowledge of necessary and eternal truths,” says Leibniz, “distinguishes us from simple animals, and makes us have reason and science, elevating us to the knowledge of ourselves. We are thus developed to self-consciousness; and in being conscious of ourselves we are conscious of being, of substance, of the simple, of the spiritual, of God.” And again he says that “those that know necessary truths are rational spirits, capable of self-consciousness, of recognizing what is termed Ego, substance, and monad. Thus they are rendered capable of demonstrative knowledge.” “We are innate to ourselves; and since we are beings, being is innate to us, for knowledge of it is implicit in that which we have of ourselves.”

Knowledge, in fine, may be regarded as an ascending series of four terms. The first is constituted by sensations associated together in such a way that a relation of antecedence and consequence exists between them. This is “experience.” The second stage comes into existence when we connect these experiences, not by mere relations of “consecution,” but by their conditions, by the principle of causality, and especially by that of sufficient reason, which connects them with the supreme intelligence, God. This stage is science. The third is knowledge of the axioms and necessary truths in and of themselves, not merely as involved in science. The fourth is self-consciousness, the knowledge of intelligence, in its intimate and universal nature, by which we know God, the mind, and all real substance. In the order of time the stage of experience is first, and that of self-consciousness last. But in the lowest stage there are involved the others. The progress of knowledge consists in the development or unfolding of this implicit content, till intelligence, spirit, activity, is clearly revealed as the source and condition of all.