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.