RATIONALISM OF SPINOZA AND LEIBNIZ At first sight the contrast between the rationalism of Spinoza and that of Leibniz (1646-1716) seems sufficiently sharp and decisive. Leibniz repudiates emphatically enough the monism of Spinoza, and substitutes a monadism, according to which the constituents of reality are strictly individual entities, psychical in nature, dependent, indeed upon an ultimate ground but not contained therein. He reverts in a way, to the Aristotelian defini tion of substance as that which can only be the subject of a proposition, and never a predicate; but this definition, he con tends, is not sufficient, and is in itself merely verbal. Every true predication must have a basis in the nature of things, and even when the predicate is not explicitly contained in the subject, it is still necessary that it should be implicitly contained in it. The content, then, of the subject must always include that of the predicate in such a way that, if one understood perfectly the subject-concept, one would know that the predicate necessarily belongs to it.
The concept, therefore, of any individual substance involves everything which can happen to that substance; and, in contem plating this concept, a perfect intelligence would be able to discern whatsoever can be truly said about such individual, just as in the nature of a circle it would be able to discern all the properties which can be derived therefrom. Each monad is, in this respect, a substance, and in so far an entire world, or a mirror of the whole world. "The universe is in a manner multiplied as many times as there are substances." Moreover, since each monad is thus all-inclusive, and therefore unaffected by any other, it was necessary to assume a concomit ance (a "pre-established harmony") as subsisting in the universe, so that to each experience in one monad there would be a cor responding experience in every other. Again, since no two indi viduals can be absolutely alike and at the same time numerically different, each must mirror the universe from a different "point of view," so that the universe is in a manner multiplied as many times as there are substances. Once more, in the life of each monad there is continual development, or advance from one per ception to another, due to conation, the advance being propor tional to the clearness of apprehension on the part of the monad.
The basis of all knowledge is, according to Leibniz, perception, and of perception there are differences of degree but not of kind. The lower stage may be said to be that of unconscious or crude perception, in which there is union of a manifold in what is per ceived but of neither is the subject clearly aware. A further stage is that of "apperception" in which the perceptions have reached a certain measure of clearness and distinctness, and the subject is aware of the multiplicity which is united in the content appre hended. And a higher stage, still, is that of reflection, or of self conscious cognition, in which the subject marshals its perceptions or ideas in the light of the fundamental principles of contra diction and sufficient reason (i.e., the principle of causality).
These two principles are concerned each with a special kind of truths,—the one with truths of reason, of which the one cri terion is self-consistency, and the other with truths of fact. Whereas the Cartesians and Spinoza had maintained that all real knowledge was of one kind and that no fact could be explained except by showing its dependence on the one supreme ground, Leibniz insists that to statements relating to matters of fact the test of self-consistency cannot be satisfactorily applied, that we can only point to a sufficient reason why we believe such state ments to be true, without professing that we can fully explain why they are.
While, then, all necessary truths are expressible in analytical propositions, wherein the relation of predicate to subject can be clearly apprehended, contingent truths are not thus expressible, but only in propositions which Kant called later synthetical, wherein the relation of predicate to subject cannot be clearly apprehended. It is true that Leibniz often speaks of this dis tinction as though it were in the long run a distinction of degree, not of kind. Could we survey with perfect clearness the long series of grounds of any matter of fact, we should see that ulti mately the consequences were capable of being analytically de duced, only the series of grounds required for such a purpose would be infinite. Yet, although in consistency with his general theory Leibniz was bound to say this, it is evident that even on the score of the difference between infinite regress and finite mediation, the contention cannot be sustained.