combination of this doctrine with a tendency to think chiefly of experiment, of the controlled addition or subtraction of these elements one at a time, that we owe the theoretically premature linking of a as effect to A as cause. This too can be met by a modification of form. The other issue is perhaps of more significance. It is the oscillation which Mill manifests between the conception of his formula as it is actually applicable to concrete problems in practice, and the conception of it as an expression of a theoretical limit to practical procedure. Mill seems most often to think of the former, while tending to formulate in terms of the latter. At any rate, if relevance in proximo is interpolated in the peccant clause of the canon of the Joint-Method, the practical utility of the method is rehabilitated. So too, if the canon of the Method of Agreement is never more than approximately satisfied, intermixture of effects will in practice mean that we at least often do not know the cause or antecedent equivalent of a given effect, without the possibility of an alternative. Finally, it is on the whole in keeping with Mill’s presuppositions to admit even in the case of the method of difference that in practice it is approximative and instructive, while the theoretical formula, to which it aims at approaching asymptotically as limit, if exact, is in some sense sterile. Mill may well have himself conceived his methods as practically fruitful and normally convincing with the limiting formula in each case more cogent in form but therewith merely the skeleton of the process that but now pulsed with life.
Enough has been said to show why the advance beyond the letter of Mill was inevitable while much in the spirit of Mill must necessarily affect deeply all later experientialism. After Mill experientialism takes essentially new forms. In part because of what Mill had done. In part also because of what he had left undone. After Mill means after Kant and Hegel and Herbart, and it means after the emergence of evolutionary naturalism. Mill, then, marks the final stage in the achievement of a great school of thought.
ii. The Logic of Rationalism.
A fundamental contrast to the school of Bacon and of Locke is afforded by the great systems of reason, owning Cartesian inspiration, which are identified with the names of Spinoza and Leibnitz. In the history of logic the latter thinker is of the more importance. Spinoza’s philosophy is expounded Spinoza. ordine geometrico and with Euclidean cogency from a relatively small number of definitions, axioms and postulates. But how we reach our assurance of the necessity of these principles is not made specifically clear. The invaluable tractate De Intellectus emendatione, in which the agreement with and divergence from Descartes on the question of method could have been fully elucidated, is unhappily not finished. We know that we need to pass from what Spinoza terms experientia vaga,[1] where imagination with its fragmentary apprehension is liable to error and neither necessity nor impossibility can be predicated, right up to that which fictionem terminat—namely, intellectio. And what Spinoza has to say of the requisites of definition and the marks of intellection makes it clear that insight comes with coherence, and that the work of method on the “inductive” side is by means of the unravelling of all that makes for artificial limitation to lay bare what can then be seen to exhibit nexus in the one great system. When all is said, however, the geometric method as universalized in philosophy is rather used by Spinoza than expounded.
With Leibnitz, on the other hand, the logical problem holds the foremost place in philosophical inquiry.[2] From the purely logical thesis, developed at quite an early stage of his thinking,[3] that in any true proposition the predicate is contained in the subject, the main principles of his doctrine of Leibnitz. Monads are derivable with the minimum of help from his philosophy of dynamics. Praedicatum inest subjecto. All valid propositions express in the last resort the relation of predicate or predicates to a subject, and this Leibnitz holds after considering the case of relational propositions where either term may hold the position of grammatical subject, A = B and the like. There is a subject then, or there are subjects which must be recognized as not possible to be predicated, but as absolute. For reasons not purely logical Leibnitz declares for the plurality of such subjects. Each contains all its predicates: and this is true not only in the case of truths of reason, which are necessary, and ultimately to be exhibited as coming under the law of contradiction, “or, what comes to the same thing, that of identity,” but also in the case of truths of fact which are contingent, though a sufficient reason can be given for them which “inclines” without importing necessity. The extreme case of course is the human subject. “The individual notion of each person includes once for all what is to befall it, world without end,” and “it would not have been our Adam but another, if he had had other events.” Existent subjects, containing eternally all their successive predicates in the time-series, are substances, which when the problems connected with their activity, or dynamically speaking their force, have been resolved, demand—and supply—the metaphysic of the Monadology.
Complex truths of reason or essence raise the problem of definition, which consists in their analysis into simpler truths and ultimately into simple—i.e. indefinable ideas, with primary principles of another kind—axioms, and postulates that neither need nor admit of proof. These are identical in the sense that the opposite contains an express contradiction.[4] In the case of non-identical truths, too, there is a priori proof drawn from the notion of the terms, “though it is not always in our power to arrive at this analysis,”[5] so that the question arises, specially in connexion with the possibility of a calculus, whether the contingent is reducible to the necessary or identical at the ideal limit. With much that suggests an affirmative answer, Leibnitz gives the negative. Even in the case of the Divine will, though it be always for the best possible, the sufficient reason will “incline without necessitating.” The propositions which deal with actual existence are still of a unique type, with whatever limitation to the calculus.
Leibnitz’s treatment of the primary principles among truths of reason as identities, and his examples drawn inter alia from the “first principles” of mathematics, influenced Kant by antagonism. Identities some of them manifestly were not. The formula of identity passed in another form to Herbart and therefore to Lotze. In recognizing, further, that the relation of an actual individual fact to its sufficient ground was not reducible to identity, he set a problem diversely treated by Kant and Herbart. He brought existential propositions, indeed, within a rational system through the principle that it must be feasible to assign a sufficient reason for them, but he refused to bring them under the conception of identity or necessity, i.e. to treat their opposites as formally self-contradictory. This bore interest in the Kantian age in the treatment alike of cause and effect, and of the ontological proof of existence from essence. Not that the Law of Sufficient Reason is quite free from equivoque. Propositions concerning the possible existence of individuals put Leibnitz to some shifts, and the difficulty accounts for the close connexion established in regard to our actual world between the law of sufficient reason and the doctrine of the final cause. This connexion is something of an afterthought to distinguish from the potential contingency of the objectively possible the real contingency of the actual, for which the “cause or reason” of Spinoza[6] could not account. The law, however, is not invalidated by these considerations, and with the degree of emphasis and the special setting that Leibnitz gives the law, it is definitely his own.
If we may pass by the doctrine of the Identity of Indiscernibles, which played a part of some importance in subsequent philosophy, and the Law of Continuity, which as Leibnitz represents it is, if not sheer dogma, reached by something very like a fallacy,
- ↑ Bacon, Novum organum, i. 100.
- ↑ Russell’s Philosophy of Leibnitz, capp. 1-5.
- ↑ See especially remarks on the letter of M. Arnauld (Gerhardt’s edition of the philosophical works, ii. 37 sqq.).
- ↑ Gerhardt, vi. 612, quoted by Russell, loc. cit., p. 19.
- ↑ Ibid., ii. 62, Russell, p. 33.
- ↑ Spinoza, ed. van Vloten and Land, i. 46 (Ethica, i. 11).
