Routledge History of Philosophy Volume IV

RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM 359
deduction is watertight; at points Leibniz seems to be smuggling in certain
unstated non-logical premises.
The claim that Leibniz derived his metaphysics from his logic is more
mysterious than it need be. When Russell and Couturat put forward this thesis,
they had something quite specific in mind when they spoke of Leibniz’s ‘logic’:
they were referring to his theory of truth. The theory of truth in question is
explicitly stated, not in the Discourse on Metaphysics, but in the correspondence
with Arnauld where it appears almost as an afterthought. However, the theory
makes itself felt in the Discourse, for it seems to ground the deep analysis of the
nature of substance which Leibniz offers as a supplement to Aristotle.
Leibniz’s distinctive theory of truth can best be explained by way of contrast.
Perhaps the most intuitive doctrine of truth is some version of the
correspondence theory; in other words, truth consists in a relation of
correspondence between propositions and states of affairs in the world. It is some
version of the correspondence theory that Aristotle seems to have had in mind
when he defined truth as saying of that which is that it is and of that which is not
that it is not. 23 Although he sometimes seems to suggest that he is simply
following in Aristotle’s footsteps, Leibniz in fact advances a radically different
theory. For Leibniz, truth consists not in a correspondence between propositions
and states of affairs but in a relation between concepts. Leibniz provides a
succinct summary of his theory in a letter to Arnauld: ‘In every true affirmative
proposition, necessary or contingent, universal or particular, the concept of the
predicate is in a sense included in that of the subject: praedicatum inest subjecto;
or else I do not know what truth is.’ 24 Let us call this ‘the concept-containment
theory of truth’.
Leibniz’s theory of truth can be seen as a generalization of a more familiar and
more limited claim. Consider the proposition: ‘Gold is a metal’. It is plausible to
say that the proposition is true because the concept expressed by the predicate
term is contained in the concept expressed by the subject term; in other words, an
analysis of the concept of gold would reveal that the concept of metal is one of
its constituent concepts. (Analysis is conceived of here as a matter of replacing a
given term by its definitional equivalent.) As his comment to Arnauld shows,
Leibniz wishes to extend this insight to all affirmative propositions, including
singular ones such as ‘Julius Caesar crossed the Rubicon’. Thus Leibniz holds
that the proper name ‘Julius Caesar’ is not simply an arbitrary label; it expresses
a concept no less than the term ‘gold’ does. The proposition ‘Julius Caesar
crossed the Rubicon’ is true because the concept of crossing the Rubicon is
contained in the concept of Julius Caesar. From this general, conceptcontainment
theory of truth Leibniz’s distinctive claim about the nature of
individual substances follows as a special case; by virtue of the general theory,
all the predicates which are true of an individual substance are contained in the
concept of that substance. 25
‘From these considerations there follow a number of important paradoxes.’ 26
This remark in the Discourse is key evidence for the claim that Leibniz derived his