Stony Brook University

definition must express essential features of the thing. The import of all this is that
Leibniz claims to have a method for avoiding the kind of arbitrariness involved in
nominalism. He thinks that a real definition expresses a real possibility, an unchanging
essence, or as he often calls it, an “eternal truth.”
With this result we are lead to see that a definition is the linguistic expression of
an essence. But Leibniz’s realism about definition goes much further. When we seek the
ground of essence, we are lead to the ultimate “source” of essences, eternal truths, and
ideas, i.e., the mind of God. This account may be found in the Nouveaux Essais, where
Locke’s spokesman denies that eternal truths have any sort of extra-mental (i.e., platonic)
reality: “general certain propositions” or “aeternae veritates” are not “imprinted in our
minds from any patterns that are anywhere out of the mind.” He argues that “being once
made about abstract ideas, so as to be true, they will . . . always be true” and will always
be thought true, so long as we apply our mind to these ideas” (E 4.11.14). Like Hobbes,
Locke will not admit of any extra-mental or extra-conventional ideas.
Leibniz responds by explaining that eternal truths are fundamentally
“hypothetical” or are conditionalia: 51 “As for ‘eternal truths’, it must be understood that
fundamentally they are all conditional; they say, in effect: given [such a thing is assumed
to exist, some other thing exists” (NE 446). 52 His reason for saying this, as he explains,
goes back to a Scholastic problem called de constantia subjecti. The problem is to
explain how hypothetical propositions can be true, without supposing the subject to have
actual existence. For example, we want to make true statements about triangles (such as
“if a figure has three sides, then its angles are equal to two right angles.” But for this
statement to be true there need not be any triangles. So, for a hypothetical proposition to
be true, it is argued, the actual existence of the triangle must be assumed: If a three-sided
figure exists, then its angles are equal to two right angles. In other words, the subject
need not be supposed to exist to say that it necessarily has certain properties. Therefore,
the hypothetical proposition is an eternal truth, on the supposition that the subject
exists. 53 In Leibniz’s words, “its truth is a merely conditional one which says that if the
subject ever does exist it will be found to be thus and so” (NE 447). 54
So far, Leibniz has not really said anything that Locke could not agree with.
However, this is not the complete explanation, Leibniz says, since “there is still a reality
that does not mislead.” This seems to imply that hypothetical objects have some kind of
reality. And so, as he explains, whether or not the thing exists, the reality is in the ideas
themselves and in their connection. But for there to be a reality and connection at all,
there must be a supreme mind.
51 It can be recalled that in the Elementa Leibniz said that eternal truths are conditionalia. “We need not
wonder, therefore, that the principles of these sciences [i.e., mathematics, and the science of right] possess
eternal truth. For they are all conditionalia, conditional truths, and treat not of what does exist but of what
follows if existence be assumed. They are not derived from sense but from a clear and distinct intuition
Plato called an idea, and which, when expressed in words, is the same as a definition” (LL 133).
52 A.6.6.446: “Pour ce qui est des verités éternelles, il faut observer, que dans le fonds elles sont toutes
conditionnelles et disent en effect: telle chose posée, telle autre chose est.”
53 For categorical propositions, the existence of the subject is explicitly assumed (e.g., ‘a triangle is a threesided
figure). This means that all categorical propositions are implicitly hypothetical (NE 447).
54 A.6.6.447: “C’est que la verité n’est que conditionnelle, et dit, qu’en cas que le sujet existe jamais, on le
trouvera tel.”
156