Stony Brook University

defines definition in the following ways: “If we assume any simple term whatever
equivalent to any composite one, or expressing the same thing, the simple term will be
defined, the composite term will be the definition” (LL 245). 40 This shows that the subject
term (definiendum) is identical, in a way, to the composite terms (definiens). The
composite terms consist of a genus and a species term, and as a whole designate a
species. Therefore, “a definition is a composite substantive term equivalent to a species”
(LL 246). 41 What is said here applies to substantives. However, there is no reason to
think that the same intensional approach does not also apply to the definition of abstract
terms.
The next point to consider is the ontological import of definitions. This involves
Leibniz’s method for establishing “real” definitions as opposed to merely “nominal”
ones. The following early passage from Leibniz’s Preface to Nizolius (1670) is probably
Leibniz first expression of his opposition to Hobbes’ nominalism. He accuses Hobbes of
being not merely a nominalist, but a “super-nominalist,” since for him truth is relative to
the names humans attach to ideas.
For not content like the nominalists, to reduce universals to names,
[Hobbes] says that the truth of things itself consists in names and what is
more, that it depends on the human will, because truth allegedly depends
on the definitions of terms, and definitions depend on the human will. This
is the opinion of a man recognized as among the most profound of our
century, and as I said, nothing can be more nominalistic than it. Yet it
cannot stand. In arithmetic, and in other disciplines as well, truths remain
the same even if notations are changed, and it does not matter whether a
decimal or a duodecimal number system is used. (LL 128) 42
Leibniz apparently thinks that for Hobbes a mere change in notation entails a change in
meaning. But Hobbes does not think something as silly as that. 43 Even so, Leibniz thinks
that Hobbes’ nominalism results in an unstable and arbitrary conventionalism—wherein
the meaning of ideas ultimately depends on the human will. Quite reasonably, he objects
that if a name stands for an idea or set of ideas, and the set of ideas can be changed at
will, then a definition could be arbitrarily stipulated to suit one’s purposes, or be left
inadequately analyzed to confuse one’s understanding. To defeat the contingency of
nominalism Leibniz proposes (1) a method of analysis and (2) a realist argument that
requiruntur ad notionem auri quam metalli, et majus opus est aurum producere quam metallum
qualecunque.”
40 G.7.225-6: “Si assumsimus terminum aliquem simplicem velut composito alicui aequivalentem, seu
eandem rem exprimentem, terminus simplex erit definitum, terminus compositus erit definitio.”
41 G.227: “Definitio est terminus compositus substantivus speciei aequivalens.”
42 G.4.158: “Non contentus enim cum Nominalibus universalia ad nomina reducere, ipsam rerum veritatem
ait in nominibus consistere, ac, quod majus est, pendere ab arbitrio humano, quia veritas pendeat a
definitionibus terminorum, definitiones autem terminorum ab arbitrio humano. Haec est sententia viri inter
profundissimos seculi censendi, qua, ut dixi, nihil potest esse nominalius. Sed quae tamen stare non potest.
Uti in Arithmetica, ita et in aliis disciplinis manent eaedem veritates etsi notae mutentur, nec refert
decadica an duodenaria progressio adhibeatur.”
43 In On Man Hobbes says: “Speech or language is the connexion of names constituted by the will of men
to stand for the series of conceptions of the things about which we think. Therefore, as a name is to an idea
or conception of a thing, so is speech to the discourse of the mind” (37).
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