Stony Brook University

ideas are basically platonic entities residing in God’s mind. As we saw in the Elementa,
Leibniz claimed that definitions must be analyzed to show they are “possible.” He also
claimed that the definitions of right, law and justice, “are not derived from sense but from
a clear and distinct intuition [imaginatio], which Plato called an idea, and which when
expressed in words, is the same as a definition” (LL 133). 44 Leibniz will also maintain in
the Meditation on justice that ideas are independent of human will (indeed, independent
of God’s will) and that “these are fundamental rules of reasoning and of discourse” (RM
48). 45 Let us now see how he supports these claims will more specific arguments.
Leibniz’s realism about definition can be sharply contrasted to Hobbes’
nominalism by comparing their respective demonstrative methods. As Couturat observes,
Hobbes’s method is similar but importantly different: For both, a demonstration consists
of a chain of definitions; but for Hobbes, definitions are merely nominal and arbitrary,
“entirely relative to the definitions of words, that is to say to our conventions of
language” (C 188). For Leibniz, definitions must have real possibility (this will be
explained). Another similarity is that although definitions are primitives for Leibniz and
Hobbes, for Hobbes they are conventional primitives, and they are not to be
demonstrated. Again, for Leibniz definitions must be shown to have real possibility,
which is done through demonstration. Also, Hobbes does not explain the status of the
principles of non-contradiction and identity. While Hobbes takes them to be the “first
principles of all ratiocination,” they are neither definitions nor conventions of
reasoning. 46 However, for Leibniz they are first principles because they are
indemonstrable truths. This means, most importantly, that Leibniz has a more thoroughly
grounded method of demonstration than Hobbes. As Couturat explains, for Leibniz,
The definition expresses the real decomposition of the complex concept
into simple concepts; consequently, the substitution of the definition with
the defined operates, no longer in virtue of an arbitrary convention, but in
virtue of a principle of identity; it is therefore this principle which
constitutes the nerve of all demonstration, and which makes the truth of a
proposition demonstrated. 47
In other words, a Leibnizian demonstration depends on the principle of identity (and, as
Couturat adds, contradiction, since they are convertible principles for Leibniz, as we
saw). The complex concepts of a definition are broken down into (substituted by) simple
concepts, thus reducing the definition to a true identity. If the definition does not contain
a contradiction or any incompatible ideas, then the idea it expresses has real possibility.
In this sense the definition is said to be true, but not at all conventional.
44
Note that “imaginatio” is inconsistent with Leibniz’s insistence in various places that ideas are not
images, since an image always involves something sensible. But ideas themselves, such as ‘being,’ and
those mentioned in “On What is Independent of Sense and Matter,” and especially those of ‘justice,’ have
no sensible content.
45
Mollat 45: “Ce sont là les regles fondamentales du raisonnement et du discours.”
46
See Wilson, p. 20.
47
C 188: “La définition exprime la décomposition réelle du concept complexe en concepts simples; dès
lors, la substitution de la définition au défini s’opère, non plus en vertu d’une convention arbitraire, mais en
vertu du principe d’identité; c’est donc ce principe qui constitue le nerf de toute demonstration, et qui fait la
vérité des propositions démontrées.”
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