Stony Brook University

Leibniz also seems to think that these eternal truths or conditionalia are much like
Platonic ideas. This should raise the question of how Leibniz supposes we are to know
what the Platonic idea of justice is, or how we are to get a distinct intuition of it. Yet he
never explicitly says that his definition of justice, when offered, is the Platonic idea of
justice. Nor does he say that we have immediate knowledge of the true definition. At the
same time, he wants to say that if we have a “clear and distinct idea” of something, then
we have a true definition. But how do we get a clear and distinct idea, or what he calls
here, an intuition? In the following passages, Leibniz indicates some methodological
points for doing so. They mainly involve criteria for definition and truth, a method of
demonstration, and an “epagogic” induction. First, Leibniz makes a sketchy reference to
his (not fully developed at this point) criteria for definition and truth: 53
That which can be understood clearly, however, is not always true, though
it is always possible; and it is also true, in addition, whenever the only
question is that of possibility. But whenever there is a question of
necessity, there is also one of possibility; for if we call something
necessary we deny the possibility of its opposite. (LL 133) 54
The passage may be understood this way: To understand an idea or definition clearly
(indeed, clearly and distinctly) one must know that it is possible. A possible definition is
one that contains no contradiction among its notions. To determine this requires analysis
of the definition—what Leibniz also calls a demonstration (see next paragraph). For
example, the definition of man as ‘rational animal’ is a possible definition if and only if
an analysis of the notions ‘rational’ and ‘animal,’ and any related notions, reveals that
‘rational’ and ‘animal’ are logically compatible. If they are, then the definition is
possible. That is, the definition expresses a true idea. However, this does not show that
the idea in question refers to an existing thing or state of affairs. 55 It just shows that the
idea is clearly and distinctly understood. Furthermore, the above passage implies that
definitions are necessary truths. This is because definitions are identity statements. That
is, a definition posits an identity between the definiens and the definiendum (man =
rational animal); and identity statements are necessary truths. What makes an identity a
necessary truth is that, implied here by Leibniz, the denial of an identity statement entails
a contradiction; and non-contradiction is the principle of necessary truths. 56 That is to say
that the opposite of a contradiction is necessarily true. This explains why, as he says in
the passage above, “if we call something necessary, we deny the possibility of its
opposite.” To say, for example, that a man is not a rational animal is to say something
impossible, since it is to say ‘man is and is not.’ Likewise, therefore, the definition of
53
Leibniz’s more mature views on clear and distinct ideas, necessity, truth, and definition can be found in
several papers throughout the 1670’s, as well as in his well-known Meditationes de Cognitione, Veritate, et
Ideis (1684). I discuss these texts, along with Leibniz’s method of demonstration, in greater detail in
Chapter Four.
54
A.6.1.460: “Qvicqvid autem clarè intelligi potest, non verum qvidem semper, possibile est tamen, imo et
tunc verum est qvoties de possibilitate sola qvaestio est. Qvoties autem de necessitate qvaestio est, de
possibilitate qvaestio est, nam si qvid necessarium dicitur, possibilitas oppositi negatur.”
55
It only shows you have a “real” as opposed to a “nominal” definition, as Leibniz says in Meditationes de
Cognitione, Veritate, et Ideis.
56
This claim is found in a letter to Conring (1678), which I will discuss in Chapter Four.
57