Leibniz’s rationalism leads him to hold the conceptual containment theory of truth,
that is, in any true proposition, the concept of the predicate is contained in or a part
of the concept of the subject. Thus all truths for Leibniz are analytic in this sense
of analyticity. Of course, the problem is that analytic truths are usually associated
with necessary truths, so Leibniz’s conceptual containment theory of truth seems
to lead to the Spinozistic conclusion that all truths are necessary truths. If the
concept of the predicate is in the concept of the subject then it appears that an
analysis of the subject will reveal this conceptual connection between subject and
predicate concept. Leibniz’s famous solution is to say that while in necessary truths
the conceptual connection between subject and predicate can be revealed by a
finite analysis, in contingent truths, finding the conceptual connection requires an
infinite analysis, that is, an analysis that will never end. Thus in On Freedom from
around 1698 Leibniz writes:
But in contingent truths, even though the predicate is in the subject, this
can never be demonstrated, nor can a proposition ever be reduced to an
equality or an identity, but the resolution proceeds to infinity, God alone
seeing, not the end of the resolution, of course, which does not exist, but
the connection of the terms or the containment of the predicate in the
subject, since he sees whatever is in the series. (AG 96)
