Stony Brook University

which we cannot. But this epistemological distinction does not capture what is supposed
to be a logical one. Despite these difficulties, the point relevant to our purposes is that
Leibniz considered the termination of analysis to be the essential criterion for
distinguishing necessary from contingent truths, and this has direct applicability to
propositions used in demonstrations. This is well expressed in the following passage.
But in contingent truths, even though the predicate is in the subject, this
can never be demonstrated, nor can a [contingent] proposition ever be
reduced to an equality or to 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. (“On
Freedom” (1689) AG 96) 14
Just as above, a contingent proposition is one in which God “sees” all that connects the
predicate to the subject, but this connection can never be strictly demonstrated since the
connection is interminable. This means that contingent propositions cannot be strictly
demonstrated. Only necessary connections can be strictly demonstrated, since their
analysis terminates in identities. This requirement will become clearer in Section 3. It can
be noted that this passage shows that Leibniz recognizes that an infinite analysis has no
end to its resolution, although God sees the (whole?) series of connections. Perhaps this
suffices to establish the sufficient reason; despite the fact that there is no end to the
resolution, the sufficient reason is found in the unending series of connections,
approaching infinity.
For reasons that will become clearer later, I want to emphasize the distinction
between necessity and contingency in terms of the modes of necessity, possibility, and
impossibility. This difference is brought out by the following passage:
An absolutely necessary proposition is one which can be resolved into
identical propositions, or whose opposite implies a contradiction. . . . This
type of necessity, therefore, I call metaphysical or geometrical. That which
lacks necessity I call contingent, but that which implies a contradiction, or
whose opposite is necessary, is called impossible. The rest are called
possible. (PM 96-7) 15
From this, we can distinguish necessary truths from contingent by mode: Necessary
(metaphysical, geometrical) truths are those whose contraries are contradictions.
Contradictions are impossible, that is, can never be true. But contingent truths are those
whose denials are not contradictions, and so are possible, that is, are true in some world.
14 FC.182: “Sed in veritatibus contingentibus, etsi praedicatum insit subjecto, nunquam tamen de eo potest
demonstrari, neque unquam ad aequationem seu identitatem revocari potest propositio, sed resolutio
procedit in infinitum, Deo solo vidente non quidem finem resolutionis qui nullus est, sed tamen
connexionem [terminorum] sic involutionem praedicati in subjecto, quia ipse videt quidquid seriei inest.”
15 From 1686, CO.17: “Absolute necessaria propositio est quae resolvi potest in identicas, seu cujus
oppositum implicat contradictionem. . . . Hanc ergo Necessitatem appello Metaphysicam vel Geometricam.
Quod tali necessitate caret, voco contingens, quod vero implicat contradictionem, seu cujus oppositum est
necessarium, id impossibile appellatur. Caetera possibilia dicuntur”
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