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§5. Some Comments on Leibniz ’s Account of Truth
Leibniz often uses this name, “the Principle of Sufﬁcient Reason,” to refer
to various less general principles. The form above is, I think, the most
general form of the principle. Thus he says: “There are two ﬁrst principles of all reasonings, the principle of contradiction . . . and the principle
that a reason must be given, that is, that every true proposition which is
known per se, has an a priori proof, or that a reason can be given for
every truth, or as is commonly said, that nothing happens without a cause.
Arithmetic and geometry do not need this principle, but physics and
Another quotation brings out how contingent truths depend on God’s
decrees and choice of the best of all possible worlds.
The demonstration of this predicate of Caesar [that he resolved to cross
the Rubicon] is not as absolute as are those of numbers or of geometry,
but presupposes the series of things which God has chosen freely, and
which is founded on the ﬁrst decree of God, namely to do always what
is most perfect, and on the decree which God has made [in consequence of the ﬁrst], in regard to human nature, that man will always
do (though freely) what appears best. . . . [E]very truth which is
founded on decrees of this kind is contingent, although it is certain.
(Discourse:§ [Ariew and Garber:])
. A second comment on Leibniz’s account of truth is that today we
use the term “a priori” as an epistemological term. It says something about
how a proposition can be known, namely, that it can be known independently of experience. But this is not Leibniz’s idea of the a priori: when he
says that true propositions have an a priori proof, he means a proof based
on the ultimate reasons for their being true and not false. Clearly Leibniz
does not mean that we (human beings) can know contingent propositions
to be true independent of experience. The proofs he has in mind can be
known only by God, because only God sees by intuitive vision of the possible existences the answer to the requisite inﬁnite analysis.
A further comment, related to the preceding one, is that Leibniz’s con6. Gerhardt, Philosophischen Schriften, VII:, in Leibniz Selections, ed. Philip R. Weiner (New
York: Scribners, ), p. .
ception of the contingent is, we might say, proof-theoretic.7 That is, it draws
the distinction between necessary and contingent true propositions according to how they can be, or are, established by someone who is omniscient. This is seen from how he uses the conception of contingency and
by his saying, for example, in referring to the Principle of Sufﬁcient Reason,
that “the principle that nothing ever happens without the possibility that
an omniscient mind could give some reason why it should have happened
rather than not” (Bodeman’s Catalogue of Leibniz’s MSS , in Wiener:
). And he says in “Necessary and Contingent Truths” (.) that “existential
or contingent propositions differ entirely from these [the eternal truths
about essences]. Their truth is understood a priori by the inﬁnite mind
alone, and cannot be demonstrated by any resolution.” These quotations
show the extent to which Leibniz’s distinction between necessary and contingent truths looks at the question from God’s point of view.
. A third comment: it is tempting to object that Leibniz’s account of
contingency in terms of proofs requiring an inﬁnite analysis that only God
can see the answer to does not give us a real, bona ﬁde conception of
contingency. The contingency that we complain is missing is perhaps that
of brute fact: that is, a fact that simply has no explanation even when everything is known, as, for example, the ultimate laws of nature, should there
be such. That conception of contingency, though, is precisely what Leibniz
rejects: it violates his principle of sufﬁcient reason. This principle requires
that the world must be fully intelligible through and through, not to us,
admittedly, but to a perfect inﬁnite intelligence. Thus the ultimate laws of
nature, even as subordinate maxims, will manifest an appropriate perfection. Leibniz believes that the laws of physics do this in the form of principles of conservation, for example, as well as of maximum and minimum
principles leading to the calculus of variations (Discourse:§§–). Nothing
is opaque to God. That our world satisﬁes this condition is part of Christian
faith (no doubt of other faiths as well). It is also a thesis of idealism.
A last comment: above we reviewed two beginnings for Leibniz’s account of the predicate-in-subject doctrine. One was the idea of a true proposition as one whose predicate concept is in the subject concept; the other
7. See R. M. Adams, “Leibniz’s Theory of Contingency,” in Leibniz: Critical and Interpretative
Essays, ed. M. Hooker (Minneapolis: University of Minnesota Press, ), pp. ff.
was the idea of a monad as a windowless form of mental life speciﬁed
completely by a list of all its properties over time. It is natural to ask which
of these is better, and which came ﬁrst in Leibniz’s mind.
Concerning the last question, I have no opinion, though a study of further texts might give an answer. I think, though, the second idea, beginning
with windowless monads, may be better: it goes deeper into Leibniz’s overall doctrine, and together with the idea of perfection it enables us to see
quite easily why the predicate-in-subject doctrine holds of all true afﬁrmative contingent propositions. So I think it to be more instructive and in any
case sufﬁcient to render Leibniz’s view intelligible. Certainly he has additional ideas in mind, as his use of the analogy to an inﬁnite series shows;8
note his mention of surd relations and of showing that the error is less than
any assignable quantity (“Necessary and Contingent Truths,” paragraph ).
But I don’t think that these other things are necessary to give sense to the
predicate-in-subject doctrine. The elementary intuitive idea of monads as
discussed above seems sufﬁcient to do that.
Note in conclusion that obviously Leibniz’s theory of truth is framed
for his philosophical theology and its apologetic aims. It is not an account
of how we, human beings, learn the meaning and reference of the terms
in our language and apply them in everyday life. Certainly Leibniz could
not have been unaware of this. But for him, that is not the point. He is
not trying to explain our use of language, how its terms get their meaning
and reference. Rather, he wants to maintain certain very general considerations about all truths seen as fully accessible only from God’s point of
view. He thinks that our actual language hooks up suitably in some way
with these truths; and this enables us to understand his theory. And that
is enough for his purposes. It is not what we think of today as philosophy
of language, however suggestive and valuable it might be for that.
8. What these ideas might be are instructively discussed by John Carriero in “Leibniz on Inﬁnite
Resolution and Intra-mundane Contingency, Part One: Inﬁnite Resolution,” Studia Leibnitiana
(), pp. –.
Spirits as Active Substances: Their Freedom
§. The Complete Individual Concept Includes Active Powers
. Leibniz’s predicate-in-subject account of truth, which we took up last time
in sections –, with its distinction between necessary and contingent truths,
serves his purposes provided that it helps him to maintain two things:
(a) The world is freely created by God, who has attributes of reason,
moral perfection, and will, and who creates the world for the best of reasons, not arbitrarily or by logical necessity.
(b) This requires that the actual world must be the best of all possible
worlds, and that the created things that make up the world—the complete
substances—must be genuinely created things, having their own active
forces and tendencies that move them to act in accordance with their own
Now, Leibniz believes that to speak of God’s, or anyone’s, free choice,
there must exist alternatives: this is a necessary condition of freedom. Thus
he thinks of the best of all possible worlds, and other less favored worlds,
including ones with much evil, as possible and of God’s choice of the best
as contingent. But how are we to understand a possible world?
Following Robert Adams’s suggestion, perhaps the clearest explanation
is to form the basic concept of a possible world just as we form the complete
concept of an individual.1 Such a concept of an individual contains in itself
1. See R. M. Adams, “Leibniz’s Theory of Contingency,” in Hooker, Leibniz: Critical and Interpretative Essays, pp. f.
no contradiction: it has a consistent description. We get the basic concept
of a possible world by combining into a world a plurality of individuals, or
monads, and by supposing relations between the monads to be arranged
by preestablished harmony. Should this be done so that the world so conceived has a consistent description and contains no contradiction, then Leibniz says it is possible in itself. So long as we specify possible worlds without
bringing in God’s choice of the best, we avoid any complications arising
from the fact that God’s choice of the best possible world is in some way
necessary. It is at least morally necessary, that is, practically necessary as
required by moral reasons or by God’s moral perfections. But I avoid the
tangles of this question, which troubled Leibniz and which he seems never
to have resolved.2 I don’t know if he thought that the proposition that
God creates the best world is contingent, though he did think it morally
. To satisfy condition (b) above, Leibniz hopes his predicate-in-subject
view of truth enables him to regard complete individual substances as genuinely created things, and for this they must have active powers of their
own. This is essential for him in the case of spirits (minds with reason and
will), for it enables them to think, deliberate, and act on their own, and to
be spontaneously active, voluntarily moved, and able to follow the dictates
of their reason. The succession of thoughts, feelings, and actions that they
undergo must not be merely lifeless happenings—simply part of the divine
picture show—as Leibniz thinks is the case, in their different ways, with
Descartes and Spinoza.
To explain Leibniz’s criticisms of Descartes and Spinoza, let’s begin by
asking what a complete individual concept, where the substance in question
is a spirit, is a concept of. Suppose ﬁrst that we think of the complete individual concept of Caesar as a complete story of Caesar’s life. (Let’s restrict
ourselves to this for simplicity.) The story starts with Caesar’s birth at such
and such a time, his crossing the Rubicon, his assassination, and the rest.
To this we add the story of Caesar’s thoughts, feelings, desires, perceptions,
and so on. And much else: the story recounts a complete and full sequence
of events over the life of Caesar. Think of this life as the complete ﬁlm of
Caesar, as it were. Given this story, we suppose that when God creates
2. See ibid., pp. –.