Stony Brook University

claims are contingent. But a valid a priori demonstrative proof cannot rely on any
contingent premises, e.g., on any empirical matters of fact. Thus Leibniz’s version of the
ontological proof is not a priori. He may still want to say that “something exists” is a
primary and indemonstrable truth, since, as he has said about the cogito, it proves that
something exists, namely ‘I’, even so that I exists contingently. Thus, even so “something
exists” is indemonstrable in the weaker sense, Leibniz may want to give it presumptive
validity. That is, given the state of our knowledge (something exists!), it is reasonable to
assume that God exists. But as it stands, technically speaking Leibniz’s proof is not a
priori demonstrable. 67
There is one more related issue that I will mention only briefly. Leibniz also holds
that probability has been a neglected part of moral philosophy and reasoning. He alludes
to this in several places in the Nouveaux Essais, but most notably in the chapter called
“Of the degrees of our knowledge.” Here Leibniz mentions that demonstrations in
metaphysics and morals (la Morale) are actually more difficult than in mathematics,
because only in mathematics can experience vouch for each step of reasoning (NE 371).
But for metaphysics and morals there might yet be another method of sound reasoning.
Perhaps opinion, based on likelihood, also deserves the name of
knowledge; otherwise nearly all historical knowledge will collapse, and a
good deal more. But without arguing about names, I maintain that the
study of the degrees of probability would be very valuable and is still
lacking, and that this is a serious shortcoming in our treatises on logic. For
when one cannot absolutely settle a question one could still establish the
degree of likelihood on the evidence, and so one can judge rationally
which side is the most plausible. . . . Moralists who are lax about this have
gone wrong largely because they have had an inadequate and over-narrow
67 The issue could be pursued further, since Leibniz has what appears to be an a priori alternative to this
observation premise. In a paper titled Quod Ens Perfectissimum existit (1676 G.7.261-2), he claims that
God’s possibility lies in being the subject of all perfections, i.e., all compatible possibilities. The argument
runs, roughly. (1) A perfection is absolutely simple, positive, and without limit. (However, the meaning of
‘without limit’ cannot be ‘infinite’ or ‘endless’ but rather must be ‘maximum,’ i.e., a maximum totality of
all possible degrees. Otherwise, the perfections would not be absolute. I thank Professor Baum for pointing
this out.) (2) Anything that is such is compatible with anything else that is such (having no limitations or
negations, all perfections are compatible). (3) Therefore, it is possible that all perfections co-exist in the
same subject (and this subject is God). He explains the proof this way: Premise (2), ‘all perfections are
compatible’, would be false if ‘perfections A and B are incompatible’ were proven to be necessary. For this
premise to be necessary, it must be either proved or known through itself (per se notae). Proving it would
require that either or both A and B be analyzed. But by hypothesis, perfections are unanalysable (absolutely
simple), so the proposition cannot be proven. Nor is the premise known to be necessary through itself.
Therefore, the premise is not necessarily true. Therefore, since it is not necessary that A and B are
incompatible, it is possible that A and B are compatible. Therefore, “there is or can be understood to be the
subject of all perfections.” However, it should be pointed out that the move from the possibility of
compatibility to the possibility of a subject of all compatibilities is not warranted. For one, while all
perfections may be compatible, nothing in the premises gives us a subject of all perfections, nor that this
subject is God. But Leibniz depends on the ontological proof. Since the idea of God is possible, then, since
existence is a perfection, God exists: “From which it is obvious that he also exists, since existence is
included in the number of perfections.” He then says he showed this proof to “Mr. Spinoza” who agreed it
was valid. (For this analysis I depend on George McDonald Ross’ unpublished translation of Leibniz’s
Latin.)
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