his letters to Arnauld, which contain a part of his more profound philosophy, were published in
the nineteenth century; but I was the first to notice their importance. Arnauld's reception of these
letters was discouraging. He writes: "I find in these thoughts so many things which alarm me, and
which almost all men, if I am not mistaken, will find so shocking, that I do not see of what use a
writing can be, which apparently all the world will reject." This hostile opinion no doubt led
Leibniz, thenceforth, to adopt a policy of secrecy as to his real thoughts on philosophical subjects.
The conception of substance, which is fundamental in the philosophies of Descartes, Spinoza, and
Leibniz, is derived from the logical category of subject and predicate. Some words can be either
subjects or predicates; e.g., I can say "the sky is blue" and "blue is a colour." Other words--of
which proper names are the most obvious instances --can never occur as predicates, but only as
subjects, or as one of the terms of a relation. Such words are held to designate substances.
Substances, in addition to this logical characteristic, persist through time, unless destroyed by
God's omnipotence (which, one gathers, never happens). Every true proposition is either general,
like "all men are mortal," in which case it states that one predicate implies another, or particular,
like "Socrates is mortal," in which case the predicate is contained in the subject, and the quality
denoted by the predicate is part of the notion of the substance denoted by the subject. Whatever
happens to Socrates can be asserted in a sentence in which "Socrates" is the subject and the words
describing the happening in question are the predicate. All these predicates put together make up
the "notion" of Socrates. All belong to him necessarily, in this sense, that a substance of which
they could not be truly asserted would not be Socrates, but some one else.
Leibniz was a firm believer in the importance of logic, not only in its own sphere, but as the basis
of metaphysics. He did work on mathematical logic which would have been enormously important
if he had published it; he would, in that case, have been the founder of mathematical logic, which
would have become known a century and a half sooner than it did in fact. He abstained from
publishing, because he kept on finding evidence that Aristotle's doctrine of the syllogism was
wrong on some points; respect for Aristotle made it impossible for him to believe this, so he
mistakenly supposed that the errors must