every X there is a Y which is
Z; therefore, some Zs are not Xs.

Sir William Hamilton of Edinburgh was one of the best friends and allies I
ever had. When I first began to publish speculation on this subject, he
introduced me to the logical world as having plagiarized from him. This
drew their attention: a mathematician might have written about logic under
forms which had something of mathematical look long enough before the
Aristotelians would have troubled themselves with him: as was done by John
Bernoulli,[711] {336} James Bernoulli,[712] Lambert,[713] and
Gergonne;[714] who, when our discussion began, were not known even to
omnilegent Hamilton. He retracted his accusation of _wilful_ theft in a
manly way when he found it untenable; but on this point he wavered a
little, and was convinced to the last that I had taken his principle
unconsciously. He thought I had done the same with Ploucquet[715] and
Lambert. It was his pet notion that I did not understand the commonest
principles of logic, that I did not always know the difference between the
middle term of a syllogism and its conclusion. It went against his grain to
imagine that a mathematician could be a logician. So long as he took me to
be riding my own hobby, he laughed consumedly: but when he thought he could
make out that I was mounted behind Ploucquet or Lambert, the current ran
thus: "It would indeed have been little short of a miracle had he, ignorant
even of the common principles of logic, been able of himself to rise to
generalization so lofty and so accurate as are supposed in the peculiar
doctrines of both the rival logicians, Lambert and Ploucquet--how useless
soever these may in practice prove to be." All this has been sufficiently
discussed elsewhere: "but, masters, remember that I am an ass."

I know that I never saw Lambert's work until after all Hamilton supposed me
to have taken was written: he himself, who read almost everything, knew
nothing about it until after I did. I cannot prove what I say about my
knowledge of Lambert: but the means of doing it may turn up. For, by the
casual turning up of an old letter, I _have_ {337} found the means of
clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I
took from Ploucquet the notion of a logical notation in which the symbol of
the conclusion is seen in the joint symbols of the premises. For example,
in my own fashion I write down ( . ) ( . ), two symbols of premises. By
these symbo