ry unlawful wish is a sin," which "corroborates or supports" the
preceding: and, lastly, "therefore every unlawful wish deserves death,"
which is the "conclusion or proof." We learn, also, that "sometimes the
first is called the premises (_sic_), and sometimes the first premiss"; as
also that "the first is sometimes called the proposition, or subject, or
affirmative, and the next the predicate, and sometimes the middle term." To
which is added, with a mark of exclamation at the end, "but in analyzing
the syllogism, there is a middle term, and a predicate too, in each of the
lines!" It is clear that Aristotle never enslaved this mind.

I have said that logic has no paradoxers, but I was speaking of old time.
This science has slept until our own day: Hamilton[707] says there has been
"no progress made in {332} the _general_ development of the syllogism since
the time of Aristotle; and in regard to the few _partial_ improvements, the
professed historians seem altogether ignorant." But in our time, the
paradoxer, the opponent of common opinion, has appeared in this field. I do
not refer to Prof. Boole,[708] who is not a _paradoxer_, but a
_discoverer_: his system could neither oppose nor support common opinion,
for its grounds were not in the conception of any one. I speak especially
of two others, who fought like cat and dog: one was dogmatical, the other
categorical. The first was Hamilton himself--Sir William Hamilton of
Edinburgh, the metaphysician, not Sir William _Rowan_ Hamilton[709] of
Dublin, the mathematician, a combination of peculiar genius with
unprecedented learning, erudite in all he could want except mathematics,
for which he had no turn, and in which he had not even a schoolboy's
knowledge, thanks to the Oxford of his younger day. The other was the
author of this work, so fully described in Hamilton's writings that there
is no occasion to describe him here. I shall try to say a few words in
common language about the paradoxers.

Hamilton's great paradox was the _quantification of the predicate_; a
fearful phrase, easily explained. We all know that when we say "Men are
animals," a form wholly unquantified in phrase, we speak of _all_ men, but
not of all animals: it is _some or all_, some may be all for aught the
proposition says. This some-may-be-all-for-aught-we-say, or _not-none,_ is
the logician's _some_. One would suppose {333} that "all men are some
animals," would have been the logical phrase in all tim