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 time: but the predicate never was quantified. The few who alluded to the possibility of such a thing found reasons for not adopting it over and above the great reason, that Aristotle did not adopt it. For Aristotle never ruled in physics or metaphysics _in the old time_ with near so much of absolute sway as he has ruled in logic _down to our own time_. The logicians knew that in the proposition "all men are animals" the "animal" is not _universal_, but _particular_ yet no one dared to say that _all_ men are _some_ animals, and to invent the phrase, "_some_ animals are _all_ men" until Hamilton leaped the ditch, and not only completed a system of enunciation, but applied it to syllogism. My own case is as peculiar as his: I have proposed to introduce mathematical _thought_ into logic to an extent which makes the old stagers cry: "St. Aristotle! what wild notions! Serve a _ne exeat regno_[710] on him!"