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A Budget of Paradoxes, Volume I by De Morgan

But in analyzing the syllogism


the publication of the above, it has been stated that the author is Mr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on: E. B. Revilo seems to be obviously a reversal.]


Old and new logic contrasted: being an attempt to elucidate, for ordinary comprehension, how Lord Bacon delivered the human mind from its 2,000 years' enslavement under Aristotle. By Justin Brenan.[706] London, 1839, 12mo.

Logic, though the other exact science, has not had the sort of assailants who have clustered about mathematics. There is a sect which disputes the utility of logic, but there are no special points, like the quadrature of the circle, which {331} excite dispute among those who admit other things. The old story about Aristotle having one logic to trammel us, and Bacon another to set us free,--always laughed at by those who really knew either Aristotle or Bacon,--now begins to be understood by a large section of the educated world. The author of this tract connects the old logic with the indecencies of the classical writers, and the new with moral purity: he appeals to women, who, "when they see plainly the demoralizing tendency of syllogistic logic, they will no doubt exert their powerful influence against it, and support the Baconian method." This is the only work against logic which I can introduce,

but it is a rare one, I mean in contents. I quote the author's idea of a syllogism:

"The basis of this system is the syllogism. This is a form of couching the substance of your argument or investigation into one short line or sentence--then corroborating or supporting it in another, and drawing your conclusion or proof in a third."

On this definition he gives an example, as follows: "Every sin deserves death," the substance of the "argument or investigation." Then comes, "Every 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.

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