The reviewer has recourse for an example, to syllogisms in the second figure (though all are, by a mere verbal transformation, reducible to the first), and asks, where is the _petitio principii_ in this syllogism, "Every poet is a man of genius, A B is not a man of genius, therefore A B is not a poet." It is true that in a syllogism of this particular type, the _petitio principii_ is disguised. A B is not included in the terms, every poet. But the proposition, "every poet is a man of genius" (a very questionable proposition, by the way), cannot have been inductively proved, unless the negative branch of the enquiry has been attended to as well as the positive; unless it has been fully considered whether among persons who are not "men of genius," there are not some who ought to be termed poets, and unless this has been determined in the negative. Therefore, the case of A B has been decided by implication, as much as the case of Socrates in the first example. The proposition, Every poet is a man of genius, is confessedly æquipollent with "No one who is not a man of genius is a poet," and in this the _petitio principii_, as regards A B, is no longer implied, but express, as in an ordinary syllogism of the first figure.
Another critic has endeavoured to get rid of the _petitio principii_ in the syllogism by substituting for the common form of expression, the following form--All _known_ men were mortal, Socrates is a man, therefore Socrates is mortal. To this, however, there is the fatal objection, that the syllogism, thus transformed, does not prove the conclusion; it wants not the form only, but the substance of proof. It is not merely because a thing is true in all _known_ instances that it can be inferred to be true in any new instance: many things may be true of all known men which would not be true of all men; while, on the other hand, a thing may be superabundantly proved true of all men, without having been ascertained by actual experience to be true of all known men, or even of the hundredth part of them.
CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
§ 1. In our analysis of the syllogism it appeared that the minor premiss always affirms a resemblance between a new case, and some cases previously known; while the major premiss asserts something which, having been found true of those known cases, we consider ourselves warranted in holding true of any other case resembling the former in certain given particulars.