A syllogism is constructed upon the principle (known as the Dictum of Aristotle) that whatever is affirmed or denied universally of a whole class of things, may be affirmed or denied of anything comprehended in that class. Thus the first proposition introduces the class of persons who have their heads cut off. Of this class it is affirmed that they ought to be allowed to ask the reason why. But women are included in the class of persons who have their heads cut off, and consequently that may be affirmed of them which is affirmed of the whole class--that they should be allowed to ask the reason why. 'To prove an affirmative,' says Mr. Mill, 'the argument must admit of being stated in this form:-- All animals are mortal; All men | Some men } are animals; Socrates | therefore All men | Some men } are mortal. Socrates | 'To prove a negative, the argument must be capable of being expressed in this form:-- 'No one who is capable of self-control is necessarily vicious; All negroes | Some negroes } are capable of self-control; Mr. A.'s negro | therefore No negroes are | Some negroes are not } necessarily vicious. Mr. A.'s negro is not | 'Although all ratiocination admits of being thrown into one or the other of these forms, and sometimes gains considerably by the transformation, both in clearness and in the obviousness of its consequence; there are, no doubt, cases in which the argument falls more naturally into one of the other three figures, and in which its conclusiveness is more apparent at the first glance in those figures, than when reduced into the first. Thus, if the proposition were that pagans may be virtuous, and the evidence to prove it were the example of Aristides; a syllogism in the third figure, Aristides was virtuous, Aristides was a pagan, therefore Some pagan was virtuous, Would be a more natural mode of stating the argument, and would carry conviction more instantly home, than the same ratiocination strained into the first figure, thus-- Aristides was virtuous, Some pagan was Aristides, therefore Some pagan was virtuous.' The best thing that can be said in favour of the syllogism, as an instrument of reasoning, is that it is a regular form to which every valid argument can be reduced; and may be accompanied by a rule, showing the validity of every argument in that form, and consequently the unsoundness of any apparent argument which cannot be reduced to it. This would be high praise if every 'valid argument' was a trusty one. But unfortunately 'the question respecting the validity of an argument is not whether the conclusion be _true_, but whether it _follows_ from the premises adduced.'* Even this small advantage is purchased at a greater expense of tedium and trouble than the bulk of mankind are willing to pay, or able to pay if they were willing. * Logic, vol. 1, pp. 232-3.