This passage is taken from the Britannica 1911 article on 'Syllogism', of which there is more here. This adds very little to what H.W.B. Joseph has to say on the subject. Indeed, it repeats his argument that if the universal judgment is a mere enumeration, then the syllogism does involve a petitio, otherwise it does not. Thus it is an interesting historical record of what clever people thought in 1911.
Edward Buckner. London, June 2007
The general criticism of the syllogism as a means of discovering truth is that it is a petitio principii, or begging of the question. This accusation is based to some extent on the Aristotelian " Dictum de omni et nullo " (Anal. Pri. a i. 24, b 26-30), generally stated as "That which is affirmed or denied of any whole may be affirmed or denied of anything contained within (or 'any part of') that whole." To take a concrete instance of a valid mood: all men are mortal, all Frenchmen are men, therefore all Frenchmen are mortal (the mood Barbara). It is argued that either there is here no real discovery (i.e. new truth) or the major premise is improperly used (begs the question) inasmuch as unless we knew that all Frenchmen are mortal we could not state that all men are mortal. The problem raised is a real one, and has been discussed by all logicians, from the time of Mill especially. In brief, the solution depends upon the view we take of the major premise, "all men are mortal." If that judgment is taken as a mere enumeration of particulars, i.e. in extension, as meaning that all men have been investigated and found to be mortal, clearly it could not be used to make the new discovery that a particular group of men are mortal; the syllogism so understood is a petitio principii. If, however, we take the true view of the major premise, namely, that it is not a mere summary of observed particulars but the enunciation of a necessary connexion between two concepts or universals, then the conclusion assumes a different character. The " whole " (omne) of the dictum, the major term, ceases to be taken in extension, and becomes intensive or connotative, and the inference consists in subsuming the minor under (bringing it into connexion with) the major. This is the true view of the scientific or inductive universal (as opposed to that of nominalism or pure empiricism). It remains true that in fact the conclusion is contained in the premises - this is essential to the validity of the syllogism - but the inference is a real one because it brings out and shows the necessity of a conclusion which was not before in our minds.
THE LOGIC MUSEUM Copyright (c) E.D.Buckner 2007.