RATIOCINATION, OR SYLLOGISM. 131 



great ingenuity and clearness of thought.* The argument, however, is one 

 and the same, in whichever figure it is expressed ; since, as we have ah-eady 

 seen, the premises of a syllogism in the second, third, or fourth figure, and 

 those of the syllogism in the first figure to which it may be reduced, are 

 the same premises in every thing except language, or, at 1-east, as much of 

 them as contributes to the proof of the conclusion is the same. We are 

 therefore at liberty, in conformity with the general opinion of logicians, to 

 consider the two elementary forms of the first figure as the universal types 

 of all correct ratiocination ; the one, when the conclusion to be proved is 

 affirmative, the other, when it is negative ; even though certain arguments 

 may have a tendency to clothe themselves in the forms of the second, third, 

 and fourth figures; which, however, can not possibly happen with the only 

 class of arguments which are of first-rate scientific importance, those in 

 which the conclusion is a universal affirmative, such conclusions being sus- 

 ceptible of proof in the first figure alone.f 



* His conclusions are, "The first figure is suited to the discovery or proof of the properties 

 of a thing ; the second to the discovery or proof of the distinctions between things ; the third 

 to the discovery or proof of instances and exceptions ; the fourth to the discovery, or exclu- 

 sion, of the different species of a genus." The reference of syllogisms in the last three figures 

 to the dictum de omni et nuUo is, in Lambert's opinion, strained and unnatural : to each of 

 the three belongs, according to him, a separate axiom, co-ordinate and of equal authority with 

 that dictum, and to which he gives the names of dictum de diverso for the second figure, 

 dictum de exemplo for the third, and dictum de reciproco for the fourth. See part i., or Dia- 

 noiologie, chap, iv., § 229 et seqq. Mr. Bailey {Theory of Reasoning, 2d ed., pp. 70-74) 

 takes a similar view of the subject. 



t Since this chapter was written, two treatises have appeared (or rather a treatise and a 

 fragment of a treatise), which aim at a further improvement in the theory of the forms of 

 ratiocination: Mr. De Morgan's "Formal Logic; or, the Calculus of Inference, Necessary 

 and Probable;" and the "New Analytic of Logical Forms," attached as an Appendix to Sir 

 William Hamilton's Discussions on Philosophy, and at greater length, to his posthumous Lec- 

 tures on Logic. 



In Mr. De Morgan's volume — abounding, in its more popular parts, with valuable observa- 

 tions felicitously expressed — the principal feature of originality is an attempt to bring within 

 strict technical rules the eases in which a conclusion can be drawn from premises of a form 

 usually classed as particular. Mr. De Morgan observes, very justly', that from the premises 

 most Bs are Cs, most Bs are As, it may be concluded with ceitainty that some As are Cs, 

 since two portions of the class B, each of them comprising more than half, must necessarily 

 in part consist of the same individuals. Following out this line of thought, it is equally evi- 

 dent that if we knew exactly what propoi'tion the "most" in each of the premises bear to the 

 entire class B, we could increase in a corresponding degree the definiteness of the conclusion. 

 Thus if GO per cent, of B are included in C, and 70 per cent, in A, 30 per cent, at least must 

 )e common to both ; in other words, the number of As which are Cs, and of Cs which are 

 .\s, must be at least equal to 30 per cent, of the class B. Proceeding on this conception of 

 'numerically definite propositions," and extending it to such forms as these: — "45 Xs (or 

 nore) are each of them one of 70 Ys," or "45 Xs (or more) are no one of them to be found 

 imong 70 Ys," and examining what inferences admit of being drawn from the various com- 

 linations which may be made of premises of this description, Mr. De Morgan establishes uni- 

 ersal formulae for such inferences ; creating for that purpose not only a new technical lan- 

 , :uage, but a formidable array of symbols analogous to those of algebra. 



Since it is undeniable that inferences, in the cases examined by Mr. De Morgan, can legiti- 

 : lately be drawn, and that the ordinary theory takes no account of them, I will not say that 

 i ; was not worth while to show in detail how these also could be reduced to formula} as rigor- 

 I us as those of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps 

 1 lore than once, as a school exercise) ; but I question if its results are worth studying and 

 1 lastering for any practical purpose. The practical use of technical forms of reasoning is to 

 1 ar out fallacies ; but the fallacies which require to be guarded against in ratiocination properly 

 i ) called, arise from the incautious use of the common forms of language ; and the logician 

 I lUst track the fallacy into that territory, instead of waiting for it on a territory of his own. 

 "^ iT'hile he remains among propositions which have acquired the numerical precision of the 

 ( alculus of Probabilities, the enemy is left in possession of the only ground on which he can 

 I ; formidable. And since the propositions (short of universal) on which a thinker has to de- 



