320 



Modality. 



[CHAR xm. 



was the branch commonly called Dialectic, in the old sense 

 of that term. Dialectic, according to Aristotle, seems to 

 have been a sort of sister art to Rhetoric. It was concerned 

 with syllogisms differing in no way from demonstrative syl 

 logisms, except that their premises were probable instead of 

 certain. Premises of this kind he termed topics, and the 

 syllogisms which dealt with them enthymemes. They were 

 said to start from signs and likelihoods rather than from 

 axioms 1 . 



25. The terms in which such reasonings are com 

 monly described sound very much like those applicable to 

 Probability, as we now understand it. When we hear of 

 likelihood, and of probable syllogisms, our first impression 

 might be that the inferences involved would be of a similar 

 character 2 . This, however, would be erroneous. In the 



1 &quot;The et/cos and o-rj/meiov them 

 selves are propositions ; the former 

 stating a general probability, the 

 latter a fact, which is known to be 

 an indication, more or less certain, 

 of the truth of some further state 

 ment, whether of a single fact, or 

 of a general belief. The former is a 

 general proposition, nearly, though 

 not quite, universal ; as, most men 

 who envy hate ; the latter is a 

 singular proposition, which however 

 is not regarded as a sign, except 

 relatively to some other proposition, 

 which it is supposed may be inferred 

 from it.&quot; (Hansel s Aldrich ; Appen 

 dix F, where an account will be 

 found of the Aristotelian enthy- 

 meme, and dialectic syllogism. Also, 

 of course, in Grote s Aristotle, Topics, 

 and elsewhere.) 



2 &quot; Nam in hoc etiam differt de- 



monstratio, seu demonstrativa argu- 

 mentatio. a probabili, quia in ilia, 

 tarn conclusio quam praemissae neces- 

 sariae sunt ; in probabili autem argu- 

 mentatione sicut conclusio ut proba- 

 bilis infertur ita prsemissae ut pro- 

 babiles afferuntur&quot; (Crackanthorpe, 

 Bk. v., Ch. 1) ; almost the words with 

 which De Morgan distinguishes be 

 tween logic and probability in a 

 passage already cited (see Ch. vi. 3). 

 Perhaps it was a development of 

 some such view as this that Leibnitz 

 looked forward to. &quot; J ai dit plus d une 

 fois qu il faudrait une nouvelle espece 

 de Logique, qui traiteroit des degre s 

 de Probability, puisqu Aristote dans 

 ses Topiques n a rien moins fait que 

 cela&quot; (Nouveaux essais, Lib. iv. ch. 

 xvi). It is possible, indeed, that he 

 may have had in his mind more what 

 we now understand by the mathema- 



