NATURE AND AXIOMS OF THE SYLLOGISM. 293 



flvai : 1 a &quot; discourse in which certain things being posited, something else 

 than what is posited necessarily follows on their being true &quot;. But this de 

 finition is far too wide for the forms of reasoning described in the Prior 

 Analytics as forms of the syllogism ; it embraces, in fact, all forms of mediate 

 inference (191). 



The confusion of the syllogism, by many writers, with mediate reasoning 

 of whatsoever form (cf. chap, vii., infra), is no doubt partially due to this 

 initial ambiguity in the use of the term. 



Suppose we were to define mediate reasoning as the process in which 

 we compare two objective concepts, [called extremes^ S and P, with some 

 third concept, [called the &quot; mean &quot; or &quot; middle term &quot;] M, in order thus to 

 discover whether or how those two extremes are related to each other : we 

 should be giving some insight into the reason for our conclusion ; S and P 

 are related in a certain way to each other because each is related in a certain 

 way to M. This definition, too, has been given as a definition of the 

 syllogism. But, like the former, it is too wide ; nor does it give us %.full 

 insight into the grounds of the necessity by which conclusion follows from 

 premisses ; for each of the concepts compared in the syllogism has two sides 

 to its meaning, extension and intension ; each stands for things, and implies 

 attributes ; and the relation or comparison expressed in each of the premisses 

 is open to a variety of interpretations ; 2 from which it follows that an 

 adequate analysis of the ground on which the conclusion follows necessarily 

 from the premisses must take into account both the extension and the in 

 tension of the concepts compared : and this brings us to the real Aristotelean 

 conception of the syllogism. 



148. NATURE AND STRUCTURE OF THE SYLLOGISM: ITS 

 MATTER AND ITS FORM. The Syllogism may be properly de 

 fined as the expression of a reasoning process in which from two 

 judgments that contain a common concept, and one at least of which 

 is universal, a third judgment, distinct from either of the former, 

 necessarily follows. 



1 Anal. Pri. a. i. 24!}, 18 : cf. Top. a. i. looa, 25 apud, JOSEPH, op. cit., p. 

 225. The term truAA-o-yicr/z^s was probably borrowed by Aristotle from mathematics, 

 where it meant a computation, or adding or putting together. 



2 Cf. Part ii., chap. iv. Some writers restrict the term syllogism to inferences 

 from two simple or categorical propositions expressive of judgments in which the 

 concepts are compared with one another as subject and predicate or attribute. Thus, 

 Mr. Joseph defines the syllogism as &quot; an argument in which, irom the given relation 

 of two terms, in the way of subject and predicate, to the same third term, there 

 follows necessarily a relation, in the way of subject and predicate, between these two 

 terms themselves&quot; (op. cit., p. 225). So that inferences involving hypothetical, dis 

 junctive, or otherwise compound judgments, would not be deemed &quot; syllogistic&quot;. No 

 doubt, the strict Aristotelean syllogism is concerned only with subject-predicate 

 relations. But seeing that many of the other modes of relating concepts in thought 

 are reducible to the subject-predicate relation, and in view of the almost universal 

 nomenclature that recognizes pure and mixed hypothetical and disjunctive &quot; syl 

 logisms,&quot; we do not think it advisable to adopt such a restricted meaning of this 

 term (cf. 149). 



