NATURE AND AXIOMS OF THE SYLLOGISM. 301 



This double axiom may be appropriately rendered as follows : 

 Whatever is predicated, whether affirmatively or negatively, of any 

 logical whole (or universal), may be predicated in like manner of 

 whatever is a logical part of that whole. 



153. ANALYSIS OF THE &quot; DICTUM &quot; : ALTERNATIVE AXIOMS. 

 It has been objected that the Aristotelean Dictum bases the 

 syllogism exclusively on the extension of the concepts compared, 

 whereas intension is the more important and more fundamental 

 feature of their meaning. This will depend on how we under 

 stand the Dictum ; and if it be rightly understood the objection 

 cannot be sustained. If we analyse the process of thought as 

 indicated in the Dictum, we shall find that it is the intension of 

 the major extreme (P) that is thought of throughout : both the 

 major premiss &quot; All (or No] M is P,&quot; and the conclusion &quot; 5 is 

 (or is not} P,&quot; are read predicatively (100), P being thought of as 

 an attribute or group of attributes. The minor premiss is, no 

 doubt, read in extension, i.e. according to the class-inclusion view 

 (104), for in it the minor extreme 5 is &quot;asserted to belong to&quot; 

 the class M. It is, therefore, the extension of the minor extreme 

 that is uppermost in the mind both in the minor premiss and in 

 the conclusion. There remains the middle term, M, to be ex 

 amined. It is predicate in the minor premiss of the typical 

 Aristotelean syllogism, and here, unquestionably, it is thought of 

 as a &quot; class,&quot; to the extension of which 5 is found &quot; to belong &quot;. 

 But which aspect of M is before the mind when M occurs as sub 

 ject of the major premiss ? This is a more important question. 

 There can be no doubt that Aristotle laid stress, perhaps undue 

 stress, upon the extensive aspect of the middle term in the major 

 premiss ; but neither can there be any doubt that, according to 

 his general logical teaching, the major premiss must be an 

 abstract or generic universal, and not merely a concrete or collective 

 universal, expressing the result of an actual enumeration of in 

 stances (92, a). It must be a principle or law, expressing some 

 kind of necessary relation (195, 198), between the attribute (or 

 group of attributes), P, and the attributes which make up the in 

 tension of M, which, therefore, constitute the nature of M in the 

 abstract, and, accordingly, of all the concrete individuals in which 

 the attributes M are realized. 1 



We have already seen that it is because such propositions are 

 &quot; necessary &quot; that they are &quot; universal &quot; (92) ; that the ground or 



1 Cf. JOSEPH, op. cit., pp. 224, n. and 284, 



