NATURE AND CHARACTERISTICS OF INFERENCE 387 



figures of the categorical syllogism. The question is not whether 

 these relations, expressed in the individual propositions, can or 

 cannot be reduced to the subject-attribute relation, and be inter 

 preted accordingly. Theoretically at least, all relations expressed 

 in a judgment may be so reduced : ordinary logic assumes the 

 possibility of such reduction (82, 99, 118). But the question 

 rather is this, whether there are combinations of those other 

 relations, which, as they stand, yield mediate inferences, while if 

 they were reduced to the subject-attribute relation they would 

 yield no conclusion according to the nature and laws of the 

 syllogism. Take, for instance, this simple example, which is 

 typical of a very wide class of mathematical inferences : 

 (I) A is greater than B ; 

 B is greater than C ; 

 . . A is greater than C. 



This is certainly a mediate inference : it is certainly valid : its 

 constituent propositions can certainly be reduced to the &quot; subject- 

 attribute &quot; form (&quot; A is a subject endowed with the attribute 

 of being greater than B &quot; : &quot;A ( is greater than B &quot; ; etc.) ; and, 

 nevertheless, when its propositions are read in this way as they 

 must be in order to get a connexion of two objects of thought 

 by the logica copula, &quot; is&quot; the given argument is just as certainly 

 not a syllogism. For it has four terms, viz. (i) &quot;A,&quot; (2) &quot;greater 

 than B; (3) &quot; B&quot; (4) &quot;greater than C&quot;. 



The truth is that when the mind goes through this simple 

 inference it has three objects of thought before it, viz. A, B, and 

 C ; that in the three constituent judgments it relates these terms 

 (in pairs), not by the logical copula &quot; is&quot; which would express 

 subject-attribute identity, but by a copula which expresses a 

 directly and intuitively apprehended relation of magnitude between 

 the terms of each pair by the copula &quot; is greater than &quot;. And 

 the mediate axiom on which the inference is based is this self- 

 evident mathematical axiom : A magnitude which is greater than 

 another is greater than all magnitudes than which this latter is 

 itself greater. 1 This mediate axiom underlies the argument in 

 question in precisely the same manner as the Dictum de omni 

 underlies the syllogism : 



(II) Man is mortal ; 



Socrates is a man ; 

 .*. Socrates is mortal. 



l Cf. KEYNES, op. cit., p. 385. 

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