234 THE SCIENCE OF LOGIC. 



But the rule of quantity brings us face to face with the fact 

 that, in the process of conversion, by making the predicate of 

 the convertend the subject of the converse, we must turn from the 

 connotation of this term to its denotation ; from regarding it as 

 the name of an attribute (or group of attributes), we must pass to 

 regarding it as the name of a class of objects ; from the predicative 

 or attributive reading of the proposition, we must pass to its exten 

 sive or class-inclusion reading. It is this change of standpoint in 

 reference to the predicate that involves a distinct movement of 

 thought, and makes the conversion of the traditional predicative 

 judgments, A, E, and I, rank as a real process of interpretative in 

 ference. 



In the equational scheme of propositions (109), conversion is, of course, 

 not an inference at all. But the process analogous to the contraposition of 

 the predicative proposition the process by which we pass from 5=S/ ) to 

 P PS is inference. 



In the existential schedule, SaP is represented by SP = O. Here the 

 conversion of SaP to PiS is represented by the passage from &quot; SlF=O,&quot; to 

 &quot;Either SP&amp;gt;O or S = O&quot;; and this is a process of inference. But the 

 contraposition of SaP (to PaS] which is a process of inference is repre 

 sented by the passage from &quot; 5/ r = O &quot; to &quot; PS = O,&quot; which process is only 

 a verbal change : &quot; Conversion, but not contraposition, now appears as a 

 process of inference. It follows that there is inference when we pass to this 

 schedule from either of the others, or vice versa.&quot; a 



We have seen that obversion gives us what are really equivalent or 

 equipollent prepositional forms, rather than any new judgments deserving of 

 the name of inferences. Some logicians contend that this is equally true of 

 conversion ; ~ and, consequently, of contraposition and inversion : which are 

 nothing more than repeated applications of the two former processes. 



Mr. Joseph s treatment of conversion u is instructive and deserving of 

 notice. He contends that the conversion of A to I, if both propositions be 

 understood as concrete or historical propositions, referring to actual in 

 dividuals or groups of individuals (92, 93), or if both be understood as 

 scientific or modal propositions, is not inference : inasmuch as we recognized 

 and intended from the outset in the A proposition what is stated in the con 

 verse. That we intended in A what is stated in the converse, I, might per 

 haps be denied, if we draw a clear distinction between import and implication. 



He admits that there is inference if one of the two propositions be under 

 stood as historical and the other as scientific, but denies that the inference is 

 immediate : &quot; Suppose the proposition * All X is Y to be understood histori 

 cally, and the converse * Some Y is X scientifically ; then there is inference. 

 If in fact all the ruminants do part the hoof, then generally rumination is 



1 KEYNES, op. cit., p. 423. 9 C/. J. S. MILL, Logic, ii., i. 2. 



3 op. cit., pp. 218 sqq. 



