236 THE SCIENCE OF LOGIC. 



proof ? Its legitimacy is self-evident. It is the immediate application of the 

 Principle of Identity l to the concepts of which our judgments are composed. 

 These concepts, each with its two aspects of meaning, intensive and extensive, 

 afford us different views of the same thing in the process of judgment, and 

 thus constitute that diversity within which alone we can discern identity (12). 

 What justifies the process of conversion is the consciousness that we are 

 looking throughout at the same reality under different manifestations. 



Appeals have been made to Euler s diagrams 2 to illustrate and justify 

 conversion and the other forms of immediate inference. 



Aristotle s attempt to prove, or rather, to illustrate indirectly, the process 

 of conversion, by showing the absurdity that would result from denying its 

 legitimacy succeeds rather in showing that the legitimacy of the process 

 cannot be proved without assuming it in the proof ; in other words, that the 

 validity of the process is too evident to need proof. 



He argues thus : No S is /&amp;gt;, therefore No P is S ; for if not, Some 

 individual P, say Q, is S ; and hence Q is doth S and P ; but this is inconsist 

 ent with the original proposition. 3 That is quite true ; but it assumes the 

 equivalence of the propositions &quot;5 is Q &quot; and &quot; Q is S&quot; which, after all, is 

 the point to be proved. 



&quot; Conversioper Actidens &quot; (of A). We cannot pass legitimately 

 from &quot;All S s are P&quot; to &quot;All P s are 5,&quot; because the former 

 proposition gives us information only about an indefinite some &quot; 

 of the P s, and, therefore, does not empower us to make any 

 assertion about all the P s but only about the indefinite &quot;some &quot;. 

 Our inference, therefore, must be about &quot; some P s &quot;. In other 

 words, from a universal affirmative (A) we can reach by conver 

 sion only a particular affirmative (I) &quot; Some P s are S s a 

 proposition which is not equivalent to the convertend, and from 

 which we cannot get back by conversion to the convertend : thus 

 showing that we have lost some of the meaning of the convertend 

 in our passage from this to the converse. 



Conversion of this kind in which we infer only a particular 

 from a universal, in which the quantity of the convertend is not 

 retained but depressed, in which there is a loss of import in the 

 passage from convertend to converse is called Partitive Conver 

 sion ; Conversion by Limitation (/cara yLte/ao?) ; or, again, Conversio 

 per accidens (Kara o-vppeftrjKos). 



It is called &quot;partitive&quot; or &quot; by limitation &quot; because we can 

 predicate 5 only of an indefinite portion of P. It is called 



1 Those who maintain that whatever of real inference there is in conversion is 

 syllogistic, or hypothetical, would hold that its legitimacy is embodied in the self- 

 evident axioms in which such reasonings may be formulated (cf. 151, 152). 



2 C/. KEYNES, op. cit., pp. 131, 157 sqq. :i ibid&amp;gt;, p. 130. 



