CA TEGORICAL JUDGMENTS AND PROPOSITIONS. 2 2 1 



alternate : from the Latin terms subalternans and subalternata, 

 respectively. An inference from universal to particular (of same 

 quality) is called a condusio ad subalternatam ; an inference 

 from particular to universal (of same quality) is called a condusio 

 ad subalternantem ; furthermore, to suppose a proposition true is 

 to &quot; posit &quot; it, to suppose it false is to &quot; sublate &quot; it. Given either 

 a universal, or the particular of the same quality, as true, or as 

 false, what can we infer about the truth or falsity of the other ? 

 The answer is given in the following two laws : 



1 I ) The truth of the particular follows from the truth of the 

 universal * of like quality, but not vice versa. 



(2) The falsity of the universal follows from the falsity of the 

 particular of like quality, but not vice versa. 



These rules are immediate applications of the Principle of 

 Identity (12). Thus, in regard to rule (i), if we assert that &quot;all 

 men are mortal&quot; we may assert that &quot;some men are mortal,&quot; 

 or if we assert that &quot; no men are angels&quot; we may assert that 

 &quot; some 2 men are not angels &quot; ; but if we assert that &quot; some men 

 are fools &quot; we have no right to infer that &quot; all men are fools&quot; nor 

 if we assert that &quot; some men are not learned&quot; have we a right to 

 assert that &quot; no men are learned&quot; . 



Similarly, in regard to rule (2), by denying the truth of &quot;all 

 men are fools &quot; we merely deny that folly can be predicated of all 

 men, and cannot thence deny that &quot;some men are fools&quot; ; and 

 by denying the truth of &quot; no men are wise &quot; we merely deny that 

 wisdom can be excluded from all, and do not deny that it may 

 be excluded from some, or that the proposition &quot; some men are 

 not wise &quot; is true. But if we deny the truth of &quot; some men are 

 wise &quot; we a fortiori deny the truth of &quot; all men are wise&quot; just as 

 by denying the truth of &quot;some men are not mortal&quot; we a fortiori 

 deny the truth of the assertion that &quot; no men are mortal &quot;. 



Whenever we meet two propositions, however they be formulated, so 

 related to each other that one of them may be formally inferred from the 

 other but not vice versa, we may extend our present meaning of the term 

 sub alternation to such propositions, always describing such a relation as 

 subalternation. 



112. CONTRADICTORY OPPOSITION may be defined as that 



1 This and other statements in the present chapter may have to be modified 

 by what will be said below (chap, viii.) on the existential import of propositions. 



2 It must be borne in mind that &quot; some &quot; does not mean &quot; some only,&quot; but 

 &quot; some, possibly all &quot;. 



