CATEGORICAL JUDGMENTS AND PROPOSITIONS 245 



triangles &quot; ? The answer is that unless we assume this latter as given with 

 the original proposition our inference should be stated hypothetically, 

 &quot;Some non-triangles, // there be any such things, are,&quot; etc. ; and, further 

 more, that unless we assume as also given that there are things that are not 

 P, inversion is not a valid process. 1 It is from the original proposition under 

 stood as accompanied by this assumption, that the inverse is derived ; this 

 tacitly assumed proposition, &quot; Some things are not P&quot; with P distributed, 

 justifies the distributed P in the inverse. The validity of the inversion of A 

 is therefore contingent on the existence of 5 and P in the universe of dis 

 course. It will be found, similarly, that the validity of the inversion of E is de 

 pendent on the existence of S and P; that of its conversion on the existence 

 of/*/ that of the contraposition of A on the existence of/ 3 . 



Thus we see that the inferences we have reached in the present chapter 

 are based on the assumption that 6&quot;, P, S and P represent classes actually 

 existing in the universe referred to by the original propositional form, S P. 

 How these results will be modified by other assumptions we shall see in 

 Chap. VII. 



121. SUMMARY OF RESULTS: TABLE OF EDUCTIONS. It 

 will be noticed from the subjoined table that universal proposi 

 tions yield seven eductions each, and particulars three each ; that 

 we can infer from the former in terms of S, S, P and P, from the 

 latter in terms of 5 and of either P or P ; that the converses of 

 A and 1 are the same, and the contrapositives of E and O the 

 same. 



122. MATERIAL EDUCTIONS. The inferences we have been 

 discussing so far depend largely on the formal elements the 

 quantity and quality of the proposition, and have, therefore, 



1 For example, the inverse of the proposition &quot; All future free acts are foreseen 

 by the Deity &quot; would be &quot; Some things that are not future free acts are not foreseen 

 by the Deity &quot;. But this is valid only on an implied assumption which is false, viz. 

 that God does not foresee all things. 



