CA TEGORICAL JUDGMENTS AND PROPOSITIONS 243 



laws from analysis of particular facts, the contrapositive of the universal pro 

 position is of importance. For, in order to establish the truth of the ideally 

 scientific or reciprocal universal (92, 138), we must know that P is an in 

 separable natural property of S alone^ so that not merely all the S s are P s 

 (S a P\ but that furthermore all the things possessing the property (or pro 

 perties), P, are S s (P a S}. Hence, after having satisfied ourselves by 

 positive observations and experiments that &quot;All S^s are P&quot; (S a P), we 

 may aim at proving that &quot; All P s are S&quot; (Pa S). Now this latter is most 

 easily proved by proving its contrapositive, namely, that No non-S s are P, 

 or, None but S s are P (S e P\ This is done by instituting a series of obser 

 vations and experiments on negative instances, to show that wherever 5 

 is absent P is absent (cf. 221-2 ; 229-30). 



1 20. INVERSION is that process of immediate inference by which 

 from a given proposition we infer another having for its subject 

 the contradictory of the original subject. 



The original proposition is called the Invertend, the inferred 

 proposition the Inverse. 



Here, as in contraposition, we may arrive at two forms, one 

 the obverse of the other : the one with P for predicate we will 

 call the partial inverse ; the one with P for predicate the full 

 inverse. 



Here, too, as in contraposition, the forms we seek can be 

 reached only by a repeated, combined application of obversion 

 and conversion. For, since the only way to get the contradictory 

 of a term in a proposition is to make it predicate and then obvert 

 the proposition, it is plain that, starting with 5 as subject, we must 

 make it predicate by conversion, then make it 5 by obversion, 

 and finally transfer this latter to the position of subject by another 

 conversion. 



Let us take the four traditional propositions in turn and see 

 what results we shall reach, first by commencing (a) with con 

 version, then by commencing (b] with obversion, and applying 

 each alternately. The ineffectual attempts to reach an inverse 

 will be enclosed in brackets. 



(1) Inversion of A, [(a) S a P converts to P i S which ob- 

 verts to P o S which cannot be converted^ (b]S a P obverts to 

 S e P, which converts to P e S, which obverts to P a S which 

 converts to S i P, which obverts to S o P : thus giving the two 

 desired inverses, S i P and S o P. 



(2) Inversion of E. (a] S e P converts to P e S, which 

 obverts to P a 5, which converts to 5 / P, which obverts to S o~P 



16* 



