CATEGORICAL JUDGMENTS AND PROPOSITIONS 227 



owing to our indefinite interpretation of &quot; some &quot; ; were we to inter 

 pret &quot;some&quot; as meaning &quot;some, not all &quot; we could lay down as 

 the law of subcontraries that they must be either true together 

 or false together. 



Subcontraries might, then, be also generally defined as propositions one 

 of which MUST be ttue and both of which MAY be true. 



115. OPPOSITION IN SINGULAR AND IN MODAL CATEGORI- 

 CALS: SUMMARY OF RESULTS. (a) Singular propositions \ixvz no 

 formal contraries, but only contradictories. &quot; Socrates is wise &quot; is 

 contradicted by the simple denial, &quot; Socrates is not wise &quot;. 

 This opposition of singulars is called secondary opposition. 



Of course, if we introduce a secondary quantification into a 

 singular (94) by such qualifications as &quot; always,&quot; &quot; in all respects,&quot; 

 etc., we can complete the square of opposition ; but the proposi 

 tion so treated ceases to be singular in the proper and strict sense 

 of the word. If such quantification is implicit in a statement 

 about a singular subject, it should be made explicit in order to 

 avoid fallacies in opposition. 



We may, of course, also find a material contrary for a singular 

 proposition, by means of a &quot; contrary&quot; predicate if we can find 

 such. A pair of such contraries would be &quot; Socrates is happy &quot; 

 and &quot; Socrates is miserable &quot;. 



(b] Modal categoricals yield, of course, all the inferences 

 of the ordinary square of opposition for assertoric propositions ; 

 the modal forms being respectively A, S must be P ; E, S cannot 

 be P ; \, S may be P ; O, 5 need not be P. We have dealt already 

 with the import of these forms (89, 90). 



(c) The following table summarizes all the inferences obtain 

 able by the Square of Opposition : 



(1) If A is true: I is true, E is false, O is false; 



(2) If A is false : O is true, E is doubtful, I is doubtful ; 



(3) If E is true : O is true, A is false, I is false ; 



(4) IfE is false : I is true, A is doubtful, O is doubtful ; 



(5) If I is true: E is false, A is doubtful^ O is doubtful ; 



(6) If\ is false: O is true, A is false, E is true; 



(7) If O is true : A is false, E is doubtful, I is doubtful ; 



(8) I/O is false: I is true, E is false, A is true. 



From this table it will be noticed that (a) positing a universal 

 is the same as sublating the contradictory particular, and yields the 



15* 



