3io THE SCIENCE OF LOGIC 



&quot;speakers of Spanish,&quot; is distributed in the conclusion, being the 

 predicate of a negative proposition, whereas it was undistributed in 

 the major premiss, being there predicate of an affirmative pro 

 position. If we could, convert the major premiss simply (to &quot; All 

 who speak Spanish are Spaniards &quot;) the conclusion would be 

 valid ; but we cannot do so, for an A proposition cannot be con 

 verted simply. 



It will be noted that the fallacy of illicit minor can occur 

 only when the conclusion is universal (and S undistributed in the 

 minor premiss) ; and that the fallacy of illicit major can take place 

 only when the conclusion is negative : for P, being always the 

 predicate of the latter, is not distributed unless when the latter 

 is negative. The fallacy then arises if P was not distributed 

 in its premiss (the major premiss) as well. 



C (5). The first rule of quality appears to be very simple. 

 From two negative premisses of a syllogism nothing can follow. 

 If 5 is not M, and ifP is not M, we evidently cannot know whether 

 5 and P are identical x or not. They may be, or they may not 

 be, identical. Neither of the extremes is connected with the 

 middle term : there is, therefore, really no common bond or link 

 between the extremes. They may indeed agree de facto, wholly, 

 partially, or not at all, with each other : but nothing of this can 

 we know from the fact that neither of them is identical with a 

 certain third thing. 



A Reference to Euler s circles (104) will illustrate this. If we simply draw 

 a circle representing the class M alongside (and outside) each of the five 

 combinations of 5 and P, every single trio so formed will illustrate the two 

 premisses &quot; No S is M ; no P is M&quot; : thus showing that every possible rela 

 tion between S and P is compatible with those premisses, and that therefore 

 no conclusion whatsoever about S and P can be drawn from them. If, instead 

 of two E premisses, we have E and O, or two O premisses, we may see, by 

 drawing the M circle so as to intersect either or both of the circles S and P, 

 that, while we make the number of alternative pairs of premisses still greater, 

 all the five possible relations of 5 and P are still compatible with every pair 

 of premisses so formed. Besides which we must remember that an O proposi 

 tion never excludes the possibility of E ; and that therefore the conclusion 

 from E and O, or from two O premisses, cannot possibly be any more de 

 finite than from two E premisses. 2 



1 The terms, &quot;identity,&quot; &quot;agreement,&quot; &quot;disagreement,&quot; etc., do not express 

 exactly the affirmative or negative relation of predicate to subject in a categorical 

 proposition. (C/. JOSEPH, op. cit., pp. 248, n., 257, n.) The relation is sui generis, 

 and the terms used are the best to be found. 



*WELTON, op. cit., pp. 294-5. 



