SECT. 6.] Modality. 301 



different general views of logic from which these two accounts 

 of modality spring 1 . 



6. There is one kind of modal syllogism which it 

 would seem unreasonable to reject on the ground of its not 

 being formal, and which we may notice in passing. The 

 premise Any A is probably B, is equivalent to Most A are 

 B! Now it is obvious that from two such premises as Most 

 A are B t Most A are C, we can deduce the consequence, 

 Some C are B! Since this holds good whatever may be 

 the nature of A, B, and C, it is, according to ordinary usage 

 of the term, a formal syllogism. Mansel, however, refuses to 

 admit that any such syllogisms belong to formal logic. His 

 reasons are given in a rather elaborate review 2 and criticism 

 of some of the logical works of De Morgan, to whom the 

 introduction of numerically definite syllogisms is mainly 

 due. Mansel does not take the particular example given 

 above, as he is discussing a somewhat more comprehensive 

 algebraic form. He examines it in a special numerical 

 example 3 : 18 out of 21 Fs are X; 15 out of 21 Fs are Z; 

 the conclusion that 12 Zs are X is rejected from formal logic 

 on the ground that the arithmetical judgment involved is 

 synthetical, not analytical, and rests upon an intuition of 

 quantity. We cannot enter upon any examination of these 



1 He has also given a short 2 Letters, Lectures and Reviews, 



discussion of the subject elsewhere p. 61. Elsewhere in the review (p. 



(Discussions, Ed. n. p. 702), in which 45) he gives what appears to me a 



a somewhat different view is taken. somewhat different decision. 



The modes are indeed here admitted 3 It must be remembered that 



into logic, but only in so far as they this is not one of the proportional 



fall by subdivision under the relation propositions with which we have 



of genus and species, which is of been concerned in previous chapters : 



course tantamount to their entire it is meant that there are exactly 21 



rejection ; for they then differ in no Fs, of which just 18 are X, not that 



essential way from any other exam- on the average 18 out of 21 may be 



pies of that relation. so regarded. 



