OF ARTS AND SCIENCES : APRIL 9, 1867. 267 



§ 4. Of the First Figure. 



Since, in the general form, S may be any subject and P any predi- 

 cate, it is possible to modify Barbara by making the major premise and 

 conclusion negative, or by making the minor premise and conclusion 

 particular, or in both these ways at once. Thus we obtain all the 

 modes of the first figui'e. 



It is also possible to have such arguments as these : — 



Some M is P, 



S has all the common characters of that part of 31 (whatever 

 that part may be, and therefore of each and every M), 



.'. S is P, 

 and 



All not-Jf is P, 



S is not M, 



.: S is P; 



but as the theory of apagogical argument has not obliged us to take 

 account of these peculiar modifications of subject and predicate, these 

 arguments must be considered as belonging to Barbara. In this sense 

 the major premise must always be universal, and the minor affirmative. 

 Three propositions which are related to one another as though major 

 premise, minor premise, and conclusion of a syllogism of the first figure 

 will be termed respectively Hule, Case, and Result. 



§ 5. Second and Third Figures. 

 Let the first figure be written thus : — 



Fig. 1. 



Any IVI 



IS 



is not 



Some S '^ 



Any « is Q 



Some %]9 is not j^^ 



Then its two apagogical modifications are the second and third 

 figures. 



