OF ARTS AND SCIENCES : APRIL 9, 1867. 281 



combines the modifications of E and 7, just as the 2d-3d figure 

 combines the 2d and 3d. In the second-third figure, only can be 

 concluded, in the third only / and 0, in the second only E and 0, in 

 the fir^t either A E I 0. Thus A is the first figure of proposition, 

 E the second, I the third, the second-third.* 



§ 7. Mathematical Syllogisms. 



A kind of argument very common in mathematics may be exem- 

 plified as follows : — 



Every part is less than that of which it is a part, 

 Boston is a part of the Universe ; 

 . • . Boston is less than the Universe. 



This may be reduced to syllogistic form thus : — 



Any relation of part to whole is a relation of less to greater, 

 The relation of Boston to the Universe is a relation of part to whole ; 

 . • . The relation of Boston to the Universe is a relation of less to greater. 



e>* 



If logic is to take account of the peculiarities of such syllogisms, 

 it would be necessary to consider some propositions as having three 

 terms, subject, predicate, and object ; and such propositions would be 

 divided into active and passive. The varieties in them would be 

 endless. 



Part III. § 1. Induction and Hypothesis. 

 In the syllogism, 



Any M is P, 

 X S' is M; 



.-. tS is P; 



where J? S' denotes the sum of all the classes which come under M. 

 if the second premise and conclusion are known to be true, the first 



* Hypotheticals have not been considered above, the well-known opinion having 

 been adopted that, " If A, then B," means the same as " Every state of things in 

 which A is true is a state of things in which B is (or will be) true." 



vol. vii. 36 



