CHAP. XV.] ARISTOTELIAN LOGIC. 231 



reasoning. This remark is equally applicable to the case of 

 Syllogism, which we proceed next to consider. 



5. The nature of syllogism is best seen in the particular in- 

 stance. Suppose that we have the propositions, 



All X's are F's, 

 All Y's are Z'a. 



From these we may deduce the conclusion, 

 All X'a are 



This is a syllogistic inference. The terms X and Z are called 

 the extremes, and Y is called the middle term. The function 

 of the syllogism generally may now be defined. Given two pro- 

 positions of the kind whose species are tabulated in (1), and in- 

 volving one middle or common term Y, which is connected in 

 one of the propositions with an extreme X, in the other with an 

 extreme Z\ required the relation connecting the extremes X and 

 Z. The term Y may appear in its affirmative form, as, All Y's, 

 Some Ps ; or in its negative form, as, All not- Y* s, Some not- 

 Y's ; in either proposition, without regard to the particular form 

 which it assumes in the other. 



Nothing is easier than in particular instances to resolve the 

 Syllogism by the method of this treatise. Its resolution is, in- 

 deed, a particular application of the process for the reduction of 

 systems of propositions. Taking the examples above given, 

 we have, 



whence by substitution, 



x = vv'z, 



which is interpreted into 



All X's area's. 



Or, proceeding rigorously in accordance with the method deve- 

 loped in (VIII. 7) 5 we deduce 



x (1 - y) = 0, y (1 - z) = 0. 



Adding these equations, and eliminating y> we have 



