474 A N T I E N T METAPHYSICS. Book V. 



ftrativc reafoning, and, indeed, all reafoning ot every kind, is redu- 

 cible, depends upon this propofition, That, it one idea contains, or 

 does not contain, the whole of another ; and, if that other does con- 

 tain, or does not, tiie whole of a third, then does the firft contain, or 

 not contain, the whole of the third ; or, in other words, if one of 

 the ideas is a part, or not a part of another, and, if a third idea is a 

 part, or not a part of that idea which is a part of the firfi:, then will 

 the third idea be a part, o ■ no part, of the firfl. But, as thofe things 

 are not cafiiy exprefled by words, I will do, as Ariftotle has done in 

 his logical works, I will ufe letters, as general characters, to exprefs 

 them. The propofition, then, exprelTed ni that manner, is this, That, 

 if A contains the whole of B, and B contains the whole of C, then A. 

 contains the whole of C : Vr, if A does not contain B, nor any part of 

 it, or, what is the fame thing, excludes B, and, it B contains the whole 

 of C ; then does A exclude C, and €very part of it And, to make the 

 matter ftill clearer, I will do, as Ari^otle's commentators do, and 

 fometimes himfelf, apply thefe general characters to a particular ex- 

 ample ; as thus, if the general idea oifubjlance contain the whole idea 

 of an'imaU and if animal contain the whole idea of man^ then will Juh- 

 fiance contain the whole idea of man. Or, to put it in the ordinary 

 fyllogiflical form, Every animal is a fubftance ; Every man is an ani- 

 mal : Therefore every man is a fubltance. And this is afyllogifm of 

 which the conclufion is affirmative. And, as for the negative conclu- 

 fion, take this for an exam.ple : The idea of a flone does not contain, 

 or, what is the fame thing, excludes the whole idea of animaL T he 

 idea of animal contains, or includes the whole idea of man ; there- 

 fore the idea of Jlone excludes the whole idea of man ; which, in the 

 fyllogillical form, runs thus : No {tone is an animal ; Every man 

 is an animal \ Therefore no man is a ftone. 



In 



