CHAP. XV.] ARISTOTELIAN LOGIC. 229 



propriate, but the former term is already employed in a fixed 

 sense in other parts of this work. 



4. From the symbolical forms above given the laws of con- 

 version immediately follow. Thus from the equation 



representing the proposition, " All Y'a are X'a," we deduce, on 

 eliminating v t 



which gives by solution with reference to 1 - a, 



i-*-5<i-y); :' ..,;!' 



the interpretation of which is, 



All not-X's are not- Y'a. 



This is an example of what is called " negative conversion." 

 In like manner, the equation 



y = v (I - x), 

 representing the proposition, " No Y'a are X's," gives 



the interpretation of which is, "NoX's are Y'a." This is an 

 example of what is termed simple conversion ; though it is in re- 

 ality of the same kind as the conversion exhibited in the previous 

 example. All the examples of conversion which have been noticed 

 by logicians are either of the above kind, or of that which con- 

 sists in the mere transposition of the terms of a proposition, with- 

 out altering their quality, as when we change 



vy = vx, representing, Some Y'a are X's 9 

 into 



vx = vy, representing, Some X 'a are Y'a ; 



or they involve a combination of those processes with some auxi- 

 liary process of limitation, as when from the equation 



y = vx, representing, All Y*s are X'a, 

 we deduce on multiplication by v 9 



vy = vx, representing, Some Y*s are X's, 

 and hence 



vx - vy, representing, Some X's are Y'a. 



