230 ARISTOTELIAN LOGIC. [CHAP. XV. 



In this example, the process of limitation precedes that of 

 transposition. 



From these instances it is seen that conversion is a particu- 

 lar application of a much more general process in Logic, of which 

 many examples have been given in this work. That process has 

 for its object the determination of any element in any proposition, 

 however complex, as a logical function of the remaining elements. 

 Instead of confining our attention to the subject and predicate, 

 regarded as simple terms, we can take any element or any 

 combination of elements entering into either of them ; make that 

 element, or that combination, the " subject" of a new proposition ; 

 and determine what its predicate shall be, in accordance with the 

 data afforded to us. It may be remarked, that even the simple 

 forms of propositions enumerated above afford some ground for 

 the application of such a method, beyond what the received laws 

 of conversion appear to recognise. Thus the equation 



2/= vx, representing, All Y's are X's, 



gives us, in addition to the proposition before deduced, the three 

 following : 



1st. y (1 - a?) = 0. There are no Y's that are not-X's. 



2nd. 1 -y= -x + (l-x). Things that are not- Y's include all 



things that are not-X's, and an 

 indefinite remainder of things 

 that are X's. 



3rd. x = y + - (I - y). Things that are X'a include all things 



that are F's, and an indefinite 

 remainder of things that are not- 



Y's. 



These conclusions, it is true, merely place the given propo- 

 sition in other and equivalent forms, but such and no more is 

 the office of the received mode of " negative conversion." 



Furthermore, these processes of conversion are not elemen- 

 tary, but they are combinations of processes more simple than 

 they, more immediately dependent upon the ultimate laws and 

 axioms which govern the use of the symbolical instrument of 



