ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



457 



Pwrt and Part. 



Any part of X is any part of Y := 



Some part of X is not some part of Y := denied 



Any part of X is some part of Y ) ) 



Some part of X is not any part of Y ( • ( 



Some part of X is any part of Y ( ( 



Any part of X is not some part of Y ) • ) 



Some part of X is some part of Y ( ) 



Any part of X is not any part of Y ) • ( 

 Only (•) ) ( excluded. 



Fart and Whole. 



Any part of X is any whole of Y S : 



Some part of X is not some whole of Y g : denied 



Any part of X is some whole of Y := 

 Some part of X is not any whole of Y := denied 



Some part of X is any whole of Y =: 



Any part of X is not some whole of Y r=: denied 



Some part of X is some whole of Y ( ( 

 Any part of X is not any whole of Y ) • ) 

 Only ( ( )•) included. 



Whole and Whole. 



Any whole of X is any whole of Y =: 

 Some whole of X is not some whole of Y =: denied 



Any whole of X is some whole of Y ( ( 

 Some whole of X is not any whole of Y ) ■ 



Some whole of X is any whole of Y ) ) 

 Any whole of X is not some whole of Y ( • ( 



Some whole of X is some whole of Y ) ( 

 Any whole of X is not any whole of Y (•) 

 Only ) • ( () excluded. 



Whole and Part. 



Any whole of X is any part of Y %: 



Some whole of X is not some part of Y %: denied 



Any whole of X is some part of Y :=:: 



Some whole of X is not any part of Y r=: denied 



Some whole of X is any part of Y :::z; 



Any whole of X is not some part of Y := denied 



Some whole of X is some part of Y ) ) 

 Any whole of X is not any part of Y ( • ( 

 Only ) ) (•( included. 



The symmetry and compensation of this table is an instance of what we shall always find 

 whenever correlatives are fairly and equally used. By carrying the whole through Xy, xy, 

 and xY, as well as XY, we produce the main system eight times, and complete the system 

 of restrictives. We may call the system of part and part and of whole and whole by the 

 name of balanced^; the others being unbalanced. The rules of distinction and identification 

 of forms are as follows: — 1. Balanced readings exclude from the general system nothing but 

 any affirmed of any and some denied of some: unbalanced readings admit nothing but some 

 affirmed of some and any denied of any. 2. When exclusion is not thereby made admis- 

 sion, or vice versa, 'any part' and 'some whole' are convertible, as also 'any whole' and 

 ' some part'. Thus ' Some part of X is some whole of Y' is the same proposition as ' Any 

 whole of X is some whole of Y '. 



There are two positions which have, alone or together, been expressed or implied in several 

 distinct quarters. First, that the mere completed distribution of the quantifying words is the 

 completion of a true logical system, dictated by the laws of thought. Secondly, that the eight 

 forms first obtained by complete distribution of contrary terms through the old forms is an 

 arbitrary system, which might have been something else if the framer had so pleased. I con- 

 tend that these descriptions should be exchanged : that the arbitrary character, but not to 

 so great an extent as asserted of the other, belongs to Hamilton's system before the correc- 

 tion which makes it simply the true extension of the real Aristotelian system ; and that the 



I These useful terms, suggested by Hamilton, may be used in reference to any pair of correlatives. 



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