AND ON LOGIC IN GENERAL. 



211 



XXVII. Logico-tnathematical Reading. Terminal Precision, § xi. 



Proposition of Asgertion. 



X and more contained in Y 



X contained in and containing Y 



X containing Y and more 



X and more contained in y 



X contained in and containing y 



X containing y and more 



Here X )o) Y is a compound of X )) Y and X ) •) Y, coexisting. We deny it by deny- 

 ing either X )) Y or X)-) Y, or by asserting either X(-(YorX((Y. Let this aggregate 

 be represented by X(,(Y. Then X)o)Y is denied by X(,(Y, X(o(Y by X),)Y, 

 X)o(Y by Y(,)Y, X(o)Y by X),(Y. And identity, X | | Y, is denied by either 

 X ( • ( Y or X ) • ) Y ; and contrariety, X | • | Y, by either X ( ) Y or X ) (Y. When we read 

 in mathematical intension, the prepositions sub and super change places. 



XXVIII. Logico-metaphysical Reading. Terminal Ambiguity, § xvii. 2. 



Proposition of Assertion or Denial. 



Assertion of Y a component of X 

 Denial of Y a component of X 



Assertion of Y incompatible with X 

 Denial of Y incompatible with X 



Assertion of Y a component of x 

 Denial of Y a component of x 



Assertion of Y incompatible with x 

 Denial of Y incompatible with x 



T predicated of 

 X as 



Essential 

 Inessential 



Repugnant 

 Irrepugnant 



Alternative 

 Inalternative 



Dependent 

 Independent 



X subjected to 

 Yas 



Dependent 

 Independent 



Repugnant 

 Irrepugnant 



Alternative 

 Inalternative 



Essential 

 Inessential 



Beading in aritlimetical whole 

 {by intension only). 



Y always in X 



Y sometimes not in X 



Y never in X 



Y sometimes in X 



In everything either X or Y 

 In some things neither X nor Y 



In Y always X 



In Y sometimes not X 



Notation. 



X]]Y 

 X[-CY 



x:-cY 



XQY 



Xn-]Y 

 X]CY 



XC[Y 

 X]-]Y 



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