198 



of the terminally ambiguous and terminally precise, four modes of 

 combination are obtained. Logicians have but the copula is for all 

 cases. Mr. De Morgan proposes to use a complete system of 

 schetical terms, by which the combination of relations shall be ex- 

 hibited. Leaving eut the cases of terminal precision, which are 

 more complex and less usual, the two kinds of reading under which 

 the common syllogism is included are as follows : — 



Terminal Ambiguity. Mathematical reading. 

 Relation of Class X to Class Y. 



The class x is the contrary 



universe. . . 



Proposition. 



Assertion of X contained in Y 



Denial of X contained in Y 



Assertion of X excluded from Y 



Denial of X excluded from Y 



Assertion of x contained in Y 



Denial of x contained in Y 



Assertion of x excluded from Y 



Denial of x excluded from Y 



of X, or contains all the rest of the 



Terminal Ambiguity. Metaphysical reading. 

 Relation of attribute Y to attribute X. 



Assertion of Y a component of X 

 Denial of Y a component of X 

 Assertion of Yincompatible 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 



Y— ofX. 

 Essential 

 Non-essential 

 Repugnant 

 Jrrepugnant 

 Alternative 

 Inalternative 

 Dependent 

 Independent 



X— ofY. Notation. 



Dependent 



Independent 



Repugnant 



Irrepugnant 



Alternative 



Inalternative 



Essential 



Inessential 



X]]Y 



X[.[Y 

 X].[Y 

 X[]Y 

 X[.]Y 

 X][Y 

 X[[Y 

 X].]Y 



The extension of the four forms to eight, the notation, &c, are 

 treated in the second paper on syllogism. The two sets contain the 

 same propositions, differently read ; and the quantities in the two 

 are different. In the first reading X) and (X denote X taken uni- 

 versally in extension ; X( and )X denote X taken particularly. In 

 the second reading ]X and X[ are universals, X] and [X are parti- 

 culars. Thus, when we say that the classes X and Y are copartient, 

 or in common language * some Xs are Ys,' denoted by X()Y, both X 

 and Y have particular quantity in extension. In saying this we also 

 say that X and Y, as attributes, are irrepugnant, or not incompatible, 

 denoted by X[]Y. But the intensive/orce of both X and Y is uni- 

 versal ; no one attribute of X is repugnant to any one attribute of Y. 



The syllogism denoted by X))Y)(Z contains the assertions that 

 X is a genus of Y and Y a coinadequate of Z, ( Y and Z not together 

 filling the universe). The conclusion is X)(Z, X is a coinadequate of 



