316 



Cambridge Philosophical Society : — 



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

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

 hibited. I.eavinn: out the cases of terminal precision, which are 

 more com])lex 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 of X, or contains all the rest of the 



universe. Proposition. 

 Assertion of X contained in Y 

 Denial of X contained in Y 

 Assertion of X excluded from Y 

 Denicil 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 



X-of Y. 

 Species 

 Exient 

 Coexternal 

 Copartient 

 Comijlement 

 Coinadequate 

 Genus 

 Deficient 



Y-ofX 



Genus 



Deficient 



Coexternal 



Copartient 



Complement 



Coinadequate 



Species 



Exient 



Notation. 

 X))Y 

 X(.(Y 

 X).(Y 

 XQY 

 X(.)Y 

 X)(Y 

 X((Y 

 X).)Y 



Terminal Ambiguity. Metaphysical reading. 

 Relation of attribute Y to attribute X. 



Y— of X. 



Essential 



Non-essential 



Repugnant 



JiTcpugnant 



Alternative 



Inalternative 



X— of Y. 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 



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| Dependent 



Denial of Y incompatible with x | Independent 



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 ]n"opositions, 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 

 Z, and the combination of relations is seen in — Every species of a 

 coinadequate is a coinadequate. In metaphysical reading, wc have 

 X]] Y] [Z, X is a dependent of Y, Y an inalternative of Z. The con- 

 clusion is X] [Z, X is an inalternative of Z, and the combination of 

 relations is seen in — The dependent of an inalternative is an inalter- 

 native. When the terms become as familiar as genus and species, 

 the axiomatic character of the combination is as clearly manifest as 

 in — Sj)ecies of sjiecies is species. Mr. De Morgan gives the following 



