216 



Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



In the notation for mathematical reading X) and (X denote X taken universally in ex- 

 tension and particularly in intension : and X( and )X denote X taken particularly in extension 

 and universally in intension. In metaphysical reading X] and [X denote complete force in 

 extension, and incomplete force in intension: X[ and ]X denote complete force. Our usual 

 habit, then, will be to consider X), (X, X[, ]X, as universals ; X(, )X, X], [X, as particulars. 



A proposition is determined so soon as its quantities and quality (affirmative or negative) 

 are determined : this is inductively derived from the lists. Hence the proposition is com- 

 pletely symbolised by terms, quantities, and quality. To say ' I speak in extension, affirma- 

 tively, universally of X, particularly of Y ' must be to say ' X is a species of Y,' and is de- 

 noted by X )) Y, or X )••) Y. 



When a term is changed into its contrary, the spicula must be changed, and the mark of 

 quality. Thus X )) Y is X )•( y, and x (•) Y and x (( y. A term and its contrary* have 

 always opposite quantities, and opposite forces. 



A term used particularly may be replaced by a stronger of its own tension (extension or 

 intension) : a term used universally may be replaced by a weaker of its own tension. Deduc- 

 tive truth remains, though not equivalence. We have here the whole principle of common, 

 or onymatic, syllogism. 



We may state it thus, and more widely. 



In universal terms of either tension, elements of that tension are dismissible and inad- 

 missible. Thus A, B )) CD gives A )) C : but A )) C does not give A, B )) C. 



In particular terms of either tension, elements of that tension are indismissible and 

 admissible. Thus A )) B gives AC )) B : but A )) B, C does not give A )) B. 



In universal propositions, indismissibles are transposible, directly in negatives, by contra- 

 position in affirmatives. But dismissibles are intransposible. Thus in AB )) Y, A is indis- 

 missible, but transposible by contraposition; AB )) Y=B )) Y, a. But in AB)*( Y, the 

 indismissible A is directly transposible; AB )•( Y=A )•( BY. 



In particular propositions, dismissibles are transposible, directly in affirmatives, by contra- 

 position in negatives. But indismissibles are intransposible. Thus in A, B ( ) Y, where A is 

 indismissible, it is intransposible: but in AB ( ) Y, the dismissible A is directly transposible; 

 AB()Y=A()BY. Andin AB (•( Y, wehave B (•( Y, a. 



The root of these distinctions may be clearly seen in the distinction of propositions as 

 either affirming or denying coexistence. But I defer the consideration-f- of this point to a 

 subsequent paper. 



• When a universal is converted into a particular merely 

 by inserting or witlidrawing a symbol of negation, the parti- 

 cular so obtained, joined to the universal, limits the extent of 

 the universal, as in the following cases : 



)), a species ; )'), but not the largest possible. 



)•(, an external; )(, 



((, a genus ; (•(, but not the smallest possible. 



(•), a complement; (), 



The distinction thus drawn between )) and )•{, on the one 

 hand, and (( and ('), on the other, might be worded in many 

 WBys. 



+ I hope at some future time to treat of a pure form of 

 opposition which runs through all contraries. In my last paper 

 I gave some account of the way in which various words may be 

 made to replace each other, at least so far as this, that either 

 may be described in terms of any one of the others. An emi- 

 nent critic thereupon says that I "formally identify" these 

 terms. If this mean that I say, in form, that they are iden- 

 tical, he is not correct : but if it mean that I contend for a 

 common form running through all logical oppositions, he is 

 correct so far as this, that I ventured to predict the future 

 establishment of such a form. My critic adds that my system 



