382 PROFESSOR DE MORGAN, ON THE STRUCTURE OF THE SYLLOGISM, 



This notation is established with reference to the order A'Y: the inversion of the order interchanges 

 small and large letters. 



The propositions (A) and (O) are the assertion and denial of complete inclusion of the first 

 name in the second. And («) and {it), the assertion and denial of complete inclusion of contrary in 

 contrary, are, as appears, equivalent to the assertion and denial of complete inclusion of the second in 

 the first. Ao-ain, (£) and (/) are the assertion and denial of complete non-interference, or that each 

 name is wholly contained in the contrary of the other. But (e) and (j), the propositions which I 

 propose to add to those commonly received, may be explained as follows: 



The proposition (/) or .ry, affirming that there are individuals in the universe of the jiroposition 

 which are neither Xs or Vs, merely affirms that vV and Y are not contraries, and do not between 

 them contain the universe. The contradiction of this, (e), or w y, affirming that it is false that there 

 are any individuals which are neither X or Y, might seein at first sight to declare that X and Y are 

 contraries. But it is not so, since the preceding is perfectly consistent with there being individuals 

 which are both ..^s and Ks. In fact, to express that X and Fare contraries we must have both 

 ,1' . y and X . Y. 



The following tables show the relations of these propositions. 



Or each universal proposition denies, besides its own contradictory, the two universals of a different 

 name; contains both particulars oi the same name; and is independent of the other universal of the 

 same name and its contradictory. Each particular proposition denies only its own contradictory ; is 

 contained in both the universals of the same name ; and is independent of either of the other three 

 particulars, as well as of the other universal (not its own contradictory) of a contrary name. 



It is usual in modern works to say that a term which is universally spoken of is distributed. 

 But in truth every proposition distributes, wholly or partially, among the individuals of the 

 predicate, or of its contrary. It will be sufficient to call a term universal or particular, according 

 to the manner in which it is spoken of. It will then be found that every proposition speaks 

 indifferent ways of each term and its contrary; making one particular or universal, according as 

 the other is universal or particular. The manner in which the subject is spoken of is expressed ; as 

 to the predicate, it is universal in negatives but particular in affirmatives. And of the two terms and 

 their contraries, each proposition speaks universally of two, and particularly of two. 



Let S signify that the subject is changed into its contrary, P, the same of the predicate. Let 

 C signify that the copula is changed, from positive to negative, or vice versa. Let T denote trans- 

 formation or interchange of subject and predicate : to avoid confusion, either this must be done last, 

 or the original subject and predicate are to retain those names after the transformation. Then we 

 have the following tables, L standing for letting the proposition remain unaltered 



L 

 PC 



T \SP 

 SCT SC 



SPT 

 PCT 



L 

 PC 



PT 

 SPCT 



S 

 SPC 



ST 

 CT 



Cnanges and combinations of changes that are written under one another, are in all cases of the same 

 effect: thus by writing PT and SPCT under one another, I mean that change of subject, pretlicate, 

 copula, and order, are always of the same effect as change of predicate and order only. Thus the 

 operation SPTC performed upon X) Y gives y . x. But PT only gives y) X and y .x = y) X, 

 as appears above. Further, when a single line separates two vertical pairs, the two pairs are 

 identical when performed upon inconvertible piopositions : when a double line, the same with 



-A 



