Note 184 — Chapter VI

This is the only possible reading in connotation, so far as real propositions are concerned, if the term connotation is used in the strict sense as distinguished both from subjective intension and from comprehension. Unfortunately confusion is apt to be introduced into discussions concerning the intensive rendering of propositions simply because no clear distinction is drawn between the different points of view which may be taken when terms are regarded from the intensive side. Hamilton distinguished between judgments in extension and judgments in intension, the relation between the subject and the predicate in the one case being just the reverse of the relation between them in the other. Thus, taking the proposition All S is P, we have in extension S is contained under P, and in intension S comprehends P. On this view the intensive reading of All men are mortal is “mortality is part of humanity” (the extensive reading being “the class man is part of the class mortal”). This reading may be accepted if the term intension is used in the objective sense which we have given to comprehension, so that by humanity is meant the totality of attributes common to all men, and by mortality the totality of attributes common to all mortals. To this point of view we shall return in the next section. Leaving it for the present on one side, it is clear that if by humanity we mean only what may be called the distinctive or essential attributes of man, then in order that the above reading may be correct, the given proposition must be regarded as analytical. In other words, if humanity signifies only those attributes which are included in the connotation of man, then, if mortality is included in humanity, we shall merely have to analyse the connotation of the name man, in order to obtain our proposition. Hence on this view it must either be maintained that all universal affirmative propositions are analytical, or else that some universal affirmatives cannot be read in intension. But obviously the first of these alternatives must be rejected, and the second practically means that the reading in question breaks down so far as universal affirmatives are concerned.

Hamilton’s reading breaks down even more completely in the case of particulars and negatives. The attributes constituting the intensions of S and P partly coincide is clearly not equivalent to Some S is P ; for example, the intension (in any sense) of Englishman has something in common with the intension of Frenchman, but it does not follow that Some Englishmen are Frenchmen. Again, from the fact that the intension of S has nothing in common with the intension of P, we cannot infer that No S is P ; suppose, for example, that S stands for “ruminant,” and P for “cloven-hoofed.” Compare Venn, Symbolic Logic, pp. 391–5.