CA TEGORICAL JUDGMENTS AND PROPOSITIONS. 2 1 5 



The U proposition is equivalent to the combination of the two predicative 

 forms S a P and P a S. The form &quot; All S*s are all P s &quot; is rarely met 

 with ; but there are forms equivalent to it : (i) propositions which state 

 explicitly that two classes are coextensive, e.g. &quot; Equilateral triangles and 

 equiangular ti tangles are coextensive &quot; / &quot; Christianity and Civilization are 

 coextensive&quot;; &quot; Bluestone is the same as sulphate of copper&quot; ; &quot;Sunday, 

 Monday . . . Saturday are all the days of the week &quot;. A sub-class of those 

 would be propositions with singular subjects and singular predicates, e.g. 

 &quot; The present Pope is Pius X &quot;. (ii) All definitions may, of course, be inter 

 preted as U propositions if the denotation of the terms be attended to ; for 

 the subject and predicate, being identical in connotation, are coextensive in 

 denotation. But this reading is quite subsidiary to the primary one, which, 

 in the case of definitions, is always the connotative reading relation of attri 

 butes being thought of in the first place. 1 The U proposition is, therefore, 

 not a simple but an exponible form, if the quantification of its predicate is to 

 be interpreted as in the predicative scheme. It is better, therefore, to use its 

 two equivalents, for logical purposes, than to retain the U proposition itself. 



The A proposition is the same in both schemes. 



The Y proposition expresses what we have described as exclusive and 

 exceptive propositions in the predicative view. &quot; Graduates alone are elig 

 ible &quot; yields, as we have seen (95), the proposition Some graduates are all 

 eligible people : which is the Y form. This, no doubt, preserves the original 

 subject and predicate, but it is not a simple predicative form, any more than 

 the original. Its converse, however, All eligible people are graduates, is 

 a simple predicative form (A), and conveys the same information about the 

 compared classes as Y does, viz. that one class is contained in an indefinite 

 portion of the other. It is better, then, to use the A form for general logical 

 processes than the Y form. 



The I proposition will be the same as in the predicative scheme. 



The E proposition will also be the same in both schemes. 



The 77 proposition is never met with ; but a form that is said to be equi 

 valent 2 occasionally occurs : the form &quot; Not S alone is P&quot; provided this is 

 not taken to convey that any S is necessarily P. For instance, to the boy s 

 generous wish &quot; I should like to be a millionaire in order to be a great public 

 benefactor,&quot; the philosopher may reply &quot; It is not millionaires alone who are 

 great public benefactors &quot; : which asserts that &quot; some great public benefactors 

 are not millionaires &quot; (or that &quot; some non-millionaires are great public bene 

 factors &quot;) and does not assert that any great millionaires are great public 

 benefactors. This example might be expressed, in accordance with the ?; 

 form, to mean that &quot; the whole class of millionaires is excluded from an in 

 definite portion (possibly the whole) of the class of great public benefactors,&quot; 

 or, equally, by the O form of the predicative scheme &quot; Some P s are not 

 (any) S s &quot; &quot; Some great public benefactors are not millionaires &quot;. The 

 form 77 is thus seen to be equivalent to O. It is, moreover, the contradictory 

 of Y : a relation which will be more easily, realized if Y be written &quot; S alone 

 is P,&quot; and 77 &quot; Not S alone is P &quot;. &quot; The virtuous alone are happy &quot; is con 

 tradicted by &quot; Not the virtuous alone are happy &quot;. 



1 Cf. JOSEPH, op. cit., p. 200 n. 8 Cf, KEYNES, op. cit., p. 206, 



