2i6 THE SCIENCE OF LOGIC. 



The O proposition is the same in both schemes. 



The o&amp;gt; proposition is really a sort of logical monstrosity. We have seen 

 how it involves U when &quot; some &quot; means &quot; some only &quot;. Taking &quot; some &quot; now 

 in the more indefinite sense, the o&amp;gt; proposition will be found to assert nothing 

 and to deny nothing. It denies nothing, for it is compatible with all the affirma 

 tive forms, even with U. Although, for example, &quot; all equiangular triangles are 

 all equilateral triangles,&quot; yet it is still true that &quot; any one (indefinite) equi 

 angular triangle is not any other (indefinite) equilateral triangle,&quot; and this is 

 all that the o&amp;gt; form asserts. But this assertion is no assertion where &quot; some &quot; 

 is an indefinite class term, for it can be made about any two members of a 

 class ; conveying only what we know already that in any class of things no 

 one member is identical with another. 



Of course, where S and P are both singular terms, and both names of 

 the same individual, the truth of &amp;lt;o is excluded ; but in this case o&amp;gt; is inappro 

 priate, for there is no place for the indefinite reference of &quot; some &quot; in such 

 a proposition. 



Dr. Keynes points to some interesting results l that might be obtained by 

 supplementing the traditional fourfold scheme of propositions by the two 

 mutually contradictory forms, U and r;, with &quot; some &quot; interpreted in the in 

 definite sense. But for ordinary purposes it is better to replace these forms, 

 as well as the U form, by their respective predicative equivalents. 



109. EQUATION AL READINGS OF THE LOGICAL PROPOSITION. 

 We may now draw attention to the question whether it is 

 possible, or in what sense it is possible, to regard a logical pro 

 position as an equation and, more especially, whether the eight 

 Hamiltoman forms are really equational forms. 



When we introduce the sign of equality into logic and write 

 the proposition in the form &quot; 5 = P &quot; : &quot; Equilateral triangles = 

 equiangular triangles&quot; &quot; men = mortal men &quot; : what sort of identity 

 is it that we endeavour to express ? It is an identity analogous 

 to mathematical equality, to numerical identity. It is, therefore, 

 not an identity of connotation in the terms compared, but an 

 identity of denotation. It asserts that the class denoted by the 

 subject-term is coextensive and identical with the class denoted 

 by the predicate-term ; and it implies that this class can be 

 reached or determined in either of two different ways through 

 the connotation of the subject, or through the connotation of the 

 predicate. Every equational scheme of interpreting propositions 

 is, therefore, an &quot; extensive &quot; or &quot; class &quot; scheme, and labours under 

 all the defects of this latter. 



An equational reading must necessarily, of course, possess 

 this one advantage the value of which, however, seems to have 

 been greatly overestimated that, since the logical copula &quot; is &quot; 



1 op. cit. t p. 207, 



