214 THE SCIENCE OF LOGIC. 



hopeless confusion of different interpretations in Hamilton s own writings. 

 Let us see a few of the chief results to which the various interpretations 

 of &quot; some &quot; will lead us. 



108. VARIOUS ALTERNATIVES AND THEIR UNSATISFACTORY RESULTS. 

 (a} If &quot;some&quot; means &quot;some only&quot; the scheme is redundant ; for each 

 affirmative proposition containing &quot; some &quot; involves a negative, and vice 

 -versa. Thus A and 77 mutually involve each other, and similarly Y and O, 1 

 while to is actually equivalent to U incredible as this may seem at first 

 sight. &quot; Some (but not all] S s are not some (but not all) P s &quot; asserts that 

 certain .S^s are not to be found in a certain section of the P s but are to be 

 found elsewhere among the /&quot;s, while the remaining S s are to be found in 

 the former section of the P s, and thus All the S s are P s; and in precisely 

 the same way it is seen that all the P s are S s. That is, All S is all P ; or 

 a) is equivalent to U. 



We are thus left with five forms instead of eight, viz., U (or o&amp;gt;), A (or 77), 

 Y (or O), I, E expressing the five alternative relations of two actual classes 

 (104). Each of these propositions is incompatible with each of the others; 

 but it is by no means a &quot; simple &quot; process to find the contradictory of any 

 one of these. We can contradict U, for example, only by affirming an alter 

 native between A, Y, I, and E. The traditional fourfold scheme is simplicity 

 itself compared to this. 



If it is an essential of any scheme of formulating propositions that the 

 forms be simple and irreducible, we see that the present interpretation is 

 very defective indeed, containing, as it does, forms that are exponible, 

 and forms that are ambiguous. This indeed is the necessary outcome of 

 interpreting &quot; some &quot; to mean &quot; some only,&quot; instead of giving it the simpler 

 and more fundamental meaning of &quot; some at least &quot;. &quot; Some only &quot; implies 

 the formation of two judgments ; that &quot;some are . . . &quot; and that &quot; some are 

 not ...&quot; and presupposes, or rather fails to take account of, that prior and 

 more indefinite stage of knowledge at which we know that &quot; some are . . . ,&quot; 

 but do not know anything about the remainder of the class. 



(b) &quot; Some &quot; interpreted as &quot; some at least&quot; in two of the eight forms. 

 Hamilton himself does not keep consistently to either view of &quot;some &quot; : 

 when it enters into both terms of the judgment, i.e. in I and o&amp;gt;, he inclines to 

 retain the traditional meaning, &quot; some at least &quot; ; but he does not adhere to this 

 view in the confusing applications to which it would lead. 2 It does not 

 remove the difficulty that A is equivalent to r\, and Y to O. Its combination, 

 in one and the same scheme, with the meaning &quot; some only,&quot; is very confus 

 ing ; and we shall see presently that its application to I and o&amp;gt; does not lead 

 to any useful results. 



(c) &quot;Some&quot; interpreted as &quot;some at least, possibly all&quot;. Returning 

 to this, which is the traditional logical interpretation, adopted in the predica 

 tive scheme, let us apply it to each form of the present scheme in turn. 



1 And besides this, 77 and O may each be interpreted as equivalent to I so that 

 these forms do not succeed in giving definite information, but are ambiguous. The 

 passage from A to T? and from Y to O is called &quot; Integration &quot; : because, given a part, 

 it &quot; integrates &quot; the whole by introducing the other part (BowEN, Logic, pp. 

 169, 170). 



2 C/. KRYNBS, op. cit., p. 201. 



