212 THE SCIENCE OF LOGIC. 



Here the classes are represented by circles called &quot; Euler s circles,&quot; 

 from their first application by Euler, a Swiss logician of the eighteenth century. 

 It will be seen that they suppose &quot; Some &quot; to mean u a definitely known 

 portion less than all &quot;. That is, they express all the relations that are objec 

 tively possible between two classes of things ; not our possibly imperfect and 

 indefinite knowledge of those relations. Whether or not the class-inclusion view 

 necessarily leads to the above fivefold scheme of propositions, we shall see 

 presently. Were we, in the predic ative view, to interpret &quot; some &quot; as above, 

 instead of indefinitely, we should have a threefold instead of the traditional 

 fourfold scheme * ; for, either particular, I or O, would then involve the 

 other and convey the knowledge that &quot; Some 5 is, and some 5 is not, P &quot;. 

 Any attempt to use combinations of the above five figures for the purpose of 

 expressing the four traditional propositions, A, E, I, O, will bring out the con 

 trast between the full and definite knowledge implied in the judgments repre 

 sented by each of Euler s diagrams, and the imperfect knowledge contained 

 in the A, E, I, O, judgments. 



105. QUANTIFICATION OF THE PREDICATE : HAMILTON S EIGHTFOLD 

 SCHEME. While recognizing, therefore, certain uses and advantages in the 

 class-inclusion view, we must, nevertheless, reject the claims put forward by Sir 

 William Hamilton on its behalf. He enlarged the traditional fourfold, to an 

 eightfold scheme of propositions, by explicitly quantifying the predicate and 

 thus making its distribution or non-distribution in every case independent of 

 the quality of the proposition (91). This gave rise to the following scheme : 



From AH &quot;&quot;&quot; &amp;lt;*/? U S &quot; P p 



I All S is some P a ft ... A ... S a P 



Fm * f Some S is all P ifa...Y...SyP 



irom I { ~ . .,. T c D 



( Some S is some P ift .../... o z P 



(No S is any P ana . . . E . . . S e P 



From E ^ , r ~ . ^ . CD 



( No S is some P am ...?/... o rj P 



- f Some S is not any P . . . ina . . . O . . . S o P 



From O { ^ ^ . r, . . CD 



( Some S ts not some P tnt . . . o&amp;gt; . . . o &amp;lt;o P 



The symbols used by Hamilton himself were afa, etc., /meaning affirmation, 

 n negation, a distribution, z non-distribution. The symbols more commonly 

 employed are U, A, Y, etc., introduced by Archbishop Thomson. 2 



106. HAMILTON S POSTULATE. Hamilton justified this interpretation of 

 the judgment by an appeal to the postulate of logic, that we &quot; be allowed to 

 state explicitly in language all that is implicitly contained in the thought &quot;. 

 The meaning of the postulate, thus stated, is not clear. I f it demands the right to 

 make mere verbal changes that will not alter the meaning of a proposition 

 (82), it is unimpeachable. If it refers to the inference or drawing out of 

 implications, latent in the meaning of a judgment or judgments, it indicates 

 rather what it is the function of logic to teach us how to do correctly. But 

 in its application to the present subject-matter it is evidently intended to mean 

 rather that we have a right to state in language what is actually and explicitly 

 in our thought. We certainly have ; but Hamilton abuses the right by 



1 KEYNES, op. cit., p. 183. 



3 An Outline of the Laws of Th^ipht, p. 137. 



