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of what is meant by the Quantification of the Predicate 

 thus : " Whereas the ordinary forms of proposition leave it 

 uncertain whether we are speaking of the whole predicate, 

 or part only, in afiirmation, and decide that we must be 

 speaking of the whole predicate in negation ; we thus leave 

 four possibilities unrecognised : that in fact we may think 

 the predicate, either as a whole or as a part, and must think 

 it as one of the two, in both affirmation and negation alike. 

 Moreover, since what exists in thought should be expressed 

 in words, a really complete scheme of propositions demands, 

 and is satisfied by, eight forms." This is a very clear and 

 succinct statement of what Hamilton calls the " thorouo-h- 

 going quantification of the predicate." But it may be 

 observed that many who accept Hamilton's principle refuse 

 to recognise the validity of one or more of his forms, 

 special objection being taken by some of his disciples to 

 the forms, ' Some x is not some y' and ' No cc is some y.' 

 But the essential point insisted upon by all quantifiers of 

 the predicate, is this, that the extent of each of the two 

 terms of a judgment is known, and should therefore be 

 expressed in language ; in other words, that to the predi- 

 cate, as well as to the subject, a quantitative sign should be 

 affixed, to indicate whether the whole, or part only, of the 

 term is meant. " Every notion," says Baynes, in his New 

 Analytic of Logical Forms, " holding the place of predicate 

 in a proposition must have a determinate quantity in 

 thought." The whole controversy turns on the question 

 whether this is so or not; for it will be admitted that in 

 Formal Logic what exists in thought should be expressed in 

 words. To me it seems that the quantification of the pre- 

 dicate is not a necessary law of thought, but merely a sym- 

 bolic convention, and not a very useful convention either. 

 A man may know that 'x is y,' and yet not know, perhaps 

 not have the means of determining, whether x is the whole, 

 or part only, of y. We may write 'aXixisy' in the form 



