ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



433 



singly partitive; some-not-all, some-at-most, but without any assertion or denial about the 

 rest. Thirdly, as doubly partitive; some-at-most, and the rest the other way. As Hamilton 

 says, this' some is "both affirmative and negative", meaning that it makes any proposition 

 which contains it both affirm and deny. 



I cannot find any notice of the distinction between non-partition and single partition. 

 The logicians are much given to halt between the two. Perhaps they would defend their 

 course, as follows: — When we say " Some are", meaning "Some-not-all are", we say nothing 

 at all about the rest. Perhaps also •' the other some are". In what way then, do we differ from 

 those who say "Some-perhaps-all are". Not at all, I reply, in the expressed "some" of 

 particular subjects: but much in the implied "some" of particular predicates, in which 

 " some not all " is of double partition by necessary inference. For example, say ' all men 

 are some animals' ; some-perhaps-all and some-not-all no longer give equivalents. If it be some- 

 not-all, even though nothing were intended about the rest, the exhaustion of man contained 

 in all forces double partition : the rest of the animals are not men. 



Hamilton confronted wow-partition, under the name of indefinite definitude, with double 

 partition, under the name of definite indefinitude: the second phrase is defensible; the first is 

 false contrast. Of single partition he takes no distinctive notice whatever. That his par- 

 tition is really double cannot be doubted. His " some" is " both affirmative and negative"; 

 he represents ' Some X is not any Y' as inconsistent with 'No X is Y'. This must mean 

 that ' Some X is not any Y' tells us that the remaining X is Y. There is however no need 

 to enlarge upon this : the diagrams and explanations (VI. 631*, 632*) are sufficient. Had 

 Hamilton advocated single partition, all his syllogisms would have been valid ; and my chal- 

 lenge would have had a host of respondents. One opponent nearly committed himself: 

 he imagined that Hamilton really did adopt single partition ; but he found out his mistake in 

 time. 



,1 The system which was to form the base — or one of the bases, for Hamilton permitted the 

 old system to exist alongside of his own — of the New Analytic consisted in applying the 

 quantifiers 'some' and ' alV — in negatives ^ any'' universally taken — in every way to both 

 subject and predicate: the word ^ some' was intended to be doubly partitive, affirmation or 

 denial of it was intended to convey denial or affirmation as to that ' other some' which in 



' The common usage of mankind inclines to partition : 

 even the affirmation of none is, whenever it can be so made, 

 affirmation of some of the alternative kind. No person pays 

 any respect to the doctrine that from negative premises nothing 

 can follow: the negatives have their implied affirmatives. This 

 happens from the earliest childhood: for example. 

 Jack Sprat could eat no fat, 



His wife could eat no lean; 

 And so, betwixt them both, 

 They licked the platter clean. 

 How this arose we learn from the second verse, long lost to 

 the nursery, but recovered by Mr Halliwell. 



For (i.e. as implied) Jack ate all the lean. 



And Joan ate all the fat, 

 The bone they picked quite clean, 

 And gave it to the cat. 



The same ambiguity accompanies the mention of definite 

 number. Thus ' four of them ' may be any four, or certain 

 four. The context only can decide. When we are told that 

 a man had his horse out four times in one day, we must know 

 what we are talking about before we can tell whether it was 

 one or other horse, or one particular horse: and the same if the 

 phrase were 'one of his horses.' If the statement be made in 

 proof of his almost living on horseback, we shall certainly sup- 

 pose various horses : if of his want of consideration for his poor 

 beasts, we see that one only is meant. Here the difficulty is 

 real : raise it upon a matter in which context is not required, 

 and we pass into the region of jokes; as in the case of the man 

 who is reported to have been reduced to despair of compliance 

 with the prescription by seeing on the apothecary's label, 'Two 

 of the pills to be taken three times a day.' 



55 — 2 



