442 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



' some at least ' was ' possibly none', it presented itself as on the cards that ' some at most ' 

 might be 'possibly all', and the system in some unfathomable way Aristotelian, , 



It must be noted that a person might take " some at most " to be singly partitive, 

 by supposing that the limitation " at most " refers to what are spoken of: thus " some at 

 most are..." might be read as "we speak of some at most, be the rest what they may; 

 of these we say they are..." But Hamilton takes pains to explain his meaning. His 

 ' some ' is laid down as both affirmative and negative ; his ' some are ^ is declared inconsistent 

 with ' all are', and his ' some are not ' with ' none are', &c. [I have insisted on this, being 

 in doubt whether it might not be denied : but I believe it is admitted. There is, however, a 

 mode of speaking which may lead to error. It is said that Hamilton gives two systems, 

 the "some at least" of the older logicians, and his own "some at most": and the headings of 

 his own table (VI. 637*) adopt this distinction. But it must be remembered that the ' some' 

 of the table is always 'not-none'; so that his new system is that of 'some at least and 

 at most.' In no other way could IFI, or 'Some — is some — ' be a combination of my 



)') (■(> ^s (^I- 632* diagram d) it certainly is. December, 1862.] 



I now come to the consideration of the genuine Aristotelian system: I mean the system 

 which was sketched out by Aristotle and held its ground down to the end of the seventeenth 

 century. When (1847) I began this long discussion I knew Aristotle only, or almost entirely, 

 as a collection of books of reference. Now and then it became necessary to decide for myself 

 which of two contradicting statements about an opinion of his was true : so soon as one or both 

 were rejected, my business with the Organon was settled for the time. In all cases of agree- 

 ment I took it for granted that the leader was correctly followed. This assumption lasted 

 until I was shaken by the translation of apiOno^ kul Koyo^ into number and speech^ which 



1 exposed in my second paper. Being thus led to suspect that the mathematician Aristotle 

 had been but loosely read, and shamelessly interpolated, by unmathematical followers, I paid 

 more attention to his text. I took for my principle of interpretation that he meant what he 

 said : and truly he is a writer who deserves this compliment. And I found that, though the 

 great bulk of his ancient followers are faithful translators, our modern logicians, though 

 nominally his adherents, have drifted into a system of quantification of their own, and have 

 towed his name after them. 



When I discussed Hamilton's system in my second paper, imagining it to be non-partitive 

 in quantity, after pointing out that two of its propositions were without contradiction in 

 the system, I noticed that very slight change would produce perfect logical consistency. 

 This change was nothing but the substitution of any for all, in affirmatives as well as 

 negatives. I proposed, though this is not absolutely required, that the implicit singularity 

 should become explicit, as in ' any one ' and ' some one.' This gives to six of the eight 



' Plato, in the Phadrus, says that ToCtop &i riv QeZd 

 irpuiTov dptdfjLotf T6 Kal Xoyier^ov iiipclv : hut whether Thoth is 

 held to have invented speech I cannot say. Conic sections are 

 for mathematicians only, or it might have been that Apollonius 

 would have passed for the first inventor of curtailment and 

 exaggeration. Smiglecius (Disp, 9, qu. 6) remarks that Aris- 

 totle does not count speech as quantity in the fifth book of the 



Metaphysics: he will not allow it to be a quantity; and he 

 says that Aristotle made it quantity in the Categories only as 

 ' vulgarem ea de re opinionem secutus.' But when or how the 

 world at large joined number and speech as cognate quantities 

 he does not state: nor how a writer must be held to have con- 

 cealed his own opinion from deference in an example freely 

 chosen by himself, where another would have done as well. 



