446 



Mr de morgan, on the syllogism. No. v. and 



"omnis homo egt omne risibile": that is, the logicians are, almost to a man, exemplar. Let 

 who will believe that they nearly all refused a form tantamount to ' the class A is the class 

 B', because they thought that each individual in A would thereby be pronounced to be all the 

 class B. They meant the proposition in the sense of its correct translation, ' Every man is 

 every risible', at which they laughed because, in Latin, as in English, the form implies that 

 every separate man is every risible animal. 



I cannot here properly give the volume of proof which it is easy to collect of the old 

 mode of enunciation being what I call exemplar. What I have given will be sufficient 

 for unbiassed minds, so soon as it shall appear that no equal force of citation is to be produced 

 on the other side. I affirm then that the exemplar table which I gave in 1850 is the Aristo- 

 telian system, fully quantified, and made as complete in its forms as it can be so long as 

 privative terms are excluded. But it must be remarked, — 



First, that the system is not originally derived from distributions of quantification and. 

 search after their meanings. The leading idea is that of assertion or denial of class being 

 contained in class, and of class being excluded from class. Indications of this origin are not 

 wanting. Particular negation is very frequently enunciated by ov was ecm, that is, by 

 denial of total inclusion or agreement : the greatest interest in ' some are not' is seen in, 

 ' not every one is.' If quantification had been a leading idea in the mind of Aristotle, he 

 would not have been unable to use the pepper-box : but to him' the signs of quantity were; 

 but incidents of expression. 



Secondly, when a term was a genus, the exempla were species taken individually, not 

 ultimate individuals. Thus when the quantified term was omne animal, the hie, iste, ille, 

 5tc. of the distribution would be homo, bos, asinus, &c. : when omnis homo, if homo were 

 infima species, the details would be Plato, Socrates, &c. 



Hamilton disputes the rational existence of ' Any one X is any one Y', and affirms 

 (VI. 628*) that ' any^ and ' any one' necessarily imply that there are more. This is not true : 

 we have but a strong presumption of more. My critic had arrived at a conviction that some 

 ought to be doubly partitive : but this was his own exclusive possession. The examination 

 of his argument will show that any has no difficulty about it except what applies equally to 

 all. When it is clearly understood that part is that which may be the ivhole — that is, when 

 partition is formally excluded — it will then be seen that if there be that which is any part 

 of Y, there can be but one part of Y, the smallest part is the whole, the whole is an 

 individual. Any does not necessarily imply more than one : speaking of existence at this 

 moment, any Queen of England is any Queen of Scotland: every Queen of England that can 

 be found is all the Queens of Scotland there are; it would be treason to deny it. 



The following addition to my statement as to quantification appears to me so evidently 

 the true reading of the ancients, that I see no means of proving it to any one who, having 



' My belief is that, in the mind of Aristotle, the four 

 forms were merely intended to signify, in common language, 

 the affirmation and denial of total inclusion, and the af- 

 firmation and denial of total exclusion. The entrance of 

 quantifying adjectives or pronouns was only a non-essential 

 incident of common language. Hence the old notion, so long 



retained, that the proposition was universal or particular, not 

 the subject. The departure from principle, which gradually 

 clouded the theory, was the expression of denial of totality by 

 a destructive example: as denial of ' X wholly in Y' by ' cer. 

 tain X not in Y '. But there is a vestige of creation in ov -ras 

 eo-Ti, as mentioned in the text. 



