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



this or that Y is spoken of by failui'e of definite knowledge of the Xs. If I say ' all man is 

 animal', and cannot say that I have spoken of that animal, it is only because I do not know 

 whether that object was spoken of under ' man'. 



What notion, then, has been brought forward and discussed under the name of quantity ? 

 Distinction between affirmation and non-affirmation of all or any: totality affirmed, totality 

 not affirmed, without any reference to the quantity of the totum, the more or fewer indivi- 

 duals existent in the class. To speak of X at all is to speak of the whole class, to speak of 

 all X as a class, or not to speak of it as a class. ' Man is animal' : do you speak of man 

 as a whole class ? yes ; do you speak of animal as a whole class .-" I say nothing about it ; 

 you are to take this proposition for purposes of inference without knowing whether I speak 

 totally or partially ; there is neither assertion nor denial, but reserve ; it may be that I 

 know the truth ; it may be that you know the truth ; but this proposition says nothing about 

 it, and is intended to say nothing. This is all that is meant by ' animal' being particular. 



If this view had been taken from the beginning, the difficulties of the singular propo- 

 sition and of the indefinite proposition would never have appeared. All the confusion which 

 has arisen from want of care in stating the meaning of ' some' would have been avoided. 

 Tlie Hamiltonian quantification, if it had appeared at all, would have appeared in a sound 

 form. It would have been remembered that affirmation and denial are not alternatives ; and 

 the three quantifiers of which I have shown the united effect would have been allowed full 

 operation. To this I may add that Hamilton would never, even while denying its utility, 

 have allowed 'most' (half plus some) to have been legitimate. This importation from truly 

 arithmetical quantification would have remained in its proper sphere, in company with other 

 fractions. 



In my third paper I closed the controversy with my late opponent, as to every strictly 

 personal matter : in this paper I hope to do the same with the purely logical questions, so far 



as his criticism on my own views is concerned. What remains of a polemical character 



' save only the question treated in the addition — concerns neither this logician nor that mathe- 

 matician, but the logician and the mathematician. I believe that tiie necessary laws of 

 thought constitute as wide a study as the necessary matter of thought : and that Kant's 

 opinion on the finality of the Aristotelian system has as much truth and sense as any similar 

 opinion — if any such were ever held — about the finality of the elements of Euclid. 



To the logician I say that the system which he owes to a mathematician, Aristotle by 

 name, is a system of which none but mathematicians have ever shown a disposition to 

 extend or vary the forms which has been followed by general respect : as Boethius, Ramus, 

 Leibnitz, Lambert, Kant. There is but one logician of great note who, not having mathe- 

 matical habit, has attempted to depart from routine in the construction of a system of infer- 

 ence. It is not for me, appointed by himself his most prominent opponent, to pass sentence 

 upon his system : but I suspect I have shown that system to be none the better for its 

 author's ignorance of the other branch of exact science. The growth of logic has been 

 stunted by its separation from mathematics : I feel certain that my learned and acute antago- 

 nist will be cited in time to come as the great champion of reunion, though appearing and 

 intending to fight on the other side. 



