318 MEMOIR OF AUGUSTUS DE MORGAN. 



1863. 1 bring the chief difficulties of quantitative infinity to some- 



thing like this : 



When of A and B one and one only must be, when A is 

 visibly self -contradictory and B only incomprehensible, I vote 

 forB. 



I shall be very glad to see anything of Ellis's. The thoughts 

 of his long illness would be valuable. He gained an enormous 

 power of thinking about mathematics without pen and paper. 

 I repeat my wish that his preface to Bacon could be separately 

 published. With kind regards to Lady Affleck, 



I am, yours very truly, 



A. DE MORGAN. 



To Rev. Dr. Wh&well. 



April 7, 1863. 



MY DEAR SIR, Now I will provoke an opinion, not an 

 answer to a matter of fact ; and if anybody in College has ever 

 thought about the subject, I wish he would think about it again. 



Aristotle has a chapter in the * Metaphysics ' about the 

 aircipov, translated ' the infinite.' The chapter opens with a 

 description of the meaning of the word, which has come down 

 without any strong objection that I can find. I give the sen- 

 tence itself, with a literal translation from MacMahon. I 

 hardly ever had to look closely at a sentence of Aristotle without 

 finding what reason might take either for a gross corruption or 

 an obvious interpolation. This chapter I suppose to have had 

 much sway in determining the logician's obstinate confusion 

 between the infinite, unlimited in qualities, powers, &c., and the 

 simple infinite of magnitude. Now from 'Metaphysics,' lib. x. 

 or xi., cap. 10 : 



To 8' aTTCLpOV TJ TO O&VVO.TOV $L\6eiV T(2 fJLrj 7T<j>VKVa.L 8uVOLL, KaOd- 



iTp rj <(ov>) doparos, rj TO 6WoSov *x ov ttTeXevnyrov, fj o yu.oA.is, ^ o 



rj 



' But the infinite is either that which it is impossible to pass 

 through in respect of its not being adapted by nature to be per- 

 meated, in the same way as the voice is invisible ; or it is that 

 which possesses a passage without an end, or that which is 

 scarcely so, or that which by nature is adapted to have, but has 

 not, a passage or termination. Further, a thing is infinite from 

 subsisting by addition or subtraction, or both.' 



