TI 



A 4 ft 



deed, logical algebra conclusively proves that mathematics extends over the \vhol< 



realm of formal logic; and any theory of cognition which cannot he adjusted to th 

 fact must be abandoned. We may reap all the advantaj which the mathemati- 

 cian is supposed to derive from intuition by simply making g neral supposition- 



of individual cases. 



In reference to the doctrine of individuals, two distinctions should he borne in mind. 

 The logical atom, or term not capable of logical division, must he one of which every 

 predicate may be universally affirmed or denied. For. let A 1* such si t> nm Then, 

 if it is neither true that all A is X nor that no A is X, it must be true that some A 

 is X and some A is not X; and therefore A may be divided into A that i- X ad A 

 that is not X, which is contrary to its nature as a logical atom. Such a term n I* 

 realized neither in thought nor in sense. Not in sense, because our orga 



pecial, — the eye, for example, not immediately inform i 



■o that an 



image on 



the retina is indeterminate in respect to >w Hneas and non tm 



fc w 



t ■ 



When I see a thing, I do not see that it is not -weet, nor do I 

 and therefore what I see is capable of logical division in 



the not 



sweet. It is customary to assume 



absolutely determin 



respect to color, but even this may he doubted. 1 know no fact- which prove that 



III lIlOUL'ht 



there is never the least vagueness in the immediate 



lutely determinate term cannot be realized, because, not being given by MOW, such 



a concept wonld have to be formed by synthesis, and tier, would be no end to 



the synthesis because there is no limit to the number of po-ible predial A log.- 



cal atom, then, like a point in space, would involve for its precise ton.in.tm an 



endless process. We ean only say, in a general way, that a term, however o ,,,,,,- 



nate, may be made more determinate still, but not that i, can b. ma.lc a >■ lately ,1c 

 terminate Such a term as - the second Philip of Macedon • is s.,11 capable of log.ca 



d 



Philip drunk and Philip sober, for example ; but wc call 



It is a term 



because that which is denoted by it is in only one pi 

 not absolutely indivisible, but indivisible as long as we neglect tfferen es t m d 

 the differences which accompany them. Such diflerences wc h*^^£ » 



_ of substances. In the division of relation-, etc., we do not. of 



vir Knt «-p disregard some others. There B nothing 



course disregard these differences, but we disregaiu bu.i 

 course, disre ara * fliffpre „ C e from being convent iomilly neglected in some 



to prevent almost any sort of difference nom g WoniP8 indivisible 



discourse, and if I be a term which in consequence of such n ;lect becomes 



in that discourse, we have in that discourse, 



the logical division 



in 



i . 





ti 



