344 • MEMOIRS OF THE AMERICAN ACADEMY. 



This distinction between the absolutely indivisible and that which is one in number 

 from a particular point of view is shadowed forth in the two words individual 

 (to arofxov) and singidar (to Ka0' etcacrrov) ; but as those who have used the word indi- 

 vidual have not been aware that absolute individuality is merely ideal, it has come 

 to be used in a more general sense,* 



The old logics distinguish between individuum signatum and individuum vagum. 

 * Julius Caesar " is an example of the former ; " a certain man," of the latter. The 

 individuum vagum, in the days when such conceptions were exactly investigated, 

 occasioned great difficulty from its having a certain generality, being capable, appar- 

 ently, of logical division. If we include under the individuum vagum such a term as 

 " any individual man," these difficulties appear in a strong light, for what is true of 

 any individual man is true of all men. Such a term is in one sense not an individual 



# 



term ; for it represents every man. But it represents each man as capable of being 

 denoted by a term which is individual ; and so, though it is not itself an individual 

 term, it stands for any one of a class of individual terms. If we call a thought about 

 a thing in so far as it is denoted by a term, a second intention, we may say that such 

 a term as " any individual man " is individual by second intention. The letters which 

 mathematician uses (whether in algebra or in geometry) are such individuals by 



second 



Such individuals are one in number, for any individual man 



man; they may also be regarded as incapable of logical division, for any individual 

 man, though he may either be a Frenchman or not/is yet altogether a Frenchman or 



ther not, and not some one and some the other. Thus' all the formal 1< 



^ / _ 



lating to individuals will hold good of such individuals by second intention, and 

 same time a universal proposition may at any moment be substituted for 



© 



o 



the 



proposition about such an individual, for nothing can be predicated of such an indi- 

 vidual which cannot be predicated of the whole class. 



There are in the logic of relatives three kinds of terms which involve general sup- 

 positions of individual cases. The first are individual terms, which denote only indi- 

 viduals ; the second are those relatives whose correlatives are individual : I term these 

 infinitesimal relatives ; the third are individual infinitesimal relatives, and these I term 

 elementary relatives. 



• The absolute individual cau no. ouly „„. be realized in «« or though., but cannot cxirt, properly speaking. For 

 whatever lasts for any .,me, however short, i, capable of logical division, because in that time it will undergo some 



t T ' i ' nrt T S ' T d<KS "°' MiSt fOT "* """■ h ° WeVer !hOTt > to «* «* - ■»• All, therefore, that 



«i s rrr fi l '", ', " eX "" S ', " ge ° eral - S ° <*' there " tn " h m the d ° c " iM ° f •**»*> realism. But all that 

 on Uh con nd , , ' f 1 S infi ° itely detCrmin3te " "" aWlut ^ M «"-'- This seem, paradoxical, 



mad rZ dcterm,!' 5 7' ^ ^ *** "*" * ** "**«• ° f « """ ~«P*»- This concepL may be 



EtT^ST ^ " ^ COnCeP ' i0 " ' ^ theref ° re " l8 ^ " * t ™ i — tb " k " "I** " °° 



K 



