OF ARTS AND SCIENCES : NOVEMBER 13, 1867. 423 



Again, logicians differ as to whether by extension they mean the 

 concepts, species, things, or representations to which the term is habit- 

 ually applied in the judgment, or all to which it is truly applicable. 

 The latter position is held by Herbart, Kiesevvetter, etc. ; the former 

 by Duncan, Spalding, Vorlander, Uberweg, etc. 



Some logicians include only actual things, representations, etc., under 

 extension (Bachmann, Fries, Herbart) ; others extend it to such as 

 are merely possible (Esser, Ritter, Gerlach). 



Finally, some few logicians speak of the two quantities as numerical, 

 while most writers regard them as mere aggregates of diverse objects 

 or marks. 



§ 4. Denials of the Inverse Proportionality of the two Quantities, and 

 Suggestions of a third Quantity. 



Until lately the law of the inverse proportionality of extension and 

 comprehension was universally admitted. It is now questioned on 

 various grounds. 



Drobisch says that the comprehension varies arithmetically, while 

 the extension varies geometrically. This is true, in one sense. 



Lotze, after remarking that the only conception of a universal which 

 we can have is the power of imagining singulars under it, urges that 

 the possibility of determining a concept in a way corresponding to each 

 particular under it is a mark of that concept, and that therefore the 

 narrower concepts have as many marks as the wider ones. But, I 

 reply, these marks belong to the concept in its second intention, and are 

 not common marks of those things to which it applies, and are there- 

 fore no part of the comprehension. They are, in fact, the very marks 

 which constitute the extension. No one ever denied that extension is 

 a mark of a concept ; only it is a certain mark of second intention. 



Vorlander's objection is much more to the purpose. It is that if 

 from any determinate notion, as that of Napoleon, we abstract all 

 marks, all determination, what remains is merely the conception some- 

 thing, which has no more extension than Napoleon. " Something" has 

 an uncertain sphere, meaning either this thing or that or the other, but 

 has no general extension, since it means one thing only. Thus, before 

 a race, we can say that some horse will win, meaning this one, that 

 one, or that one; but by some horse we mean but one, and it therefore 

 has no more extension than would a term definitely indicating which, — 

 although this latter would be more determinate, that is, would have 



