424 PROCEEDINGS OF THE AMERICAN ACADEMY 



more comprehension. I am not aware that those who adhere to Kant's 

 unmodified doctrine have succeeded in answering this objection. 



Uberweg has the following remarks.* " To the higher representa- 

 tion, since conformably to its definition it contains only the common 

 elements of content of several lower representations, belongs in com- 

 parison to each of the loAver a more limited content, but a wider circuit. 

 The lower representation, on the contrary, has a richer content but 

 narrower circuit. Yet by no means by every diminution or increase 

 of a given content does the circuit increase or diminish, nor by every 

 increase or diminution of a given circuit does the content diminish or in- 

 crease." I am surprised that he does not explain himself further upon 

 this point, which it is the principal object of this paper to develop. 



De Morgan says : f " According to such statements as I have seen, 

 'man residing in Europe, drawing breath north of the equator, seeing 

 the sun rise before those in America,' would be a more intensively 

 quantified notion than ' man residing in Europe ' ; but certainly not 

 less extensive, for the third and fourth elements of the notion must 

 belong; to those men to whom the first and second belong." Mr. De 

 Morgan adopts the definitions of extension and comprehension given by 

 the Port Royalists. According to those definitions, if the third and 

 fourth elements necessarily belong to the notion to which the first and 

 second belong, they are parts of the comprehension of that second no- 

 tion which is composed of the first and second elements, and therefore 

 the two notions are equal in comprehension ; but if this is not the case, 

 then the second notion can be predicated of subjects of which the first 

 cannot, for example, of" man residing in Europe drawing breath south 

 of the Equator " ; for that there is really no such man will not affect 

 the truth of the proposition, and therefore the second notion is more 

 extensive than the first. 



Two logicians, only, as far as I remember, Archbishop Thomson j 

 and Dr. W. D. Wilson, § while apparently admitting Kant's law, wish 

 to establish a third quantity of concepts. Neither gentleman has de- 

 fined his third quantity, nor has stated what its relations to the other 

 two are. Thomson calls his Denomination. It seems to be the same 

 as Extension regarded in a particular way. Dr. Wilson terms his new 

 quantity Protension ; it has something to do with time, and appears to 

 be generally independent of the other two. It is plain, indeed, that as 



* Logik, 2 te Atifl. § 54. X Laws of Thought, 4th ed., §§ 52, 80. 



t Formal Logic, p. 234. His doctrine is different in the Syllabus. 

 § Logic, Part I. chap. ii. § 5. 



