OF ARTS AND SCIENCES : NOVEMBER 13, 1867. 421 



% 3. Of the Different Senses in which the Terms Extension and Com- 

 prehension have been accepted. 



The terms extension and comprehension, and their - synonymes, are 

 taken in different senses by different writers. This is partly owing to 

 the fact that while most writers speak only of the extension and com- 

 prehension of concepts, others apply these terms equally to concepts 

 and judgments (Rosling), others to any mental representation (Uber- 

 weg and many French writers), others to cognition generally (Baum- 

 garten), others to "terms" (Fowler, Spalding), others to names 

 (Shedden), others to words (McGregor), others to "meanings" (Jev- 

 ons), while one writer speaks only of the extension of classes and the 

 comprehension of attributes (De Morgan in his Syllabus). 



Comprehension is defined by the Port Royalists as " those attributes 

 which an idea involves in itself, and which cannot be taken away from 

 it without destroying it." 



It will be remembered that the marks of a term are divided by logi- 

 cians first into the necessary and the accidental, and that then the 

 necessary marks are subdivided into such as are strictly essential, that is, 

 contained in the definition, and such as are called proper. Thus it is an 

 essential mark of a triangle to have three sides; it is a proper mark to 

 have its three angles equal to two right angles ; and it is an accidental 

 mark to be treated of by Euclid. 



The definition of the Port Royalists, therefore, makes comprehen- 

 sion include all necessary marks, whether essential or proper. 



The Port Royalists attribute comprehension immediately to any 

 ideas. Very many logicians attribute it immediately only to concepts. 

 Now a concept, as defined by them, is strictly only the essence of an 

 idea ; they ought therefore to include in the comprehension only the 

 essential marks of a term. These logicians, however, abstract so 

 entirely from the real world, that it is difficult to see why these essential 

 marks are not at the same time all the marks of the object as they sup- 

 pose it. 



There can, I think, be no doubt that such writers as Gerlach and 

 Sigwart make comprehension include all marks, necessary or accidental, 

 which are universally predicable of the object of the concept. 



A wain, most German writers regard the comprehension as a sum 

 either of concepts (Drobisch, Bachmann, etc.) or of elements of in- 

 tuition (Trendelenburg). But many English writers regard it as the 



