204 NAMES AND PROPOSITIONS. 



nition of a line, is the real existence, not of length 

 without breadth, but merely of length, that is, of long 

 objects. This is quite enough to support all the 

 truths of geometry, since every property of a geo- 

 metrical line is really a property of all physical objects 

 possessing length. But even what I hold to be the 

 false doctrine on the subject, leaves the conclusion 

 that our reasonings are grounded upon the matters of 

 fact postulated in definitions, and not upon the defini- 

 tions themselves, entirely unaffected ; and accordingly 

 I am able to appeal in confirmation of this conclusion, 

 to the authority of Mr. Whewell, in his recent treatise 

 on The Philosophy of the Inductive Sciences. On the 

 nature of demonstrative truth, Mr. Whewell's opinions 

 are greatly at variance with mine, but on the par- 

 ticular point in question it gives me great pleasure to 

 observe, that there is a complete agreement between us. 

 And here, as in many other instances, I gladly acknow- 

 ledge that his writings are eminently serviceable in 

 clearing from confusion the initial steps in the analysis 

 of the mental processes, even where his views respect- 

 ing the ultimate analysis (a matter generally of far less 

 importance) are such as (though with unfeigned respect) 

 I cannot but regard as fundamentally erroneous. 



8. Although, according to the views here pre- 

 sented, Definitions are properly of names only, and 

 not of things, it does not follow that definition is an 

 easy matter. How to define a name, may not only be 

 an inquiry of considerable difficulty and intricacy, but 

 may turn upon considerations going deep into the 

 nature of the things which are denoted by the name. 

 Such, for instance, are the inquiries which form the 

 subjects of the most important of Plato's Dialogues; 

 as, u What is rhetoric ?" the topic of the Gorgias, or 



