162 NAMES ,AND PROPOSITIONS. 



B C D." Here is an assumption that a figure, such as the 

 definition expresses, may be described ; which is no other than 

 the postulate, or covert assumption, involved in the so-called 

 definition. But whether that figure be called a circle or not 

 is quite immaterial. The purpose would be as well answered, 

 in all respects except brevity, were we to say, "Through the 

 point B, draw a line returning into itself, of which every point 

 shall be at an equal distance from the point A." By this the 

 definition of a circle would be got rid of, and rendered need- 

 less ; but not the postulate implied in it ; without that the 

 demonstration could not stand. The circle being now described, 

 let us proceed to the consequence. " Since B C D is a circle, 

 the radius B A is equal to the radius C A." B A is equal to 

 C A, not because B C D is a circle, but because B C D is a 

 figure with the radii equal. Our warrant for assuming that 

 such a figure about the centre A, with the radius B A, may be 

 made to exist, is the postulate. Whether the admissibility of 

 these postulates rests on intuition, or on proof, may be a 

 matter of dispute ; but in either case they are the premises on 

 which the theorems depend ; and while these are retained it 

 would make no difference in the certainty of geometrical 

 truths, though every definition in Euclid, and every technical 

 term therein defined, were laid aside. 



It is, perhaps, superfluous to dwell at so much length on 

 what is so nearly self-evident ; but when a distinction, obvious 

 as it may appear, has been confounded, and by powerful intel- 

 lects, it is better to say too much than too little for the pur- 

 pose of rendering such mistakes impossible in future. I will, 

 therefore, detain the reader while I point out one of the absurd 

 consequences flowing from the supposition that definitions, as 

 such, are the premises in any of our reasonings, except such 

 as relate to words only. If this supposition were true, we 

 might argue correctly from true premises, and arrive at a false 

 conclusion. We should only have to assume as a premise the 

 definition of a nonentity; or rather of a name which has 

 no entity corresponding to it. Let this, for instance, be our 

 definition : 



A dragon is a serpent breathing flame. 



