202 NAMES AND PROPOSITIONS. 



dragon, while there was no doubt of its being included 

 in the definition of a circle. 



7. One of the circumstances which have con- 

 tributed to keep up the notion, that demonstrative 

 truths follow from definitions rather than from the 

 postulates implied in those definitions, is, that the 

 postulates, even in those sciences which are consi- 

 dered to surpass all others in demonstrative certainty, 

 are not always exactly true. It is not true that a 

 circle exists, or can be described, which has all its 

 radii exactly equal. Such accuracy is ideal only ; it is 

 not found in nature, still less can it be realised by art. 

 People had a difficulty, therefore, in conceiving that 

 the most certain of all conclusions could rest upon 

 premisses which, instead of being certainly true, are 

 certainly not true to the whole extent asserted. This 

 apparent paradox will be examined when we come to 

 treat of Demonstration; where we shall be able to show 

 that as much of the postulate is true, as is required 

 to support as much as is true of the conclusion. 

 Philosophers however to whom this view had not 

 occurred, or whom it did not satisfy, have thought it 

 indispensable that there should be found in definitions 

 something more certain, or at least more accurately 

 true, than the implied postulate of the real existence 

 of a corresponding object. And this something they 

 flattered themselves they had found, when they laid it 

 down that a definition is a statement and analysis 

 not of the mere meaning of a word, nor yet of the 

 nature of a thing, but of an idea. Thus, the pro- 

 position, 'A circle is a plane figure bounded by a line 

 all the points of which are at an equal distance from 

 a given point within it/ was considered by them, not 

 as an assertion that any real circle has that property, 



