DEFINITION. 165 



sition respecting an idea, the assumption on which it depends 

 may be merely that of the existence of an idea. But when 

 the conclusion is a proposition concerning a Thing, the postu- 

 late involved in the definition which stands as the apparent 

 premise, is the existence of a thing conformable to the defini- 

 tion, and not merely of an idea conformable to it. This as- 

 sumption of real existence will always convey the impression 

 that we intend to make, when we profess to define any name 

 which is already known to be a name of really existing objects. 

 On this account it is, that the assumption was not necessarily 

 implied in the definition of a dragon, while there was no doubt 

 of its being included in the definition of a circle. 



6. One of the circumstances which have contributed 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 considered 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 realized by art. People had a difficulty, 

 therefore, in conceiving that the most certain of all con- 

 clusions could rest on premises which, instead of being cer- 

 tainly true, are certainly not true to the full 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 accu- 

 rately 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 mean- 

 ing of a word, nor yet of the nature of a thing, but of an idea. 

 Thus, the proposition, " A circle is a plane figure bounded 



