DEFINITION. 161 



science of Geometry is deduced from definitions. This, so 

 long as a definition was considered to be a proposition " un- 

 folding the nature of the thing," did well enough. But 

 Hobbes followed, and rejected utterly the notion that a defi- 

 nition declares the nature of the thing, or does anything but 

 state the meaning of a name ; yet he continued to affirm as 

 broadly as any of his predecessors, that the apxai, principia, 

 or original premises of mathematics, and even of all science, 

 are definitions ; producing the singular paradox, that systems 

 of scientific truth, nay, all truths whatever at which we arrive 

 by reasoning, are deduced from the arbitrary conventions of 

 mankind concerning the signification of words. 



To save the credit of the doctrine that definitions are the 

 premises of scientific knowledge, the proviso is sometimes 

 added, that they are so only under a certain condition, namely, 

 that they be framed conformably to the phenomena of nature ; 

 that is, that they ascribe such meanings to terms as shall suit 

 objects actually existing. But this is only an instance of the 

 attempt so often made, to escape from the necessity of aban- 

 doning old language after the ideas which it expresses have 

 been exchanged for contrary ones. From the meaning of a 

 name (we are told) it is possible to infer physical facts, pro- 

 vided the name has corresponding to it an existing thing. 

 But if this proviso be necessary, from which of the two is 

 the inference really drawn ? From the existence of a thing 

 having the properties, or from the existence of a name meaning 

 them? 



Take, for instance, any of the definitions laid down as 

 premises in Euclid's Elements ; the definition, let us say, of a 

 circle. This, being analysed, consists of two propositions ; 

 the one an assumption with respect to a matter of fact, the 

 other a genuine definition. " A figure may exist, having all 

 the points in the line which bounds it equally distant from a 

 single point within it :" " Any figure possessing this property 

 is called a circle." Let us look at one of the demonstrations 

 which are said to depend on this definition, and observe to 

 which of the two propositions contained in it the demonstra- 

 tion really appeals. " About the centre A, describe the circle 

 VOL. i. 11 



