198 NAMES AND PROPOSITIONS. v 



tions. This, so long as a definition was considered 

 to be a proposition " unfolding the nature of the 

 thing," did well enough. But Hobbes came, and 

 rejected utterly the notion that a definition 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 apw^ 

 principia, or original premisses 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 man- 

 kind concerning the signification of words. 



To save the credit of the doctrine that definitions 

 are the premisses of scientific knowledge, the proviso 

 is sometimes added, that they are so only under a 

 certain condition, namely, that they be framed con- 

 formably 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, too often made, to escape from the 

 necessity of abandoning 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, provided 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 premisses in Euclid's Elements ; the definition, let 

 us say, of a circle. This, being analyzed, consists of 

 two propositions ; the one an assumption with respect 

 to a matter-of-fact, the other a genuine definition. 



