DEFINITION. 197 



The one is, ' There may exist a figure, bounded by 

 three straight lines :' the other, ' And this figure may 

 be termed a triangle/ The former of these proposi- 

 tions is not a definition at all : the latter is a mere 

 nominal definition, or explanation of the use and 

 application of a term. The first is susceptible of 

 truth or falsehood, and may therefore be made the 

 foundation of a train of reasoning. The latter can 

 neither be true nor false ; the only character it is 

 susceptible of is that of conformity or disconformity 

 to the ordinary usage of language." 



There is a real distinction, then, between defini- 

 tions of names, and what are erroneously called defi- 

 nitions of things ; but it is, that the latter, along with 

 the meaning of a name, covertly asserts a matter of 

 fact. This covert assertion is not a definition, but a 

 postulate. The definition is a mere identical pro- 

 position, which gives information only about the use 

 of language, and from which no conclusions affecting 

 matters of fact can possibly be drawn. The accom- 

 panying postulate, on the other hand, affirms a fact, 

 which may lead to consequences of every degree of 

 importance. It affirms the real existence of Things 

 possessing the combination of attributes set forth in the 

 definition ; and this, if true, maybe foundation sufficient 

 on which to build a whole fabric of scientific truth. 



We have already made, and shall often have to 

 repeat, the remark, that the philosophers who over- 

 threw Realism by no means got rid of the conse- 

 quences of Realism, but retained long afterwards, in 

 their own philosophy, numerous propositions which 

 could only have a rational meaning as part of a Realistic 

 system. It had been handed down from Aristotle, 

 and probably from earlier times, as an obvious truth, 

 that the science of Geometry is deduced from defini- 



