DEFINITION. 113 



latter is a mere nominal definition, or explanation of the use and applica- 

 tioti 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 definitions of names, and what 

 are erroneously called definitions 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 iden- 

 tical proposition, which gives information only about the use of language, 

 and from which no conclusions affecting matters of fact can possibly be 

 drawn. The accompanying postulate, on the other hand, afiirms a fact, 

 which may lead to consequences of every degree of importance. It afiirms 

 the actual or possible existence of Things possessing the combination of 

 attributes set forth in the definition ; and this, if true, may be 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 overthrew Realism by no means got rid of the con- 

 sequences of Realism, but retained long afterward, 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 prob- 

 ably from earlier times, as an obvious truth, that the science of Geometry 

 is deduced from definitions. This, so long as a definition was considered 

 to be a proposition " unfolding the nature of the thing," did well enough. 

 But Hobbes followed, and rejected utterly the notion that a definition de- 

 clares the nature of the thing, or does any thing but state the meaning of 

 a name; yet he continued to affirm as broadly as any of his predecessors, 

 that the apxal, 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 sig- 

 nification 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 at- 

 :empt so often made, to escape from the necessity of abandoning old lan- 

 guage after the ideas which it expresses have been exchanged for contrary 

 )nes. From the meaning of a name (we are told) it is possible to infer 

 )hysical facts, provided the name has corresponding to it an existing thing. 

 3ut if this proviso be necessary, from which of the two is the inference 

 eally drawn ? From the existence of a thing having the properties, or 

 rom 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 analyzed, con- 

 I ists of two propositions ; the one an assumption with respect to a matter 

 « f fact, the other a genuine definition. " A figure may exist, having all the 

 ] 'Oints in the line which bounds it equally distant from a single point with- 

 i a it :" " Any figure possessing this property is called a circle." Let us 

 1 )ok at one of the demonstrations which are said to depend on this defini- 

 1 ion, and observe to which of the two propositions contained in it the dem- 

 < nstration really appeals. " About the centre A, describe the circle B C P." 



8 



