DEFINITION. 99 



imal,' &:c., the sense would remain unchanged : in the second, ' A tri- 

 angle means,' &c., the meaning would bo altered, since it would be 

 obviously impossible to deduce any of the truths of geometry from a 

 proposition expressive only of the maimer in which we intend to em- 

 ploy a particular sign. 



" There are, therefore, expressions, commonly passing for definitions, 

 which include in themselves more than the mere explanation of the 

 meaning of a temi. But it is not correct to call an expression of this 

 sort a peculiar kind of definition. Its difference fi-om the other kind 

 consists in this, that it is not a definition, but a definition and sometliing 

 more. The definition above given of a triangle, obviously comprises 

 not one, but two propositions, perfectly distinguishable. The one is, 

 * There may exist a figure, bounded by three straight lines :' the other, 

 ' And this figui'e may be termed a triangle.' The former of these pro- 

 positions is not a definition at all : the latter is a mere nominal defini- 

 tion, or explanation of the use and application of a term. The first is 

 susceptible of truth or falsehood, and may therefore be made the foun- 

 dation 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 discon- 

 formity to the ordinary usage of language." 



There is a i-eal 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 identical 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, affirms a fact, which may lead to consequences of 

 every degi-ee of importance. It affii-ms the real 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 ti'uth. 



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 consequences of Realism, but retained long afterwards, in their 

 own philosophy, numerous propositions which could only have a ra- 

 tional 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 fi-om definitions. This, so 

 long as a definition was considered to be a proposition " unfoldino- the 

 nature of the thing," did well enough. But Hobbes came, and re- 

 jected utterly the notion that a definition declares the natm-e of the 

 thing, or does anything but state the meaning of a name ; yet he con- 

 tinued to affirm as broadly as any of his predecessors, that the dpxac, 

 principia, or original premisses of mathematics, and even of all science, 

 are definitions ; producing the singular paradox, that systems of scien- 

 tific truth, nay, all truths whatever at which we airive by reasoning, 

 are deduced fiom the arbitrary conventions of mankind 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 firamed con- 

 formably to the phenomena of nature ; that is, that they ascribe such 



