94 



NAMES AND PROPOSITIONS. 



of the manner in which we intend to 

 employ 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 term. But it is not 

 correct to call an expression of this 

 sort a peculiar kind of detiiiition. Its 

 difference from the other kind con- 

 sists in this, that it is not a definition, 

 but a definition and something more. 

 The definition above given of a 

 triangle, obviously comprises not one, 

 but two propositions, perfectly distin- 

 guishable. 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 propositions is 

 not a definition at all : the latter is a 

 mere nominal definition, or explana- 

 tion 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 disconf ormity 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 identical proposition, which 

 gives information only about the use 

 of language, and from which no con- 

 clusions affecting matters of fact can 

 possibly be drawn. The accompany- 

 ing postulate, on the other hand, 

 affirms a fact which may lead to con- 

 sequences of every degree of impor- 

 tance. It affirms 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 

 consequences of Realism, but retained 

 long afterwards, in their own philo- 

 sophy, 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 definitions. 

 This, so long as a definition was con- 

 sidered to be a proposition " unfolding 

 the nature of the thing," did well 

 enough. But Hobbes followed, and 

 rejected utterly the notion that a de- 

 finition 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 pre- 

 decessors that the a.pxo-i< principia, 

 or original premises of mathematics, 

 and even of all science, are defini- 

 tions; producing the singular para- 

 dox, 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 natixre ; 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 abandon- 

 ing 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 neces- 

 sary, from which of the two is the 

 inference really drawn ? From the 

 existence of a thing having the pro- 



