DEFINITION. 101 



coiTcct. A dragon is a serpent breathing flame : the word means tliat. 

 The, tacit assumption, indeed (if there were any such understood 

 assertion), of the existence of an object with properties conesponding 

 to the definition, would, in the present instance, be false. Out of this 

 definition we may carve the premisses of the following syllogism : 



A dragon is a thing which breathes flame : 



But a dragon is a sei-jjent : 

 From which the conclusion is, 



Therefoie some serpent or serpents breathe flame : — 

 an unexceptionable syllogism, in the first mode of the third figure, in 

 which both premisses are true and yet the conclusion false ; which 

 every logician knows to be an absurdity. The conclusion being false 

 and the syllogism con-ect, the j^rcmisses cannot be true. But the 

 premisses, considered as parts of a definition, are true : there is no 

 possibility of controverting them. Therefore, the premisses considered 

 as parts of a definition cannot be the real ones. The real premisses 

 must be : 



A dragon is a really existing thing which breathes flame : 



A dragon is a really existing serpent : 

 which implied premisses being false, the falsity of the conclusion pre- 

 sents no absurdity. If we would determine what conclusion follows 

 from the same ostensible premisses when the tacit assumption of real 

 existence is left out, let us, according to the recommendation in the 

 Westminster Review, substitute means for is. We then have : 



A dragon is a word meaning a thing which breathes flame : 



A dragon is a word meaning a serpent : 

 From which the conclusion is. 



Some word or words whieh mean a serpent, also mean a thing 

 which breathes flame : 

 where the conclusion (as well as the premisses) is true, and is the only 

 kind of conclusion which can ever follow from a definition, namely, a 

 proposition relating to the meaning of words. If it relate to anything 

 else, we may know that it does not follow from the definition, but from 

 the tacit assumption of a matter of fact. 



It is only necessary further to inquire, in what cases that tacit as- 

 sumption is really made, and in what cases not. Unless we declare 

 the contrary, we always convey the impression that we intend to make 

 the assumption, when we profess to define any name which is already 

 known to be a name of really existing objects. On this account it is, 

 that the assumption was not necessarily implied in the definition of a 

 dragon, while there was no doubt of its being included in the defini- 

 tion of a circle. 



§ 7. One of the circumstances which have contributed to keep up 

 the notion, that demonstrative truths follow from definitions rather 

 than from the postulates implied in those definitions, is, that the pos- 

 tulates, even in those sciences which are considered to surpass all 

 others in demonstrative certainty, are not always exactly true. It is 

 not true that a circle exists, or can be described, which has all its radii 

 exactly equal. Such accuracy is ideal only ; it is not found in nature, 

 still less can it be realized by art. People had a difficulty, therefore, 

 in conceiving that the most certain of all conclusions could rest upon 

 premisses which, instead of being certainly true, are certainly not true 



