112 NAMES AND PROPOSITIONS. 



minster Hevleic for January, 1828, and containing some opinions which I 

 no longer entertain, I find the following observations on the question now 

 before us ; observations with which my present view of that question is 

 still sufficiently in accordance. 



"The distinction between nominal and real definitions, between defini- 

 tions of words and what are called definitions of things, though conforma- 

 ble to the ideas of most of the Aristotelian logicians, can not, as it appears 

 to us, be maintained. We apprehend that no definition is ever intended to 

 ' explain and unfold the nature of a thing.' It is some confirmation of our 

 opinion, that none of those writers who have thought that there were defini- 

 tions of things, have ever succeeded in discovering any criterion by which 

 the definition of a thing can be distinguished from any other proposition 

 relating to the thing. The definition, they say, unfolds the nature of the 

 thing: but no definition can unfold its whole nature; and every proposi- 

 tion in which any quality whatever is predicated of the thing, unfolds some 

 part of its nature. The true state of the case we take to be this. All 

 definitions are of names, and of names only ; but, in some definitions, it is 

 clearly apparent, that nothing is intended except to explain the meaning of 

 the word ; while in others, besides explaining the meaning of the word, it 

 is intended to be implied that there exists a thing, corresponding to the 

 word. Whether this be or be not implied in any given case, can not be 

 collected from the mere form of the expression. 'A centaur is an animal 

 with the upper parts of a man and the lower parts of a horse,' and 'A tri- 

 angle is a rectilineal figure with three sides,' are, in form, expressions pre- 

 cisely similar ; although in the former it is not implied that any thing, con- 

 formable to the term, really exists, while in the latter it is; as may be seen 

 by substituting in both definitions, the word means for is. In the first 

 expression, 'A centaur means an animal,' etc., the sense would remain un- 

 changed : in the second, 'A triangle means,' etc., the meaning would be al- 

 tered, since it would be obviously impossible to deduce any of the truths 

 of geometry from a proposition expressive only 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 definition. Its difference from the other kind consists 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 proposi- 

 tions, perfectly distinguishable. 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 



tation of course would not be expressed by the proper definition of the word in its ordinai-y 

 employment. 



Mr. I)e Morgan, exactly reversing the doctrine of Archbishop Whately, understands by a 

 Real Definition one which contains less than the Nominal Definition, provided only that what 

 it contains is sufficient for distinction. "By real definition I mean such an explanation of 

 the word, be it the whole of the meaning or only part, as will be sufficient to separate the 

 things contained under that word from all others. Thus the following, I believe, is a complete 

 definition of an elephant : An animal which naturally drinks by drawing the water into its 

 nose, and then spurting it into its mouth." — Formal Logic, p. 36. Mr. De Morgan's gen- 

 eral proposition and his example are at variance ; for the peculiar mode of drinking of the 

 elephant certainly forms no part of the meaning of the word elephant. It could not be said, 

 because a person happened to be ignorant of this property, that he did not know what an 

 elephant means. 



