Professor Bain, in his Logic, takes a peculiar view of Definition. He holds (i., 71) with the present work, that “the definition in its full import, is the sum of all the properties connoted by the name; it exhausts the meaning of a word.” But he regards the meaning of a general name as including, not indeed all the common properties of the class named, but all of them that are ultimate properties, not resolvable into one another. “The enumeration of the attributes of oxygen, of gold, of man, should be an enumeration of the final (so far as can be made out), the underivable, powers or functions of each,” and nothing less than this is a complete Definition (i., 75). An independent property, not derivable from other properties, even if previously unknown, yet as soon as discovered becomes, according to him, part of the meaning of the term, and should be included in the definition. “When we are told that diamond, which we know to be a transparent, glittering, hard, and high-priced substance, is composed of carbon, and is combustible, we must put these additional properties on the same level as the rest; to us they are henceforth connoted by the name” (i., 73). Consequently the propositions that diamond is composed of carbon, and that it is combustible, are regarded by Mr. Bain as merely verbal propositions. He carries this doctrine so far as to say that unless mortality can be shown to be a consequence of the ultimate laws of animal organization, mortality is connoted by man, and “Man is Mortal” is a merely verbal proposition. And one of the peculiarities (I think a disadvantageous peculiarity) of his able and valuable treatise, is the large number of propositions requiring proof, and learned by experience, which, in conformity with this doctrine, he considers as not real, but verbal, propositions.
The objection I have to this language is that it confounds, or at least confuses, a much more important distinction than that which it draws. The only reason for dividing Propositions into real and verbal, is in order to discriminate propositions which convey information about facts, from those which do not. A proposition which affirms that an object has a given attribute, while designating the object by a name which already signifies the attribute, adds no information to that which was already possessed by all who understood the name. But when this is said, it is implied that, by the signification of a name, is meant the signification attached to it in the common usage of life. I can not think we ought to say that the meaning of a word includes matters of fact which are unknown to every person who uses the word unless he has learned them by special study of a particular department of Nature; or that because a few persons are aware of these matters of fact, the affirmation of them is a proposition conveying no information. I hold that (special scientific connotation apart) a name means, or connotes, only the properties which it is a mark of in the general mind; and that in the case of any additional properties, however uniformly found to accompany these, it remains possible that a thing which did not possess the properties might still be thought entitled to the name. Ruminant, according to Mr. Bain’s use of language, connotes cloven-hoofed, since the two properties are always found together, and no connection has ever been discovered between them: but ruminant does not mean cloven-hoofed; and were an animal to be discovered which chews the cud, but has its feet undivided, I venture to say that it would still be called ruminant.
In the fuller discussion which Archbishop Whately has given to this subject in his later editions, he almost ceases to regard the definitions of names and those of things as, in any important sense, distinct. He seems (9th ed., p. 145) to limit the notion of a Real Definition to one which “explains any thing more of the nature of the thing than is implied in the name;” (including under the word “implied,” not only what the name connotes, but every thing which can be deduced by reasoning from the attributes connoted). Even this, as he adds, is usually called not a Definition, but a Description; and (as it seems to me) rightly so called. A Description, I conceive, can only be ranked among Definitions, when taken (as in the case of the zoological definition of man) to fulfill the true office of a Definition, by declaring the connotation given to a word in some special use, as a term of science or art: which special connotation of course would not be expressed by the proper definition of the word in its ordinary employment.
Mr. De 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 general 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.
In the only attempt which, so far as I know, has been made to refute the preceding argumentation, it is maintained that in the first form of the syllogism,
A dragon is a thing which breathes flame,
A dragon is a serpent,
Therefore some serpent or serpents breathe flame,
“there is just as much truth in the conclusion as there is in the premises, or rather, no more in the latter than in the former. If the general name serpent includes both real and imaginary serpents, there is no falsity in the conclusion; if not, there is falsity in the minor premise.”
Let us, then, try to set out the syllogism on the hypothesis that the name serpent includes imaginary serpents. We shall find that it is now necessary to alter the predicates; for it can not be asserted that an imaginary creature breathes flame; in predicating of it such a fact, we assert by the most positive implication that it is real, and not imaginary. The conclusion must run thus, “Some serpent or serpents either do or are imagined to breathe flame.” And to prove this conclusion by the instance of dragons, the premises must be, A dragon is imagined as breathing flame. A dragon is a (real or imaginary) serpent: from which it undoubtedly follows, that there are serpents which are imagined to breathe flame; but the major premise is not a definition, nor part of a definition; which is all that I am concerned to prove.
Let us now examine the other assertion—that if the word serpent stands for none but real serpents, the minor premise (a dragon is a serpent) is false. This is exactly what I have myself said of the premise, considered as a statement of fact: but it is not false as part of the definition of a dragon; and since the premises, or one of them, must be false (the conclusion being so), the real premise can not be the definition, which is true, but the statement of fact, which is false.
Contraries:
All A is B
No A is B