Any extension of knowledge or alteration in the current opinions respecting the subject-matter may lead to a change more or less extensive in the particulars included in the science; and its composition being thus altered, it may easily happen that a different set of characteristics will be found better adapted as differentiæ for defining its name. to of common terms used in a scientific What is true of the definition of sense, are almost always of the kind any term of science is of course true last spoken of their main purpose is of the definition of a science itself; to serve as the landmarks of scientific and accordingly, (as observed in the classification. And since the classi- Introductory Chapter of this work,) fications in any science are continually the definition of a science must necesmodified as scientific knowledge ad-sarily be progressive and provisional. vances, the definitions in the sciences are also constantly varying. A striking instance is afforded by the words Acid and Alkali, especially the former. As experimental discovery advanced, the substances classed with acids have been constantly multiplying, and by a natural consequence the attributes connoted by the word have receded and become fewer. At first it connoted the attributes of combining with an alkali to form a neutral substance (called a salt); being compounded of a base and oxygen; causticity to the taste and touch; fluidity, &c. The true analysis of muriatic acid into chlorine and hydrogen caused the second property, composition from a base and oxygen, to be excluded from the connotation. The same discovery fixed the attention of chemists upon hydrogen as an important element in acids; and more recent discoveries having led to the recognition of its presence in sulphuric, nitric, and many other acids, where its existence was not previously suspected, there is now a tendency to include the presence of this element in the connotation of the word. But carbonic acid, silica, sulphurous acid, have no hydrogen in their composition; that property cannot therefore be connoted by the term, unless those substances are no longer to be considered acids. Causticity and fluidity have long since been excluded from the characteristics of the class by the inclusion of silica and many other substances in it; and the formation of neutral bodies by combination with alkalis, together with such electrochemical peculiarities as this is supposed to imply, are now the only differentia which form the fixed connotation of the word Acid, as a term of chemical science, In the same manner in which a special or technical definition has for its object to expound the artificial classification out of which it grows; the Aristotelian logicians seem have imagined that it was also the business of ordinary definition to expound the ordinary, and what they deemed the natural, classification of things, namely, the division of them into Kinds; and to show the place which each Kind occupies, as superior, collateral, or subordinate, among other Kinds. This notion would account for the rule that all definition must necessarily be per genus et differentiam, and would also explain why a single differentia was deemed sufficient. But to expound, or express in words, a distinction of Kind has already been shown to be an impossibility: the very meaning of a Kind is, that the properties which distinguish it do not grow out of one another, and cannot therefore be set forth in words, even by implication, otherwise than by enumerating them all and all are not known, nor are ever likely to be so. It is idle, therefore, to look to this as one of the purposes of a definition: while, if it be only required that the definition of a Kind should indicate what kinds include it or are included by it, any definitions which expound the connotation of the names will do this: for the name of each class must neces sarily connote enough of its properties in the pursuit of truth. According to fix the boundaries of the class. If to this, the definitions of which we the definition, therefore, be a full statement of the connotation, it is all that a definition can be required to be.* $5. Of the two incomplete and popular modes of definition, and in what they differ from the complete or philosophical mode, enough has now been said. We shall next examine an ancient doctrine, once generally prevalent, and still by no means exploded, which I regard as the source of a great part of the obscurity hanging over some of the most important processes of the understanding * 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 inIcluded in the definition. "When we are told that diamond, which we know to be a transparent, glittering, hard, and highpriced 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 organisation, mortality is connoted by man, and "Man is mortal" is a merely verbal proposition. And one of the peculiarities (I think a disadvantageous p culiarity) of his able and valuable treatise, is the large number of propositions requiring proof, and learnt by experience, which, in conformity with this doctrine, he considers as not real, but verbal, propositions. have now treated are only one of two sorts into which definitions may be divided, viz. definitions of names, and definitions of things. The former are intended to explain the meaning of a term; the latter, the nature of a thing; the last being incomparably the most important. This opinion was held by the ancient philosophers, and by their followers, with the exception of the Nominalists; but as the spirit of modern metaphysics, until a recent period, has been on the whole a Nominalist spirit, the notion of definitions of things has been to a certain extent in abeyance, still continuing, however, to breed confusion in logic, The objection I have to this language is that it confounds, or at least confuses, a much more important distinction 'han 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 cannot 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 learnt 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 thein 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. * by its consequences indeed rather | " * 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 anything 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 everything 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 fulfil 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. "The distinction between nominal and real definitions, between definitions of words and what are called definitions of things, though conformable to the ideas of most of the Aristotelian logicians, cannot, 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 definitions 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 proposition in which any quality whatever is predicated of the thing unThe folds some part of its nature. 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. 'A Whether this be or be not implied in any given case cannot be collected from the mere form of the expression. centaur is an animal with the upper parts of a man and the lower parts of a horse,' and 'A triangle is a rectilineal figure with three sides,' are, in form, expressions precisely similar; although in the former it is not implied that any thing, conformable 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,' &c., the sense would remain unchanged: in the second, 'A triangle means,' &c., the meaning would be altered, 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 propositions, 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 latter is a mere nominal definition, or explanation 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 disconformity 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 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 degree of importance. 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 philosophy, 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 considered to be a proposition "unfolding the nature of the thing," did well enough. But Hobbes followed, and rejected utterly the notion that a definition 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 predecessors that the apxal, principia, or original premises of mathematics, and even of all science, are definitions; producing the singular paradox, 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 nature; 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 abandoning 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 necessary, from which of the two is the inference really drawn? From the existence of a thing having the pro perties, or from the existence of a name meaning them? in the certainty of geometrical truths, though every definition in Euclid, and every technical term therein defined, were laid aside. It is, perhaps, superfluous to dwell at so much length on what is so nearly self-evident; but when a distinction, obvious as it may appear, has been confounded, and by powerful intellects, it is better to say too much than too little for the purpose of rendering such mistakes impossible in future. I will, therefore, detain the reader while I point out one of the absurd consequences flowing from the supposition that definitions, as such, are the premises in any of our reasonings, except such as relate to words only. If this opposition were true, we might argue correctly from true premises, and arrive at a false conclusion. We should only have to assume as a premise the definition of a nonentity; or rather of a name which has no entity corresponding to it. Let this, for instance, be our definition : A dragon is a serpent breathing flame. Take, for instance, any of the definitions laid down as premises in Euclid's Elements; the definition, let us say, of a circle. This, being analysed, consists of two propositions; the one an assumption with respect to a matter of fact, the other a genuine definition. "A figure may exist, having all the points in the line which bounds it equally distant from a single point within it: "Any figure possessing this property is called a circle.' Let us look at one of the demonstrations which are said to depend on this definition, and observe to which of the two propositions contained in it the demonstration really appeals. "About the centre A, describe the circle B CD." Here is an assumption that a figure, such as the definition expresses, may be described; which is no other than the postulate, or covert assumption, involved in the socalled definition. But whether that figure be called a circle or not is quite immaterial. The purpose would be as well answered in all respects except brevity were we to say, "Through the point B, draw a line returning into itself, of which every point shall be at an equal distance from the point A." By this the definition of a circle would be got rid of, and rendered needless; but not the postulate implied in it; without that the demonstration could not stand. The circle being now described, let us proceed to the consequence. "Since BCD is a circle, the radius B A is equal to the radius C A." BA is equal to C A, not because B C D is a circle, but because BCD is a figure with the radii equal. Our warrant for assuming that such a figure about the centre A, with the radius B A, may be made to exist, is an unexceptional syllogism in the first the postulate. Whether the admissi- mode of the third figure, in which bility of these postulates rests on both premises are true and yet the intuition, or on proof, may be a matter conclusion false; which every logician of dispute; but in either case they knows to be an absurdity. The conare the premises on which the theo-clusion being false and the syllogism rems depend; and while these are correct, the premises cannot be true. retained it would make no difference But the premises, considered as parts This proposition, considered only as a definition, is indisputably correct. A dragon is a serpent breathing flame : the word means that. The tacit assumption, indeed, (if there were any such understood assertion,) of the existence of an object with properties corresponding to the definition, would, in the present instance, be false. Out of this definition we may carve the premises of the following syllogism: A dragon is a thing which breathes A dragon is a serpent: Therefore some serpent or serpents breathe flame : |