of a definition, are true. Therefore, from the tacit assumption of a matter the premises considered as parts of a of fact.* definition cannot be the real ones. The real premises must be-- A dragon is a really existing thing which breathes flame : A dragon is a really existing serpent: which implied premises being false, the falsity of the conclusion presents no absurdity. If we would determine what conclusion follows from the same ostensible premises when the tacit assumption of real existence is left out, let us, according to the recommendation in a previous page, substitute means for is. We then haveDragon is a word meaning a thing which breathes flame: word meaning Dragon is serpent: a a From which the conclusion is, Some word or words which mean a serpent, also mean a thing which breathes flame : where the conclusion (as well as the premises) is true, and is the only kind of conclusion which can ever follow from a definition, namely, a proposi tion relating to the meaning of words. There is still another shape into which we may transform this syllogism. We may suppose the middle term to be the designation neither of a thing nor of a name, but of an idea. We then have The idea of a dragon is an idea of a thing which breathes flame : The idea of a dragon is an idea of a serpent: Therefore, there is an idea of a serpent, which is an idea of a thing breathing flame. Here the conclusion is true, and also the premises; but the premises are not definitions. They are propositions affirming that an idea existing in the mind includes certain ideal elements. The truth of the conclusion follows from the existence of the psychological phenomenon called the idea of a dragon; and therefore still When, as in this last syllogism, the conclusion is a proposition respecting an idea, the assumption on which it depends may be merely that of the existence of an idea. But when the conclusion is a proposition concerning a Thing, the postulate involved in the definition which stands as the apparent premise is the existence of a thing conformable to the definition, and not merely of an idea conformable to it. This assumption of real existence we always convey the impression that we intend to make when we profess to * 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, clusion as there is in the premises, or, "there is just as much truth in the con 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 I find that it is now necessary to alter the predicates: for it cannot 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." stance of dragons, the premises must be, And to prove this conclusion by the inA 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 stauds 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 cannot be the definition, which is true, but the statement of fact which is false. 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 definition of a circle. § 6. 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 postulates, 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 realised by art. People had a difficulty, therefore, in conceiving that the most certain of all conclusions could rest on premises which, instead of being certainly true, are certainly not true to the full extent asserted. This apparent paradox will be examined when we come to treat of Demonstration; where we shall be able to show that as much of the postulate is true, as is required to support as much as is true of the conclusion. Philosophers, however, to whom this view had not occurred, or whom it did not satisfy, have thought it indispensable that there should be found in definitions something more certain, or at least more accurately true, than the implied postulate of the real existence of a corresponding object. And this something they flattered themselves they had found, when they laid it down that a definition is a statement and analysis not of the mere meaning of a word, nor yet of the nature of a thing, but of an idea. Thus, the proposition, "A circle is a plane figure bounded by a line all the points of which are at an equal distance from a given point within it," was considered by them, not as an assertion that any real circle has that property, (which would not be exactly true,) but that we conceive a circle as having it; that our abstract idea of a circle is an idea of a figure with its radii exactly equal. Conformably to this it is said, that the subject-matter of mathematics, and of every other demonstrative science, is not things as they really exist, but abstractions of the mind. A geometrical line is a line without breadth; but no such line exists in nature; it is a notion merely suggested to the mind by its experience of nature. The definition (it is said) is a definition of this mental line, not of any actual line: and it is only of the mental line, not of any line existing in nature, that the theorems of geometry are accurately true. Allowing this doctrine respecting the nature of demonstrative truth to be correct (which, in a subsequent place, I shall endeavour to prove that it is not,) even on that supposition, the conclusions which seem to follow from a definition do not follow from the definition as such, but from an implied postulate. Even if it be true that there is no object in nature answering to the definition of a line, and that the geometrical properties of lines are not true of any lines in nature, but only of the idea of a line; the definition, at all events, postulates the real existence of such an idea: it assumes that the mind can frame, or rather has framed, the notion of length without breadth, and without any other sensible property whatever. To me, indeed, it appears that the mind cannot form any such notion; it cannot conceive length without breadth; it can only, in contemplating objects, attend to their length, exclusively of their other sensible qualities, and so determine what properties may be predicated of them in virtue of their length alone. If this be true, the postulate involved in the geometrical definition of a line is the real existence, not of length without breadth, but merely of length, that is, of long objects. This is quite enough to G which, like other practical questions of terminology, requires for its solution that we should enter, and sometimes enter very deeply, into the properties not merely of names but of the things named. Although the meaning of every concrete general name resides in the support all the truths of geometry, should be, the meaning of a name; since every property of a geometrical line is really a property of all physical objects in so far as possessing length. But even what I hold to be the false doctrine on the subject, leaves the conclusion that our reasonings are grounded on the matters of fact postulated in definitions, and not on the definitions themselves, entirely unaffect-attributes which it connotes, the obed; and accordingly this conclusion is jects were named before the attrione which I have in common with Dr. butes; as appears from the fact that Whewell, in his Philosophy of the In- in all languages, abstract names are ductive Sciences: though, on the nature mostly compounds or other derivaof demonstrative truth, Dr. Whewell's tives of the concrete names which opinions are greatly at variance with correspond to them. Connotative mine. And here, as in many other names, therefore, were, after proper instances, I gladly acknowledge that names, the first which were used: his writings are eminently serviceable and in the simpler cases, no doubt, a in clearing from confusion the initial distinct connotation was present to steps in the analysis of the mental the minds of those who first used the processes, even where his views re- name, and was distinctly intended by specting the ultimate analysis are such them to be conveyed by it. The as (though with unfeigned respect) I first person who used the word white, cannot but regard as fundamentally as applied to snow or to any other object, knew, no doubt, very well what quality he intended to predicate, and had a perfectly distinct conception in his mind of the attribute signified by the name. erroneous. § 7. Although, according to the opinion here presented, Definitions are properly of names only, and not of things, it does not follow from this that definitions are arbitrary. How to define a name, may not only be an inquiry of considerable difficulty and intricacy, but may involve considerations going deep into the nature of the things which are denoted by the name. Such, for instance, are the inquiries which form the subjects of the most important of Plato's Dialogues; as, "What is rhetoric?" the topic of the Gorgias, or "What is justice?" that of the Republic. Such, also, is the question scornfully asked by Pilate, "What is truth?" and the fundamental question with speculative moralists in all ages, "What is virtue?" It would be a mistake to represent these difficult and noble inquiries as having nothing in view beyond ascertaining the conventional meaning of a name. They are inquiries not so much to determine what is, as what But where the resemblances and differences on which our classifications are founded are not of this palpable and easily determinable kind; especially where they consist not in any one quality but in a number of qualities, the effects of which, being blended together, are not very easily discriminated, and referred each to its true source; it often happens that names are applied to nameable objects, with no distinct connotation present to the minds of those who apply them. They are only influenced by a general resemblance between the new object and all or some of the old familiar objects which they have been accustomed to call by that name. This, as we have seen, is the law which even the mind of the philosopher must follow, in giving names to the simple elementary feelings of our nature; but, where the things to be named are complex wholes, a philosopher is When a not content with noticing a general | name; so that it at last denotes a resemblance; he examines what the confused huddle of objects, having resemblance consists in: and he only nothing whatever in common; and gives the same name to things which connotes nothing, not even a vague resemble one another in the same and general resemblance. definite particulars. The philosopher, name has fallen into this state, in therefore, habitually employs his gen- which by predicating it of any object eral names with a definite connotation. we assert literally nothing about the But language was not made, and can object, it has become unfit for the only in some small degree be mended, purposes either of thought or of the by philosophers. In the minds of communication of thought; and can the real arbiters of language, general only be made serviceable by stripping names, especially where the classes it of some part of its multifarious they denote cannot be brought before denotation, and confining it to objects the tribunal of the outward senses to possessed of some attributes in combe identified and discriminated, con- mon, which it may be made to connote little more than a vague gross note. Such are the inconveniences of resemblance to the things which they a language which "is not made, but were earliest, or have been most, grows." Like the governments which accustomed to call by those names. are in a similar case, it may be comWhen, for instance, ordinary persons pared to a road which is not made, predicate the words just or unjust of but has made itself: it requires conany action, noble or mean of any senti- tinual mending in order to be passable. ment, expression, or demeanour, statesman or charlatan of any personage figuring in politics, do they mean to affirm of those various subjects any determinate attributes, of whatever kind? No they merely recognise, as they think, some likeness, more or less vague and loose, between these and some other things which they have been accustomed to denominate or to hear denominated by those appellations. Language, as Sir James Mackintosh used to say of governments, "is not made, but grows." A name is not imposed at once and by previous purpose upon a class of objects, but is first applied to one thing, and then extended by a series of transitions to another and another. By this process (as has been remarked by several writers, and illustrated with great force and clearness by Dugald Stewart in his Philosophical Essays) a name not unfrequently passes by successive links of resemblance from one object to another, until it becomes applied to things having nothing in common with the first things to which the name was given; which, how ever, do not, for that reason, drop the From this it is already evident why the question respecting the definition of an abstract name is often one of so much difficulty. The question, What is justice? is, in other words, What is the attribute which mankind mean to predicate when they call an action just? To which the first answer is, that having come to no precise agreement on the point, they do not mean to predicate distinctly any attribute at all. Nevertheless, all believe that there is some common attribute belonging to all the actions which they are in the habit of calling just. The question then must be, whether there is any such common attribute? and, in the first place, whether mankind agree sufficiently with one another as to the particular actions which they do or do not call just, to render the inquiry, what quality those actions have in common, a possible one: if so, whether the actions really have any quality in common; and if they have, what it is. Of these three, the first alone is an inquiry into usage and convention; the other two are inquiries into matters of fact. And if the second question (whether the actions form a class at all) has been answered negatively, there remains a fourth, often more arduous than all the rest, namely, how best to form a class artificially, which the name may denote. And here it is fitting to remark, that the study of the spontaneous growth of languages is of the utmost importance to those who would logically remodel them. The classifications rudely made by established language, when retouched, as they almost all require to be, by the hands of the logician, are often in themselves excellently suited to his purposes. As compared with the classifications of a philosopher, they are like the customary law of a country, which has grown up as it were spontaneously, compared with laws methodised and digested into a code: the former are a far less perfect instrument than the latter; but being the result of a long, though unscientific, course of experience, they contain a mass of materials which may be made very usefully available in the formation of the systematic body of written law. In like manner, the established grouping of objects under a common name, even when founded only on a gross and general resemblance, is evidence, in the first place, that the resemblance is obvious, and therefore considerable; and, in the next place, that it is a resemblance which has struck great numbers of persons during a series of years and ages. Even when a name, by successive extensions, has come to be applied to things among which there does not exist this gross resemblance common to them all, still at every step in its progress we shall find such a resemblance. And these transitions of the meaning of words are often an index to real connections between the things denoted by them, which might otherwise escape the notice of thinkers; of those at least who, from using a different language, or from any difference in their habitual associations, have fixed their attention in preference on some other aspect of the things. The history of philosophy abounds in examples of such oversights, committed for want of perceiving the hidden link that connected together the seemingly disparate meanings of some ambiguous word. * Whenever the inquiry into the definition of the name of any real object consists of anything else than a mere comparison of authorities, we tacitly assume that a meaning must be found for the name, compatible with its continuing to denote, if possible all, but at any rate the greater or the more important part, of the things of which it is commonly predicated. The inquiry, therefore, into the definition, is an inquiry into the resemblances and differences among those things: whether there be any resemblance running through them all; if not, through what portion of them such a general resemblance can be traced: and finally, what are the common attributes, the possession of which gives to them all, or to that portion of them, the character of resemblance which has led to their being classed together. When these common attributes have been ascertained and specified, the name which belongs in common to the resembling objects acquires a distinct instead of a vague connotation; and by possess "Few people" (I have said in another ledge of Things is required to enable a man "have reflected how great a knowplace) to affirm that any given argument turns wholly upon words. There is, perhaps, which is not used in almost innumerable not one of the leading terms of philosophy shades of meaning, to express ideas more or less widely different from one another. Between two of these ideas a sagacious and penetrating mind will discern, as it were intuitively, an unobvious link of connec tion, upon which, though perhaps unable to give a logical account of it, he will found critic, not having so keen an insight into a perfectly valid argument, which his the Things, will mistake for a fallacy turning on the double meaning of a term. And the greater the genius of him who thus safely leaps over the chasm, the greater will probably be the crowing and vainglory of the mere logician, who, hobbling after him, evinces his own superior wisdom by using on its brink, and giving up as desperate his proper business of bridging it over."' |