that the narrower the class the larger will be the number, not merely of common attributes, but also of those which are connotative or defining attributes; since these have been identified with each other. This we know to be true to some extent; but carry out the process to the end of the scale, where the class becomes a minimum by consisting of but one individual, and what do we find? The number of attributes possessed by him may be considered infinite: therefore, on the principle of including all that exist in common throughout the class, we ought to admit that in this limiting case every attribute of the individual is a part of his connotation, that is, of the meaning of his name, though the overwhelming majority of them must, from the nature of the case, be known only to the individual himself. This I should have thought was a reduction to absurdity, but it has been adopted and defended by Jevons' with the distinct assertion that singular or proper names so far from being destitute of connotation "exceed all other terms in that kind of meaning". That one class of singular names may have a maximum of connotation I, of course, admit; viz. that class which we have already described as being built up of a number of significant general names. But even here the number of implied attributes is merely the finite total of what are given by the summation of the connoted attributes of the component group of names. The view in question entirely misapprehends the nature of the Proper name. The express function of such a name when it is understood,—as it almost universally has been, -as an unmeaning mark imposed upon an individual for the purpose of distinguishing him, is to bar any such confusion, by drawing a clear distinction between names which do, and those which do not, imply attributes.

There is another view which takes the opposite extreme, and seeks to reduce the number of determining attributes to the utmost. This reduction may be effected in two slightly different ways, viz. by confining them to the smallest number which are (1) sufficient to distinguish the group of objects in question from others, or (2) sufficient to yield deductively all the attributes commonly reckoned to be included in the name. The full consideration of these views would lead us into a discussion

1 Principles of Science, p. 27.

of the nature of Definition, a subject which we must defer to a future chapter. At present it will be sufficient to remark that in each of these cases a very different design is being proposed from that which we have contemplated above; that, in fact, such writers substitute for the direct enumeration of a number of attributes, certain devices for most conveniently distinguishing the objects in possession of those attributes. These may be very convenient practical substitutes, and in some kinds of definition for artificial purposes they may be fairly employed, but nothing except a change in our general point of view can ever make them any part of the meaning of the term.

We have several times incidentally introduced the distinction between 'implication' and mere 'suggestion', claiming that what falls under the former head is, and what falls under the latter is not, part of the meaning of a term. It may be desirable to clear up this distinction a little more fully.

It must be frankly admitted that we shall find it no easy task to draw the line. By way of indicating its position take the following example: I find in a parish register an entry of the burial of "John Thistlethwaite Barker, farrier": what sort of information can we extract from this bare designation? The answer, I suppose, would be that we know for absolute certainty (if the register be correct) that his business was to shoe horses: we know with a certainty which does not feel to us to be less that he was of the male sex; we feel tolerably certain that his father's name was Barker: and we feel a strong presumption that he had some relation of the name of Thistlethwaite. I am inclined to think that the partition line between implication and suggestion must be drawn between the first two of these. The former seems to me to involve a matter of right and wrong, of truth and falsehood; the others involve at most a violent presumption. It is no part of the meaning of a second Christian name to imply relationship, and often none such is indicated. It is no part of the meaning of 'Barker' that the father also was so called; he who changes his family name may grossly mislead the genealogists, but he does not tell a falsehood. He does not even do so if he were to give a boy's name to a girl.

Much is to be learnt by a study of the way in which names are imposed, and of the way in which they are apt to acquire a

meaning. That even proper names do sometimes acquire a meaning is certain, for we may hear it said of such and such a person of that name that "he is a regular Robinson", and so forth. When we come to look into the matter the fact is found to be that so inevitably do associations spring up upon persistent or even frequent repetition of any characteristic, and so readily do associations ripen into implications, 'that the question ought rather to be framed thus, Why do proper names not mean anything? How is it that they can continue to retain their character of being mere unmeaning marks? The only answer I can offer is that under ordinary circumstances an individual presents himself under such a bewildering variety of aspects that no one of these has time to get the upper hand. The many changes of the same man, and the many men going by the same name, hinder any such lengthened contact as will result in adhesion. But directly a man begins to present himself preponderatingly under some one aspect, or a family begins from one generation to another to display some fixed characteristic, we find the usual influences of association at work; and from association to implication the step is a short one. Thus we speak of a Nero, a Judas, of Cæsarism, of out-Heroding Herod, and so forth. The true logical proper name stands, in fact, upon a very insecure footing, and requires constant and peculiar influences to prevent it from falling into the rank of ordinary general names. But it is none the less necessary to

retain in our minds an ideal of what it should be.

When we look into the matter historically we find the same facts forced upon our notice. It is however absolutely necessary that we should distinguish between the Connotation and the Etymology of any term. With the latter the logician has nothing to do. With him, for example, the name Brentford no more implies a ford through the Brent than does Wednesday imply a portion of time which is somehow consecrated to, or named after, Woden. Whatever meaning such names once possessed has long since faded away, and in their current use they possess nothing but denotation.

It is no part of our business here to examine into the historic origin of proper names, but as the enquiry lies so close to our path a few moments' notice must be devoted to this most interesting and suggestive subject. It appears then, so far back

as we can trace our steps,-I wish to keep quite free from implying that this was really the first phase of human thought upon such matters,-that almost every name was once in some way descriptive; and that the disposition to impose names for the mere purpose of reference and identification is altogether a modern acquisition. To a primitive people this kind of arbitrary invention seems never to occur, and if it could occur to them it would seem a waste of good words. Even later, when one class of originally significant names has become unmeaning,―i.e. Christian names,—we may still observe that they were commonly helped out, in order to distinguish them better from each other, by descriptive attributes, i. e. surnames;—and that it is only after a further lapse of time that these latter in turn take their place amongst the true proper names of the logician. There was a time when 'Isaac Thatcher' consisted of a proper name differentiated by a descriptive common name, just as there was a still earlier time when 'Isaac' itself was a descriptive common name. At the present time both elements stand on the same footing as proper names. But the experience of every school, workshop, and regiment, shows how naturally we select some descriptive or connotative term to aid in determining an individual, especially when his proper name is not quite sufficient for the purpose of identification.

If it be asked, where then are we to look for instances of names which have from their first imposition rigidly satisfied the logician's requirements of being mere arbitrary marks imposed upon an object? We can only reply that such are hardly to be found except where civilized and mature persons are concerned with numbers of objects which it is important for them to distinguish, and to which they have frequent occasion to refer. Truly typical instances are to be found in the names of race-horses, ships, and, for the most part, in those of newly built houses and streets. To these might be added the numbers by which convicts are distinguished, provided this is how they are commonly referred to in the prison, and that no indication of their order of conviction is conveyed. Various other analogous instances might be found which should satisfy the logician's requirements.

IV. Concrete and Abstract Terms: The next distinction which we have to notice amongst our terms is that between concrete

and abstract. As these terms are commonly defined in the text books, the notion seems to be suggested that they are absolute designations, in the sense that if any term be proposed to us by itself we ought to be able at once to refer it to one or other of these classes. We shall, however, see reason for considering them to be relative, in the sense that we can at most say of two of them, when proposed together, that they stand to each other in the relation of concrete and abstract.

The account commonly given of the distinction is that a concrete term denotes a thing, whilst an abstract term denotes an attribute of a thing. But, as we have already seen when discussing the preliminary postulates of Logic, we soon find ourselves launched into a sea of perplexity when we ask what a 'thing' is. So long as we are left to choose our own ground in the selection of our examples we can of course mark the distinction sharply enough. We may say, for instance, that a horse is concrete and its colour is abstract, and so on. But material objects of this well-defined character form but a small part of our stock of words in common use. A horse is doubtless a thing or object to almost all sentient and percipient creatures; but what would a dog (say) make of what are to us such concrete entities as a Parliamentary election, or a writ of error? A good deal of analysis and synthesis, of abstraction and limitation, has to be gone through before these objects are recognizable as individualities even by human faculties. By successive processes of this kind we may obtain higher and higher abstractions, each of which may be considered, by comparison with those from which it was derived, as being abstract; and, in turn, when compared with those derived from it may be considered concrete. 'Party spirit' might be reckoned an abstract quality of a political party;-which is itself by no means so concrete an entity as one of the persons composing that party. The virulence of that party spirit may again be reckoned as an attribute derived from the spirit itself, and so on. The fact is that hardly any object, as objects are regarded by us, can be selected, which is not to some extent a product of our powers of abstraction, and the more or less of this faculty called into play in any particular case hardly warrants us in labelling the instances respectively with such distinct desig

nations.