Chapter XXVII: Section I: Names of Names (4)

For ascertaining and knowing amounts, some contrivance is requisite. It is necessary to conceive some small amount, by the addition or subtraction of which, another becomes larger or smaller. This forms the instrument of ascertainment. Where one thing, taken separately, is of sufficient importance to form this instrument, it is taken. Thus, for ascertaining and knowing different amounts of men, one individual is of sufficient importance. Amounts of men are considered as increased or diminished by the addition or subtraction of individuals. A grain of gunpowder might also be taken; but it is not of sufficient importance; the quantity, taken as the instrument of measurement, must have an ascertainable influence upon the effect, for the sake of which, the ascertaining of the amount is of importance. In their simple state, men use principally the hand for their elementary ascertainments. A pinch, or as much as could be held between the finger and the thumb, was a small amount distinctly conceived, and formed the principle of measurement where small additions were important; a handful was not less distinctively conceived, and was the instrument, where only larger additions were of importance.

When one addition was made, or needed to be made, after another, and another after that, and so on, the next point of importance was to conceive exactly how often the addition was made. A few {91} additions are distinct to sense. Place one billiard-ball by another, the sight of the two is distinct. Place three or four, it is still distinct. Soon, however, it ceases to be so. Place a dozen, and you will not probably be able to distinguish them from eleven. You must count them, or divide them. If you divide them by the eye, into two parcels, you may see that one is six and another six; but to benefit by this, you must know the art of putting six and six together.

The next step, therefore, necessary in the process of ascertaining amounts, was, to mark these additions, one after another, in such a manner, as to make known to what extent they had gone. When men were familiar with the operation of assigning names as marks of their ideas, the course which would suggest itself to them is obvious; they would employ a name as the mark of each addition. They would say, one, for the first, two, for the second, three, for the third, and so on. These marks it was very useful to make connotative, that the other important ingredient of the process, the thing added, might be made known at the same time. Thus we say, one man, two men; one horse, two horses; and so of all other things, the enumeration of which we are performing.

Numbers, therefore, are not names of objects. They are names of a certain process; the process of addition; of putting one billiard-ball to another; not more mysterious than any other process, as walking, writing, reading, to which names are assigned. One, is the name of this once performed, or of the aggregation begun; two, the name of it once more performed; three, of it once more performed; and so on. The words, however, in these concrete forms, beside {92} their power in noting this process, connote something else, namely, the things, whatever they are, the enumeration of which is required.

In the case of these connotative, as of other connotative marks, it was of great use to have the means of dropping the connotation; and in this case, it would have been conducive to clearness of ideas, if the non-connotative terms had received a mark to distinguish them from the connotative. This advantage, however, the framers of numbers were not sufficiently philosophical to provide. The same names are used both as connotative, and non-connotative; that is, both as abstract, and concrete; and it is far from being obvious, on all occasions, in which of the two senses they are used. They are used in the connotative sense, when joined as adjectives with a substantive; as when we say two men, three women; but it is not so obvious that they are used in the abstract sense, when we say three and two make five; or when we say fifty is a great number, five is a small number. Yet it must, upon consideration, appear, that in these cases they are abstract terms merely; in place of which, the words oneness, twoness, threeness, might be substituted. Thus we might say, twoness and threeness are fiveness.[22] [23]

[Editor's footnote 22: The vague manner in which the author uses the phrase "to be a name of" (a vagueness common to almost all thinkers who have not precise terms expressing the two modes of signification which I call denotation and connotation, and employed for nothing else) has led him, in the present case, into a serious misuse of terms. Numbers _are_, in the strictest propriety, names of objects. _Two_ is surely a name of the things which are two, the two balls, the two fingers, &c. The process of adding one to one which forms two is connoted, not denoted, by the name two. Numerals, in short, are concrete, not abstract names: they denote the actual collections of things, and connote the mental process of counting them. It is not twoness and threeness that are fiveness: the twoness of my two hands and the threeness of the feet of the table cannot be added together to form another abstraction. It is two balls added to three balls that make, in the concrete, five balls. Numerals are a class of concrete general names predicable of all things whatever, but connoting, in each case, the quantitative relation of the thing to some fixed standard, as previously explained by the author.--_Ed._]

[Grote's footnote 23: Here the process of numeration generally, together with the function of numbers carrying their separate names, are clearly set forth; after which we find the remark, that no distinction is made in the name of the number, when used as an abstract and when used as a concrete. Mr. James Mill thinks that it would have been conducive to clearness if such distinction had been marked by an inflexion of the name. "The names of numbers are used in the connotative (concrete) sense, when joined as adjectives with a substantive, as when we say, two men, three men: but it is not so obvious that they are used in the abstract sense, when we say three and two make five: or when we say fifty is a great number, five is a small number. Yet it must upon consideration appear, that in these cases they are abstract terms merely: in place of which, the words oneness, twoness, threeness, might be substituted. Thus we might say, twoness and threeness are fiveness."

The last part of what is here affirmed cannot, in my judgment, be sustained. Connecting itself with one among the many arguments between Aristotle and Plato, it lays down a position from which both of them would have dissented. In the last book but one (Book M) of Aristotle's "Metaphysica," this argument will be found set forth at length; though with much obscurity, which is cleared up by the lucid commentary of Bonitz. Plato distinguished two classes of numbers--the mathematical, and the ideal. The first class were the Quanta of equal and homogeneous units (One, Two, Three, &c.), any or all of which might be added so as to coalesce into one total sum. The second class were, the ideal or abstract numbers, Two _quatenus_ Two, &c., represented by Dyad, Triad, Tetrad, Pentad, Dekad, &c., the characteristic property of which was, that they could not be added together nor coalesce into one sum. These were uncombinable numbers, "[Greek a)rithmoi\ a)su/mblêtoi]--numeri inconsociabiles."-- See Aristot. Metaph. M. 6. 1080. b. 12. Bonitz Comment. p. 540, 541, seq.

Plato regarded these uncombinable numbers as the highest representative specimens or coryphæi of the Platonic Ideas. In this character Aristotle reasoned against them, contending that they did nothing to remove the many objections against Plato's ideal theory. With the question thus opened, I have no present concern: all that I wish to point out is the view which Plato originated and upon which Aristotle reasoned, viz.: That these ideal or abstract numbers could not be added together, or fused into one sum total. The abstract term Twoness means Two _so far forth as two_: so also Threeness and Fiveness. You cannot truly predicate anything of Twoness which would be inconsistent with this fundamental characteristic: you cannot add it to Threeness so as to make Fiveness, nor can you subdivide Fiveness into Twoness and Threeness, without suppressing the fundamental characteristic of each. Neither of them admit of increase or diminution. In like manner, a Triangle, or every particular Triangle, may have one of its sides taken away, or two more sides added to it: on each of which suppositions it ceases to be a triangle. But if we speak of a Triangle _so far forth as Triangle_, neither of these suppositions is admissible. We may say that its three angles are equal to two right angles, but we cannot subtract from it one of its sides, nor add to it one or two other sides. The subject of predication is so limited and specialised, that no predicate can be allowed which would efface its characteristic feature--Triangularity.

Bonitz remarks truly that the class of numbers set forth by Plato--the ideal or uncombinable numbers which could not be either added or subtracted--were divested of all the useful aptitudes and functions of numbers, and passed out of the category of Quantity into that of Quality. The Triad was one quality; the Pentad was another: there was no common measure into which both could be resolved (Bonitz, Comment. p. 540--553). _Two_, _three_, _five_, are quantifying names, designating each so many numerable units: and the units counted in each list may be added to, or subtracted from, the units counted in the others. But when we say, Twoness or the Dyad--Threeness or the Triad--Fiveness or the Pentad--we then recognise a peculiar quality, founded upon each separate variety of aggregation or quantification: so that these separate varieties are no longer resolvable into any common measure of constituent units. Each quality stands apart from the others, and has its own predicates. In the view of Plato and the Pythagoreans, the Dekad especially was invested with magnificent predicates.

I cannot therefore agree with Mr. James Mill in his opinion that, "when we say three and two make five, we use these numbers in the abstract sense." We clearly do not mean that three, _so far forth as three_, and two, _so far forth as two_, make five. But this would be what we should mean, if we used these names of numbers in the abstract sense. What we do mean is, that the units constituting three may be added to those constituting two, so as to make five: and that this is equally true, whether the units are men, horses, stones, or any other objects. Two, three, five, &c., are general or universal terms, capable of being joined with units of indefinite variety: but they do not become abstract terms, until we limit them by _quâtenus_, [Greek: katho/son, ê(=|], _so far forth as_, &c., or by a suffix such as _ness_. Such abstracts would have been of little use as to the ordinary functions of numbers; and accordingly they have never got footing in familiar speech, though they are occasionally employed in metaphysical discussions.--_G._]

{93} It is necessary to observe, that the process, marked by the names called numbers, though used for the {94} purpose of ascertaining synchronous order, is in the mind successive; one addition follows another. {95} Numbers, therefore, in reality, name successions; and are easily applied to mark certain particulars of the {96} successive order, when the marking of those particulars is of importance.

It is of importance, when successions take place all of one kind; and when consequences of importance depend upon the less or greater length of the train. It is then of importance, to mark the degrees of that length, which is correctly done by the enumeration of the links.

To take a simple and familiar instance, that of the human steps. They are successions all of one kind. Consequences of importance may, and often do result from a knowledge of the length of any particular series of steps. The ascertainment of an aggregate, in this order, is made in the same way, as that which we have traced in the synchronous order. An element of aggregation is taken; by its successive aggregations, the amount of the aggregate is correctly conceived; and, by a proper mark for each successive aggregation, it is also correctly denoted. The continued successions of day and night are all of one kind; and it is of the greatest importance for us to know accurately the length of a series of those successions; of the series between such and such events; between the sowing of the seed in the ground, for example, and the maturity of the crop. This is done, accurately, by putting a several mark upon each {97} several succession, one for the first, two for the one after that, three for the one after that, and so on.

If there be no mystery in one sensation after another, or one idea after another; and, if having them in that order and associating the idea of the antecedent with the sensation of the consequent be to know that they are in that order; then there is no mystery in Numbers, for they are only marks to shew that one is after another.

That there is no mystery in the ideas of priority and posteriority, which are relative terms, has been shewn under the preceding head of discourse.

The word Number itself, which is only a name of the names, one, two, &c., nothing being a number but some one of those names, has also been explained, when the class of words which are distinguished as Names of Names was under consideration.

In using the terms, one, two, three, four, and so on, the object is to ascertain with precision, the amount of the aggregate in question. In some cases, however, it is of importance to ascertain the order of aggregation, as well as the amount; and that, whether a synchronous, or a successive, aggregate be the object in view. This purpose is answered by a set of names, called the ordinal numbers, which, applied to the units of aggregation in the order in which they are taken, mark precisely the order of each. Thus, when we say, first, second, third, fourth, and so on; each of these concrete, or connotative names, notes a certain position, if in the synchronous order; a certain link, if {98} in the successive; and connotes the precise object which holds that position, or forms that link.

As there is no difficulty whatsoever in tracing the ideas, which, on each occasion, receive those marks, there is no need of multiplying words in their illustration.

{99} SECTION IV.

PRIVATIVE TERMS.

Privative terms are distinguished from other terms, by this; that other terms are marks for objects, as present or existent; privative terms are marks for objects, as not present or not existent.[24]

[Editor's footnote 24: The author gives the name of Privative terms to all those which are more commonly known by the designation of Negative; to all which signify non-existence or absence. It is usual to reserve the term Privative for names which signify not simple absence, but the absence of something usually present, or of which the presence might have been expected. Thus blind is classed as a privative term, when applied to human beings. When applied to stocks and stones, which are not expected to see, it is an admitted metaphor.

This, however, being understood, there is no difficulty in following the author's exposition by means of his own language.--_Ed._]

Thus the word Light, is the mark of a certain well-known object, as existent or present.

The word Darkness, on the contrary, is the mark of the same object, as not existent or not present. Ask any man, what he means by darkness; he says the absence of light. But the absence of light, is only another name for light absent; and light absent, is only another name for light not present. Darkness, therefore, is another name for light not present.

It thus appears, that the idea called up by the {100} word light, is that of a certain object associated with its presence; the idea called up by the word darkness, is that of the same object associated with its absence.

After the explanations which have been so often given, what I mean, when I speak of the idea of an object, as one thing; the idea of its presence, as another thing; ought not to be obscure. Its presence, is its existence; its absence, is its non-existence; at least, at a particular time and place. What ideas and sensations I mark by the word existent, has already been explained. The word non-existent is the mere negation of the same sensations and ideas.

We have repeatedly seen, that what we call existence, is an inference from our sensations. We have clusters of sensations; these call up the ideas of antecedents, which we call qualities; these the idea of an antecedent common to all the qualities, which we call _Substratum_; and the _Substratum_, with its qualities, we call the Object.

When we speak, then, of this _Substratum_ and its qualities, as present, at a particular time and place: which is what we mean by its existence; what we affirm is this; that if there be sentient organs at such a time and place, there will be such and such sensations. When we speak of it as absent, we affirm, that though there be sentient organs at such a time and place, there will not be those sensations. These ideas, then, forming in combination a very complex idea, are what, in the respective cases, we call the presence, and the absence of an object. Any further analysis would be superfluous in this place.

{101} A law of some importance, which has been already explained, is, that in complex ideas there is very often some one part, so prominent, as to throw the rest into the shade, and confine the attention almost wholly to itself. There is a curious exemplification of this law, in the pair of cases before us. Thus, in the complex idea of "the object and its presence," marked by the word Light, the object is the prominent part, and the presence is so habitually neglected, that it is with some trouble it is recognised. The case is reversed in the complex idea of "the object and its absence," marked by the word Darkness. In this, the absence is the prominent part, and it so completely engrosses the attention, that it requires reflection, to discover, that the idea of the object is necessarily combined.

There is something more in these two cases, which it is of great importance to remember. We have two sets of indissoluble associations, both exceedingly numerous, the one with the idea of the object as present, the other with the idea of it as absent; that is, the one set with light, the other set with darkness. Whenever we have the perception of light, we habitually have, along with it, the perception of objects; that is, of all sorts of colours, all sorts of shapes, all sorts of magnitudes, all sorts of distances, and so on. With the idea of light, then, are indissolubly associated the ideas of all sorts of objects; of extension in all its modifications, colour in all its modifications, motion in all its modifications; the word light, therefore, serves as a name, not merely of the fluid which acts upon the eye, but of that along with its innumerable associations. Such are the perceptions and {102} ideas, which, when we have the perception of light, we have along with it. What are the perceptions and ideas, which, when we have not the perception of light, we have along with that state of privation? There is, first, the want of all the perceptions, which we have along with that of light. There is, next, the disagreeable sensations we experience from not knowing what objects are approaching us, either by our motions, or by theirs; hence the idea of dangerous objects approaching; hence, also, the inability to perform many of the acts which are conducive either to our being, or well-being. With the idea of darkness, then, are indissolubly associated a multitude of ideas, of pain, of privation, of weakness; all disagreeable; with little or no mixture of any of an opposite kind. And the word darkness, therefore, stands as a name not merely of light absent, but of that along with all the accompanying sensations and ideas.

The reader will observe, and it is necessary he should well observe, that all terms might have corresponding privative terms. We have already stated, that the ordinary names of objects are names both of the object, and of its presence or existence, combined in one complex idea. Thus, rose, horse, are names of the objects as present or existent. We might have had names of them as absent or not existent. It is only, however, in a few cases, that the absence of an object is a matter of first-rate importance. It is only in those cases that it has been found requisite to have for it a particular name. The absence of light is obviously a case of the greatest importance. Consequences of the very first order, and infinite in number, {103} depend upon it. An appropriate name, therefore, was of the highest utility.

This explanation will enable us to see, without a minute analysis, the composition of the clusters marked by other Privative Terms.

Let us take Silence, as the next example. Silence is the absence of sound, either all sound, which is sometimes its meaning; or of some particular sound, which at other times is its meaning. Sound is the name of a well-known something, as present. Silence is the name of the same well-known something, as absent. The first word, is the name of the thing, and its presence. The second, is the name of the thing, and its absence. In the case of the combination marked by the first, namely, the thing and its presence, the thing is the prominent part, and the presence generally escapes attention. In the case of the second, the thing and its absence, the absence is the important part, and the thing is feebly, if at all, attended to.

Ignorance is easily explained, in the same manner. Knowledge is the name of a certain well-known something, as present or existent. Ignorance is the name of the same well-known something, as absent or nonexistent.

Having a sensation, or an idea, is one state of consciousness; not having it is another state of consciousness.[2*] The state of consciousness called "not having" {104} it is no doubt very various; for it is any sensation or idea different from the one in question. The "Having" one sensation and another sensation, or one idea and another idea; and the "Knowing" that the one is not the other; we have often observed to be the same thing. The great majority of names are invented, to mark sensations and ideas as "had;" there are, however, cases, in which it is necessary to mark them as "not had." In what manner, in the more remarkable cases, this marking is performed by privative names, has now been shewn. But, beside the marks for particular cases, it was necessary to have a comprehensive or _general_ mark; which should include all cases, as well those provided with particular names, as those not so provided. "Absent" was such a word. "Absent," standing by itself, and unrestricted by connection with any other word, is a name of any thing, joined with the idea of its not being _then_ and _there_. What is included in that Idea has already been shewn in explaining Belief in Existence. The mark "Absent," joined with any particular name, becomes a particular Privative Term. We have observed, that the word rose, is a mark not merely of the thing, but the thing with the idea of its presence; we have also observed, that such Presence-affirming Terms, except {105} in remarkable cases, have not corresponding Privative, or Absence-affirming Terms. But if we say "absent" rose, we have a Privative Term, double worded, indeed, instead of single worded, exactly corresponding to the Presence-affirming Term, rose. And, by the use of the same word, we can form Privative Terms of this description, in all cases in which they can be wanted; thus we can say, absent man, absent horse, absence of food, &c.

[Mill's footnote 2: Mr. Locke recognised the fact, but gave an erroneous account of it: "I should offer this as a reason why a privative cause might produce a positive idea; _viz._, that, all sensation being produced in us, only by different degrees and modes of motion in our animal spirits, variously agitated by external objects, the abatement of any former motion, must as necessarily produce a new sensation, [for "abatement of any former motion," read, ceasing of a particular sensation; and for "new sensation," read, new feeling, or, new state of consciousness,] as the variation or increase of it: and so introduce a new idea. B. II. ch. viii. s. 4.--(_Author's Note_.)]

The word Nothing, _Nihil_, is another _generical_ Privative Term. That this word has a very important marking power, every man is sensible in the use which he makes of it. But if it marks, it names; that is, names something. Yet it seems to remove every thing; that is, not to leave anything to be named.

The preceding explanations, however, have already cleared up this mystery. The word Nothing is the Privative Term which corresponds to Every Thing. Every Thing is a name of all possible objects, including their existence. Nothing is a name of all possible objects, including their non-existence.[25]

[Editor's footnote 25: The analysis of the facts, in all these cases, is admirable, but I still demur to the language. I object to saying, for instance, that silence is "the name of sound and its absence." It is not the name of sound, since we cannot say Sound is silence. It is the name of our state of sensation when there is no sound. The author is quite right in saying that this state of sensation recalls the idea of sound; to be conscious of silence as silence, implies that we are thinking of sound, and have the idea of it without the belief in its presence. In another of its uses, Silence is the abstract of Silent; which is a name of all things that make no sound, and of everything so long as it makes no sound; and which connotes the attribute of not sounding. So of all the other terms mentioned. "Nothing" is not a name of all possible objects, including their non-existence. If Nothing were a name of objects, we should be able to predicate of those objects that they are Nothing. Nothing is a name of the state of our consciousness when we are not aware of any object, or of any sensation.--_Ed._]

{106} "Absent," in its unrestricted sense, above explained, comes near to this marking power of the word Nothing, but differs from it in one respect. Absent is the Privative name of all possible objects, taken one by one. Nothing is the privative name of them, taken altogether. This distinction, I presume, is sufficiently obvious, and intelligible, thus expressed; and stands in no need of a more wordy explanation.[3*]

[Mill's footnote 3: The account of Privative Terms which is given by Locke, is the same with that which is presented in the text. The difference is, that Locke, who has stated the case correctly, has not attempted its analysis. He says (B. II. ch. viii.), "We have negative names, such as insipid, silence, _nihil_, &c., which words denote positive ideas; _v.g._, taste, sound, being; with a signification of their absence."--(_Author's Note_.)]

We shall now take notice of the Privative Term EMPTY, which is a word of great importance.

Empty is a name applicable to all the things to which the name, full, is applicable; in other words, to all the things which are calculated to contain other things in position, or in the synchronous order, that is, in the order of particle adjoining particle. It is necessary to mark this limitation of the word contain; because, in another sense, a complex idea is said to contain the simple ideas of which it consists; and a chemical compound is said to contain the simple {107} substances into which it can be decomposed. Empty, and Full, are names of those things only which contain, or are adapted to contain, things in position, or in the order of particle adjoining particle.

Things adapted to contain other things in position, are, themselves, a peculiar combination of positions, to which we must very attentively advert. To understand this combination, it will be necessary to remember exactly the analysis of position; of lines, surfaces, and bulks; as it has been already given in our explanation of Relative Terms.

The word "containing," applied to anything, as when we speak of a box containing books, a cask containing liquor, a room containing furniture, generally includes the idea of limitation. That which contains, has certain boundaries within which the things contained are placed, or have their position. This idea of things having their position within another thing, is a very complex idea, the composition of which we must be at some pains to understand.

It consists, first, of the thing containing; secondly, of the things contained.

The thing containing, again, consists of two parts; first, its boundaries; and, secondly, its containing capacity within its boundaries.

Its boundaries are surfaces. How we become acquainted with surfaces; in other words, what are the sensations, the copies of which form our complex idea of surface, has been already explained. They are certain sensations of touch, and certain sensations of muscular action. This complex idea is easily distinguished into two parts; first, a certain idea of resistance; secondly, the idea of extension. The sides {108} of a box I call resisting, and I call them extended; and I call them by both names on account of certain sensations. Let us conceive the box without a lid; each of the sides is extended and resisting. What is the top without a lid? Extended, and non-resisting. The idea of the top is that of extension without resistance; extension, in a particular direction, that of a plane surface. What is the idea of the inside of the box without its contents? That of extension in all directions without resistance. This is emptiness.

So far is plain, and not doubtful. There are still, however, some things which require explanation. What are we distinctly to understand by extension without resistance? Whenever we use the concrete extended, we mean something extended; and by that something we always mean something that resists. What do we mean when we use the abstract extension? It will be easily recollected that all this is a case of association, which has been already fully explained.

Concrete Terms are Connotative Terms; Abstract Terms are Non-connotative Terms. Concrete terms, along with a certain quality or qualities, which is their principal meaning, or notation, connote the object to which the quality belongs. Thus the concrete red, always means, that is, connotes, something red, as a rose. We have already, by sufficient examples, seen, that the Abstract, formed from the Concrete, notes precisely that which is noted by the Concrete, leaving out the connotation. Thus, take away the connotation from red, and you have redness; from hot, take away the connotation, and you have heat.

{109} The very same is the distinction between the concrete extended, and the abstract extension. What extended is with its connotation, extension is without that connotation. We have then to explain, wherein the connotation consists.

When we say extended, meaning something extended, we mean one or other of three things, a line, a surface, or bulk. We have already explained sufficiently in what manner we come by the ideas of line, surface, and bulk. We have certain sensations of touch, and of muscular action, conjoined, and the ideas of those sensations, in conjunction, form our ideas of line, surface, and bulk. The sensation, or sensations, which we mark by the word resisting, seem to be those alone which are connoted by the word extending; for it is most important to observe, that what we call extending in the parts of our own body, by the operation of its own muscles, is that which we call extended in all other things; and thus the essential connotation of the concrete, extended, is, resisting, and nothing else. In other concrete terms the connotation is greater. Thus red, connotes a surface, that is, something extended; and extended connotes resisting. And thus red connotes both extended and resisting, while extended connotes resisting alone. It is true, that persons enjoying the faculty of seeing cannot conceive any thing extended, without conceiving it coloured; because in them the idea of something extended includes, by association, the visual, as well as the tactual, and muscular, ideas; and the visual being accustomed to predominate, the tactual, and muscular, are faintly observed. This, however, cannot be the case in persons born blind, {110} who have the tactual, and muscular, feelings, and not the visual at all.

Now, then, we can easily understand what extension is in all its cases. Linear extension is the idea of a line, the connotation dropped, that is, the idea of resisting, dropped; superficial extension is the idea of a surface, the same connotation dropped; and solid extension, or bulk, is merely the idea of bulk, the connotation, or resisting, dropped. But bulk, the connotation (_i.e._ resistance) dropped, is what? The place for bulk: Position. But place is, what? A portion of SPACE; or, more correctly speaking. SPACE itself, with limitation.

We thus seem to have arrived, without any difficulty, at an exact knowledge of what is noted or marked by the word SPACE; a phenomenon of the human mind hitherto regarded as singularly mysterious. The difficulty which has been found in explaining the term, even, by those philosophers who have approached the nearest to its meaning, seems to have arisen, from their not perceiving the mode of signification of Abstract Terms; and from the obscurity of that class of sensations, a portion of which we employ the word "extended" to mark. The word "space" is an abstract, differing from its concrete, like other abstracts, by dropping the connotation. Much of the mystery, in which the idea has seemed to be involved, is owing to this single circumstance, that the abstract term, space, has not had an appropriate concrete. We have observed, that, in all cases, abstract terms can be explained only through their concretes; because they note or name a part of what the concrete names, leaving out the rest. If we were {111} to make a concrete term, corresponding to the abstract term space, it must be a word equivalent to the terms "infinitely extended." From the ideas included under the name "infinitely extended," leave out resisting, and you have all that is marked by the abstract Space.[26]

[Editor's footnote 26: There is great originality as well as perspicacity in the explanation here given of Space, as a privative term, expressing when analysed, the absence of the feeling of resistance in the circumstances in which resistance is frequently felt, namely, after the sensations of muscular action and motion. The only part of the exposition to which I demur is the classing of Space among abstract terms. I have already objected to calling the word line, when used in the geometrical sense, an abstract term. I hold it to be the concrete name of an ideal object possessing length but not breadth. In like manner a Space may be said to be the concrete name of an ideal object, extended but not resisting. The sensations connoted by this concrete name, are those which accompany the motion of our limbs or of our body in all directions: and along with these sensations is connoted the absence of certain others, viz. of the muscular sensations which accompany the arrest of that motion by a resisting substance. This being the meaning of a Space, Space in general must be a name equally concrete. It denotes the aggregate of all Space.--_Ed._]

In the idea of SPACE, the idea of Infinity is included. What the idea of Infinity is, needs therefore to be explained. When the word Infinite is not used metaphorically, as it is when we speak of the infinite perfections of God, in which case it is not a name for ideas, but for the want of them, it is applied only to Number, Extension, and Duration.

We increase numbers by adding one to one, one to two, and so on, without limit, giving a name to {112} each aggregate. The association of ideas which constitutes the process has been already explained. With each number, one, two, three, four, as we go on, the idea of one more is so strongly associated, that we cannot help its existing in immediate conjunction. However high, therefore, we go in numbering, the idea of one more always forces itself upon us; and hence we say that number is infinite. That this, literally, is not true; that, indeed, it is a verbal contradiction, is obvious. Number, is something numbered; but if numbered, limited; that is, not infinite. Number is the negation of infinite; as black is the negation of white. The name infinite, in this case, is, in reality, nothing but a mark for that state of consciousness, in which the idea of one more is closely associated with every succeeding number. And Infinity, the abstract term, is the peculiar idea, without the connotation.

When we apply "infinite" to extension, we do so equally to all its three modifications, to lines, surfaces, and bulk. How we do so is obvious. We know no infinite line, but we know a longer, and a longer. A line is lengthened, as number is increased, by continual additions; a line of any length, say of an inch, is increased by the continual addition of other lengths, say of an inch. In the process, then, by which we conceive the increase of a line, the idea of one portion more, is continually associated with the preceding length; and to what extent soever it is carried, the association of one portion more, is equally close and irresistible. This is what we call the idea of infinite extension; and what some people call the _necessary_ idea; which only means, that the idea of a {113} portion more, rises necessarily, that is, by indissoluble association, so that we cannot help its rising. Infinite is the concrete term, here connoting Line; drop the connotation, you have Infinity, the abstract.

If such be the whole of what is involved in the idea of Infinity, in the case of a line; call it necessary idea, if you will; the idea of it, in the case of surface, and of bulk, is also explained; for surface, and bulk, are only lines, in such and such, or in all directions. The idea of a portion more, adhering, by indissoluble association, to the idea of every increase, in any or in all directions, is the idea of "infinitely extended," and the idea of "infinitely extended," the connotation dropped, is the idea of Infinite Space. It has been called a simple idea (so little has the real nature of it been understood); while it is thus distinctly seen, to be one of the most complex ideas, which the whole train of our conscious being presents. Extreme complexity, with great closeness of association, has this effect--that every particular part in the composition is overpowered by the multitude of all the other parts, and no one in particular stands marked from the rest; but all, together, assume the appearance of ONE. Something perfectly analogous occurs, even in sensation. If two or three ingredients are mixed, as wine and honey, we can distinguish the taste of each, and say it is compound. But if a great many are mixed, we can distinguish no one in particular, and the taste of the whole appears a simple peculiar taste.[27]

[Editor's footnote 27: This explanation of the feeling of Infinity which attaches itself to Space, is one of the most important thoughts in the whole treatise; and, obvious as its truth is to a mind prepared by the previous exposition, it has great difficulty in finding entrance into other minds.

Every object is associated with some position: not always with the same position, but we have never perceived any object, and therefore never think of one, but in some position or other, relative to some other objects. As, from every position. Space extends in every direction (i.e. the unimpeded arm or body can move in any direction), and since we never were in any place which did not admit of motion in every direction from it, when such motion was not arrested by a resistance; every idea of position is irresistibly associated with extension, beyond the position: and we can conceive no end to extension, because the place which we try to conceive as its end, raises irresistibly the idea of other places beyond it. This is one of the many so-called Necessities of Thought which are necessities only in consequence of the inseparableness of an association: but which, from unwillingness to admit this explanation, men mistake for original laws of the human mind, and even regard them as the effect and proof of a corresponding necessary connexion between facts existing in Nature.--_Ed._]

{114} This, indeed, is one great cause of the mistakes, which have been committed, in the examination of abstract ideas. We have shewn that they are all complex, and in the highest degree. Yet the greater number of them have always been treated as simple. Mr. Locke shewed that some of them, which he calls mixed modes, were undoubtedly compounded, as obligation, crime, &c. But they are no otherwise complex, than as power, quality, chance, fate, position, and space, are complex.

It is truly remarkable, how many of the cases of indissoluble association are all united in the idea of SPACE. First of all, with the idea of every object, the idea of _position_ or _place_, is indissolubly united. {115} Secondly, with the idea of position or place, the idea of _extension_ is indissolubly united. Thirdly, with the idea of extension the idea of _infinity_ is indissolubly united. Fourthly, by the unfortunate ambiguity of the _Copula_, the idea of _existence_ is indissolubly united with SPACE, as with other abstract terms. What these several ingredients, the ideas of Position, Extension, Infinity, Existence, are composed of, we have already seen. All these, forced into combination, by irresistible association, constitute the idea of SPACE.

{116} SECTION V.

TIME.

As SPACE is a comprehensive word, including all Positions, or the whole of synchronous order; so TIME is a comprehensive word, including all Successions, or the whole of successive order.

The difficulty of the exposition, in this case, consists not in the ideas; for they are clear and certain enough; but in finding expressions which will have even a chance of conveying to readers, who are not familiar with the analysis of mental phenomena, the ideas which it is my object to impart.

As all objects, considered as existing together, are said to exist in SPACE, so all objects considered as existing one after another, are said to exist in TIME.

Objects, however, are said to exist in Time, in two distinguishable cases; either when they are in constant flow; or, when they have, what we call, stability or duration. The constant passage of men, horses, vehicles, &c., in a busy and crowded street, is in Time; the permanence of St. Paul's, in its well-known position, is also in Time. If Time mean the succession of the objects in the one case, it must mean something else in the other. It cannot mean the succession of St. Paul's. But it may mean the idea of St. Paul's, associated with the idea of other successions.

Of TIME itself we conceive, that it is never still. It is a perpetual flow of instants, of which only one can ever be present. The very idea of Time, therefore, is {117} an idea of successions. It consists of this, and of nothing else.

But there are no real successions, save successions of objects, that is of feelings in our minds.[28] What, then, are the successions of TIME, which are the successions of nothing? To those who have thoroughly familiarized themselves with the account which we have given of abstract terms, and who can promptly and steadily conceive the mode of their signification, we can render an answer, which will be understood at once, and will be felt to be complete and satisfactory.

[Editor's footnote 28: There is an unusual employment of language here, which if attention is not formally drawn to it, may embarrass the reader. By objects are commonly meant, those groups or clusters of sensations and possibilities of sensation, that compose what we call the external world. A single sensation, even external, and still less if internal, is not called an object. In a somewhat larger sense, whatever we think of, as distinguished from the thought itself and from ourselves as thinking it, is called an object; this is the common antithesis of Object and Subject. But in this place, the author designates as objects, all things which have real existence, as distinguished from the instants of mere Time, which, as he is pointing out, have not; and a puzzling effect is produced by his applying the name Object, in even an especial manner, to sensations: to the tickings of a watch, or the beatings of a patient's pulse.--_Ed._]

We have shewn, how we form the abstracts, redness, from red; sweetness, from sweet; hardness, from hard; by simply dropping the connotation of the concrete term. Thus red, always means something red; redness, is the red without the something; so of sweetness, hardness, and so forth. When the ideas are more {118} complicated, the case is still the same. When we use the concrete, living, it always connotes something living; a living man, a living quadruped, a living bird, fish, insect, and so forth. When we use the abstract, life, we convey all that we convey by the term living, except the connotation. We say that John is healthy, James is healthy, on account of circumstances the idea of which forms a very complex idea. The concrete healthy always connotes an individual. Use the abstract, health, you have the idea without the connotation.

In applying this doctrine to the case of successions, we are ill supplied with appropriate names; and hence the difficulty of the case, both to the teacher, and the learner.

We have said that there are no real successions, but successions of objects. The tickings of my watch are successive sounds, that is, sensations. The beatings which are felt by the physician, in the artery of his patient, are successive feelings or sensations of touch.

When the different particulars of a scene in which a man has been engaged, of a battle, for example, in which he has commanded, pass through his mind, there is a succession of ideas. In all these cases of the successions of sensations, or ideas, there is always one present, others past, and others to come, that is, future. Drop the connotation of "something past," "something present," "something future." You have pastness, presentness, and futureness. But pastness, presentness, and futureness, are TIME. TIME can neither be shewn, nor conceived, to be any thing else. It is a single-worded abstract, involving the meaning {119} of these three several abstracts. The true meaning of these abstracts is clearly made out from their concretes. The precise idea, therefore, marked by the word TIME; if the meaning of these abstracts is sufficiently apprehended; is at last apparent. Nor is there any mysteriousness in it whatsoever, but that which has arisen from misapprehension of that grand department of Naming, which belongs to abstract terms; and from inattention to that class of words, which are invented to supply the place, each of them singly, of several other words.

To our conclusion, that TIME is the equivalent of Pastness, Presentness, and Futureness, combined, it may be objected, that the word Time is applicable to all the three cases; as we can say, past time, present time, and future time, all with equal propriety. This, however, is so far from being any presumption against the conclusion, that it is a clear confirmation of it; since Time, standing by itself, marks no particular case, and, in order to do so, must have another mark applied to it to limit its signification. It is only because Time marks all the cases of pastness, presentness, and futureness, that it needs the marks past, present, or future, to confine its meaning; present time being merely another name for presentness, future time, for futureness, and past time, for pastness. The same thing is seen in the case of all other abstracts. Redness is the name of a certain colour, in all its modifications, and to whatever object belonging. But by the addition of an appropriate mark, we confine its meaning to any particular case; as when we say, the redness of a rose, the redness of scarlet, and so on.

{120} The accounts, which have been rendered of Time by different philosophers, so far as they have in them any acknowledged accuracy, are, all of them, parts, and but parts, of the analysis which we have thus been presenting. Dr. Reid says, Memory gives us the conception and belief of finite intervals of duration; and these we enlarge by our mental processes to infinity.[4*] We have already seen what Memory is. It is not a faculty, as Dr. Reid supposes, which "gives" any thing; it is an idea, formed by association of the particulars of a certain train; a train of antecedents and consequents, of which the present feeling is one extremity. Pastness is included under the term Memory. Memory is the name of a certain whole, and Pastness is the name of a part of that whole. Memory is a connotative term; what it notes, is the antecedence and consequence of the several parts of that which forms the chain of the remembrance; what it connotes, are the feelings themselves, the objects remembered. When what it connotes is left out, and what it notes is retained, we have the idea which is expressed by pastness.

[Mill's footnote 4: Intellect. Powers. Essay III. ch. v. p. 583.]

In the chain of memory, consisting of antecedent, antecedent, antecedent, traced back to any length from the present feeling, we call that which immediately precedes the present, the nearest; the next, we call more distant; the next, more distant still; and that, between which and the present feeling the greatest number of successions intervenes, we call the most distant, also the farthest back; but the farthest back of a series of successions, is the oldest, that between {121} which and the present time the greatest length of time has intervened. Greatest length of time, therefore, in this case, is only another name for greatest number of successions.

It has been already seen, that there is nothing in which we are so deeply interested, as an accurate knowledge of the antecedents and consequents, in the midst of which we exist. Of the different innumerable trains of antecedents and consequents which it is important for us carefully to mark, it is observed, that some succeed more quickly, some less. While the long pendulum of an eight-day clock is performing one oscillation, the short pendulum of a table-clock performs two or three.

What that is, to which we give the name of quickness, or slowness, in those successions; in other words, what is the state of consciousness which we have thus occasion to mark; has already been seen. Every succession, observed by us, is a case of sensation and memory; sensation of the consequent, memory of the antecedent. If we have observed simultaneously the oscillations of the two pendulums, mentioned above, we remember two or three antecedent oscillations of the short pendulum, before we get back to one of the long. It is a mere case, therefore, of the greater or less number of antecedents in a chain of memory, expounded in a preceding chapter.

In the knowledge, so important to us, of antecedents and consequents, it is not enough that we know what antecedents are followed by what consequents; much depends upon the quickness or slowness of the successions. It is, therefore, of the highest importance that we should have the means of marking them.

{122} What we do is, to take some well-known case of successions, and to make that a standard, by which to ascertain the rest. We take, for example, the oscillations of a pendulum. So many of these we call a minute. So many minutes we call an hour. These minutes and hours, then, are so many oscillations, that is successions. We call them measures of time. But things are measurable only by parts of themselves; extension by extension, weight by weight, and so on. What is *measured by succession, therefore, is itself nothing but succession.