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where still there remains as much to be added, as if none were taken out. And this endless addition or addibility (if any one like the word better) of numbers, so apparent to the mind, is that, I think, which gives us the clearest and most distinct idea of infinity: of which more in the following chapter.
§. 1. HE that would know what kind of
Of Infinity Pußnity, in
E that would know what kind of its original intention, at tributed to
name of infinity, cannot do it better, than space, dura. by considering to what infinity is by the tion and
mind more immediately attributed, and then number.
how the mind comes to frame it. Finite and infinite seem to me to be looked upon be the mind as the modes of quantity, and to be attributed primarily in their first designation only to those things which have parts, and are capable of increase or dimi. nution, by the addition or subtraction of any the least part : and such are the ideas of space, duration, and number, which we have considered in the foregoing chapters. It is true, that we cannot but be assured, that the great God, of whom and from whom are all. things, is incomprehensibly infinite: but yet when we apply to that first and supreme being our idea of infinite, in our weak and narrow thoughts, we do it primarily in respect to his duration and ubiquity; and, I think, more figuratively to his power, wisdom, and goodness, and other attributes, which are properly in, exhaustible and incomprehensible, &c. For, when we call them intinite, we have no other idea of this infinity, but what carries with it some reflection on, and imitation of, that number or extent of the acts or ob. jects of God's power, wisdom, and goodness, which can never be supposed so great or so many, which these attributes will not alway surmount and exceed, let us
multiply them in our thoughts as far as we can, with all the infinity of endless number. I do not pretend to say how these attributes are in God, who is infinitely beyond the reach of our narrow capacities. They do, without doubt, contain in them all possible perfection : but this, I say, is our way of conceiving them, and these our ideas of their infinity.
§. 2. Finite then, and intinite, being by The idea of the mind looked on as modifications of ex
got. pansion and duration, the next thing to be considered, is, how the mind comes by them. As for the idea of finite, there is no great difficulty. The obvious portions of extension that affect our senses, carry with them into the mind the idea of finite : and the ordinary periods of succession, whereby we measure time and duration, as hours, days, and years, are bounded lengths. The difficulty is, how we come by those boundless ideas of eternity and immensity, since the objects we converse with, come so much short of any approach or proportion to that largeness.
§. 3. Every one that has any idea of any How we stated lengths of space, as a foot, finds that coine by the he can repeat that idea ; and, joining it to idea of infi. the former, make the idea of two feet; and nity. by the addition of a third, three feet ; and so on, without ever coming to an end of his addition, whether of the same idea of a foot, or if he pleases of doubling it, or any other idea he has of any length, as a mile, or diameter of the earth or of the orbis magnus: for whichsoever of these he takes, and how often soever he doubles, or any otherwise multiplies it, he finds that after he has continued his doubling in his thoughts, and enlarged his idea as much as he pleases, he has no more reason to stop, nor is one jot nearer the end of such addition, than he was at first setting out. The power of enlarging his idea of space by farther additions remaining still the same, he hence takes the idea of in
Our idea of
§. 4. This, I think, is the way whereby the mind gets the idea of infinite space. It is a quite different consideration, to examine whether the mind has the idea of such
a boundless space actually existing, since our ideas are not always proofs of the existence of things ; but yet, since this comes here in our way, I suppose I may sas, that we are apt to think that space in itself is actually boundless ; to which imagination, the idea of space or expansion of itself naturally leads us. For it being considered by us, either as the extension of body, or as existing by itself, without any solid matter taking it up (for of such a void space we have not only the idea, but I have proved as I think, from the motion of body, its necessary existence, it is impossible the mind should be ever able to find or suppose any end of it, or be stopped any where in its progress in this space, how far soever it extends its thoughts. Any bounds made with body, even adamantine walls, are so far from putting a stop to the mind in its farther progress in space and extension, that it rather facilitates and enlarges it : for so far as that body reaches, so far no one can doubt of extension : and when we are come to the utmost extremnity of body, what is there that can there put a stop, and satisfy the mind that it is at the end of space, when it perceives that it is not; nay, when it is satisfied that body itself can move into it. For if it be necessary for the motion of body, that there should be an einpiy space, though ever so little, here anongst bodies; and if it be possible for body to move in or through that empty space; nay it is impossible for any particle of matter to move but into an empty space; the same possibility of a body's moving into a void space, beyond the utmost bounds of body, as well as into a void space interspersed amongst bodies, will al. ways
rentain clear and evident: the idea of empty pure space, whether within or beyond the confioes of all bodies, being exactly the same, differing not in nature, though in bulk: and there being nothing to binder body from moring into it. So that wherever the mind places jself by any thought, either amongst or remote from all bodies, it can in this unitorm idea of space 10-where tind any bounds, any end; and so must necessarily conclude it, by the very nature and idea of each part of it, to be actually intimite.
$. 5. As by the power we find in-our- And so of selves of repeatiny, as often as we will, any duration, idea of space, we get the idea of inmensity ; so, by being able to repeat the idea of any length of duration we have in our minds, with all the endless addition of number, we come by the idea of eternity, , For we find in ourselves, we can no more come to an end of such repeated ideas, than we can come to the end of number, which every one perceives he cannot. But here again it is another question, quite different from our having an idea of eternity, to know whether there were any real being, whose duration has been eternal. And as to this, I say, he that considers something now exisimg, must necessarily come to something eternal. But laving spoke of this in another place, shall say here no more of it, but proceed on to some other considerations of our idea of infinity.
§. 6. If it be so, that our idea of infinity Why other be
got from the power we observe in our- ideas are not selves of repeating without end our own capable of ideas; it may be demanded, “ “ not attribute infinite to other ideas, as well as those “ of space and duration;" since they may be as casils, and as often repeated in our minds, as the other; and yet no-body ever thinks of infinite sweetness, or infi, nite whiteness, though he can repeat the idea of sweet or white, as frequently as those of a yard, or a day? To which I answer, all the ideas that are considered as havi ing parts, and are capable of increase by the addition of any equal or less parts, afford us by their repetition the idea of infinity; because with this endless repetitioni
, there is continued an enlargement, of which - there can be no end. But in other ideas it is not so; for to the largest idea of extension or duration that I al present have, the addition of any the least part nakes an increase; but to the perfectest idea I have of the whitest whiteness, if I add another of a less or equal whiteness, (and of a whiter than I have, I cannot add the idea) it makes no increase, and enlarges not my idea at all: and therefore the different ideas of whiteness, &c. are called degrees. For those ideas that consist of parts are capa-.. 03
why we do infinity.
ble of being augmented by every addition of the least part; but if you take the idea of white, which one parcel of snow yielded yesterday to our sight, and another idea of white from another parcel of snow you see to-day, and put them together in your mind, they embody, as it were, and run into one, and the idea of whiteness is not at all increased, and if we add a less degree of whiteness to a greater, we are so far from increasing that we diminish it. Those ideas that consist not of parts cannot be augmented to what proportion men please, or be stretched beyond what they have received by their senses ; but space, duration, anů number, being Capable of increase by repetition, leave in the inind an idea of endless room for more: nor can we conceive any where a stop to a farther addition or progression, and so those ideas alone lead our minds towards the thought of infinity Difference
§. 7. Though our idca of infinity arise bei ween infi- from the contemplation of quantity, and nity of space, the endless increase the mind is able to and space in. make in quantity, by the repeated addifinite.
tions of what portions thereof it plcases ; yet I guess we cause great confusion in our thoughts, when we join infinity to any supposed idea of quantity the mind can be thought to have, and so discourse or reason about an infinite quantity, viz. an infinite space, or an infinite duration. For our idea of infinity being as I think, an endless growing idea, by the idea of any quantity the mind has, being at that time terminated in that idea, (for be it as great as it will, it can be no greater than it is) to join infinity to it, is to adjust a standing measure to a growing bulk; and therefore I think it is not an insignificant subtilty, if I say that we are carefully to distinguish between the idea of the infinity of space, and the idea of a space infinite: the first is nothing but a supposed endless progression of the mind, over what repeated ideas of space it pleases; but to have actually in the mind the idea of a space infinite, is to suppose the mind already passed over, and actually to have a view of all those repeated ideas of space, which