and there will remain only the confus'd Idea of Multitude, but the Ideas neceffary to diftin& Numeration will not be attain'd to. . 8. This farther is obfervable in Number, That it is that which the Mind Number mea makes use of in measuring all things that by us are measurable, which principally fures all Mea are Expansion and Duration; and our Idea of Infinity, even when apply'd to furables thofe, feems to be nothing but the Infinity of Number. For what else are our Ideas of Eternity and Immenfity, but the repeated Additions of certain Ideas of imagin'd Parts of Duration and Expanfion, with the Infinity of Number, in which we can come to no end of Addition? For fuch an inexhauftible Stock, Number, of all other our Ideas, moft clearly furnishes us with, as is obvious to every one. For let a Man collect into one Sum as great a Number as he pleases, this multitude, how great foever, leffens not one jot the power of adding to it, or brings him any nearer the end of the inexhauftible Stock of Number, where ftill there remains as much to be added, as if none were taken out. And this endlefs Addition or Addibility (if any one like the word better) of Numbers, fo apparent to the Mind, is that, I think, which gives us the cleareft and most diftinet Idea of Infinity: of which more in the following Chapter. CHAP. XVII. Of Infinity. S. I. E that would know what kind of Idea it is, to which we give the name Infinity,in its Hot of Infinity, cannot do it better, than by confidering to what Infinity original Inis by the Mind more immediately attributed, and then how the Mind comes to tention, attri frame it. Finite and Infinite feem to me to be look'd upon by the Mind as the Modes of Quantity, and to be attributed primarily in their firft Defignation only to thofe things which have Parts, and are capable of Increase or Diminution, by the Addition or Subtraction of any the leaft Part: And fuch are the Ideas of Space, Duration, and Number, which we have confider'd in the foregoing Chapters. 'Tis true, that we cannot but be affur'd, That the Great GOD, of whom and from whom are all things, is incomprehenfibly Infinite: But yet when we apply to that first and fupreme Being our Idea of Infinite, in our weak and narrow Thoughts, we do it primarily in refpe&t of his Duration and Ubiquity; and I think, more figuratively to his Power, Wisdom, and Goodness, and other Attributes, which are properly inexhauftible and incomprehenfible, &c. For when we call them Infinite, we have no other Idea of this Infinity, but what carries with it fome Reflection on, and Intimation of that Number or Extent of the A&s or Objects of God's Power, Wisdom, and Goodnefs, which can never be fuppos'd fo great or fo many, which thefe Attributes will not always furmount 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 fay how thefe Attributes are in GOD, who is infinitely beyond the reach of our narrow Capacities. They do, without doubt, contain in them all poffible Perfection: but this, I fay, is our way of conceiving them, and thefe our Ideas of their Infinity. buted to Space, Duration and §. 2. Finite then, and Infinite, being by the Mind look'd on as Modifications The Idea of of Expansion and Duration, the next thing to be confider'd, is, How the Mind Finite easily comes by them. As for the Idea of Fixite, there is no great difficulty. The ob- got. vious Portions of Extenfion that affect our Senfes, carry with them into the Mind the Idea of Finite: And the ordinary Periods of Succeffion, whereby we measure Time and Duration, as Hours, Days, and Years, are bounded Lengths. The difficulty is, how we come by thofe boundlefs Ideas of Eternity and Immenfity, fince the Objects which we converse with, come so much short of any Approach or Proportion to that Largenefs. §. 3. Every one that has any Idea of any flated Lengths of Space, as a Foot, How we come finds that he can repeat that Idea; and joining it to the former, make the Idea by the Idea of of two Feet; and by the addition of a third, three Feet; and fo Infinity on, without ever coming to an end of his Additions, whether of the fame Idea of a Foot, or Our Idea of Space boundlefs. And foof Du ration. Why other Ideas are not capable of Infinity. 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 whichfoever of these he takes, and how often foever he doubles, or any otherwife multiplies it, he finds that after he has continu'd his doubling in his Thoughts, and enlarg'd his Idea as much as he pleases, he has no more reason to ftop, nor is one jot nearer the end of fuch Addition, than he was at first fetting out. The power of enlarging his Idea of Space by farther Additions remaining ftill the fame, he hence takes the Idea of infinite Space. §. 4. This, I think, is the way whereby the Mind gets the Idea of infinite Space. 'Tis a quite different Confideration, to examine, whether the Mind has the Idea of fuch a boundless Space actually exifting, fince our Ideas are not always Proofs of the Existence of things; but yet, fince this comes here in our way, I suppose I may fay, that we are apt to think, that Space in it felf is actually boundless; to which Imagination, the Idea of Space or Expanfion of it felf naturally leads us. For it being confider'd by us, either as the Extenfion of Body, or as exifting by it felf, without any folid Matter taking it up, (for of fuch a void Space we have not only the Idea, but I have prov'd, as I think, from the Motion of Body, its neceffary Existence) it is impoffible the Mind fhould be ever able to find or suppose any end of it, or be stop'd any where in its progrefs in this Space, how far foever it extends its Thoughts. Any bounds made with Body, even Adamantine Walls, are fo far from putting a ftop to the Mind in its farther Progress in Space and Extenfion, that it rataer facilitates and enlarges it; for so far as that Body reaches, fo far no one can doubt of Extenfion: and when we are come to the utmoft Extremity of Body, what is there that can there put a stop, and fatisfy the Mind that it is at the end of Space, when it perceives it is not; nay, when it is satisfy'd that Body it felf can move into it? For if it be neceffary for the Motion of Body, that there fhould be an empty Space, tho' ever fo little, here amongst Bodies; and if it be poffible for Body to move in or thro' that empty Space; nay, it is impoffible for any Particle of Matter to move but into an empty Space; the fame Poffibility of a Body's moving into a void Space, beyond the utmoft Bounds of Body, as well as into a void Space interfpers'd amongst Bodies, will always remain clear and evident: the Idea of empty pure Space, whether within or beyond the Confines of all Bodies, being exactly the fame, differing not in nature, tho' in bulk; and there being nothing to hinder Body from moving into it. So that wherever the Mind places it felf by any Thought, either amongst or remote from all Bodies, it can in this uniform Idea of Space no-where find any Bounds, any End; and fo muft neceffarily conclude it, by the very Nature and Idea of each part of it, to be actually infinite. §. 5. As by the Power we find in our felves of repeating, as often as we will, any Idea of Space, we get the Idea of Immensity; fo, 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 our felves, we can no more come to an end of fuch repeated Ideas, than we can come to the end of Number, which every one perceives he cannot. But here again 'tis another queftion, quite different from our having an Idea of Eternity, to know whether there were any real Being, whofe Duration has been eternal. And as to this, I fay, he that confiders fomething now exifting, muft neceffarily come to fomething eternal. But having spoke of this in another place, I fhail fay here no more of it, but proceed on to fome other Confiderations of our Idea of Infinity. §. 6. If it be fo, that our Idea of Infinity be got from the Power we obferve in our felves, of repeating without end our own Ideas; it may be demanded, Why we do not attribute Infinite to other Ideas, as well as thofe of Space and Duration; fince they may be as easily, and as often repeated in our Minds, as the other; and yet no body ever thinks of infinite Sweetnefs, or infinite Whitenefs, tho' he can repeat the Idea of Sweet or White, as frequently as thofe of a Yard, or a Day? To which I anfwer: All the Ideas that are confider'd as having Parts, and are capable of Increase by the Addition of any equal or lefs Parts, afford us by their Repetition the Idea of Infinity; becaufe with this endless Repetition, there is continu'd an Enlargement, of which there can be no end. But in other Ideas it is not fo; for to the largest Idea of Extention or Duration that I at pre fent fent have, the Addition of any the leaft part makes an Increafe; but to the perfecteft Idea I have of the whiteft Whiteness, if I add another of a lefs or equal Whiteness (and of a whiter than I have, I cannot add the Idea) it makes no Increafe, and enlarges not my Idea at all: and therefore the different Ideas of Whiteness, &c. are call'd Degrees. For those Ideas that confift of Parts, are capable of being augmented by every Addition of the leaft Part; but if you take the Idea of White, which one parcel of Snow yielded yesterday to your Sight, and another Idea of White from another parcel of Snow you fee to day, and put them together in your Mind, they embody, as it were, and run into one, and the Idea of Whitenefs is not at all increas'd; and if we add a lefs degree of Whitenefs to a greater, we are fo far from increasing, that we diminish it. Those Ideas that confift not of Parts, cannot be augmented to what proportion Men pleafe, or be ftretch'd beyond what they have receiv'd by their Senfes; but Space, Duration, and Number, being capable of Increase by Repetition, leave in the Mind an Idea of an endless room for more: nor can we conceive any where a ftop to a farther Addition or Progreffion, and so those Ideas alone lead our Minds towards the Thought of Infinity. 1. 7. Tho' our Idea of Infinity arife from the Contemplation of Quantity, and Difference be the endless Increase the Mind is able to make in Quantity, by the repeated Addi- tween Infinity of Space, and tions of what Portions thereof it pleases; yet I guess we caufe great confufion Space infinite. in our Thoughts, when we join Infinity to any fuppos'd Idea of Quantity the Mind can be thought to have, and fo difcourfe or reafon 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, but 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 Meafure to a growing Bulk; and therefore I think it is not an infignificant Subtilty, if I fay that we are carefully to diftinguish between the Idea of the Infinity of Space, and the Idea of a Space infinite: The firft is nothing but a fuppos'd endlefs Progreffion of the Mind, over what repeated Ideas of Space it pleases; but to have actually in the Mind the Ideas of a Space infinite, is to fuppofe the Mind already pafs'd over, and actually to have a view of all thofe repeated Ideas of Space, which an endless Repetition can never totally reprefent to it; which carries in it a plain Contradiction. §. 8. This perhaps will be a little plainer, if we confider it in Numbers. The We have no Infinity of Numbers, to the end of whofe Addition every one perceives there Idea of infiis no approach, eafily appears to any one that reflects on it: but how clear fo- nite Space. ever this Idea of the Infinity of Number be, there is nothing yet more evident, than the Abfurdity of the actual Idea of an infinite Number. Whatfoever pofitive Ideas we have in our Minds of any Space, Duration, or Number, let them be ever fo great, they are ftill finite; but when we fuppofe an inexhauftible Remainder, from which we remove all Bounds, and wherein we allow the Mind an endless Progreffion of Thought, without ever compleating the Idea, there we have our Idea of Infinity, which tho' it seems to be pretty clear when we confider nothing elfe in it but the Negation of an End, yet when we would frame in our Minds the Idea of an infinite Space or Duration, that Idea is very obfcure and confus'd, because it is made up of two Parts, very different, if not inconfiftent. For let a Man frame in his Mind an Idea of any Space or Number, as great as he will; 'tis plain the Mind refts and terminates in that Idea, which is contrary to the Idea of Infinity, which confifts in a Suppos'd endless Progreffion. And therefore I think it is, that we are so easily confounded, when we come to argue and reafon about infinite Space or Duration, &c. Because the Parts of fuch an Idea not being perceiv'd to be, as they are, inconfiftent, the one fide or other always perplexes whatever Confequences we draw from the other; as an Idea of Motion not paffing on, would perplex any one, who fhould argue from fuch an Idea, which is not better than an Idea of Motion at reft: and fuch another feems to me to be the Idea of a Space, or (which is the fame thing) a Number infinite, i. e. of a Space or Number which the Mind actually has, and fo views, and terminates in; and of a Space or Number, which in a conftant and endless enlarging and progreffion, it can in Thought never attain to. For how large foever an Idea of Space I have in my Mind, it is Number affords us the clearest Idea of Infinity. is no larger than it is that inftant that I have it, tho' I be capable the next inftant Our different S. 10. It will perhaps give us a little farther Light into the Idea we have of Infinite Divi- 9. 11. The fame happens alfo in Space, wherein, conceiving our felves to be as it were in the Center, we do on all fides pursue thofe indeterminable Lines of Number; and reckoning any way from our felves, a Yard, Mile, Diameter of the Earth, or Orbis Magnus, by the Infinity of Number, we add others to them as often as we will; and having no more reafon to fet Bounds to those repeated Ideas than we have to fet Bounds to Number, we have that indeterminable Idea of Immenfity. §. 12. And fince in any bulk of Matter our Thoughts can never arrive at the utmoft Divifibility, therefore there is an apparent Infinity to us alfo in that which has the Infinity alfo of Number; but with this difference, that in the former Confiderations of the Infinity of Space and Duration, we only use Addition of Numbers; whereas this is like the divifion of an Unit into its Fractions, wherein the Mind alfo can proceed in infinitum, as well as in the former Additions, it being indeed but the Addition ftill of new Numbers: Tho' in the Addition of the one, we can have no more the pofitive Idea of a Space infinitely great, than in the Divifion of the other, we can have the Idea of a Body infinitely little; our Idea of Infinity being, as I may say, a growing and fugitive Idea, ftill in a boundless Progreffion, that can ftop no where. §. 13. Tho' it be hard, I think, to find any one fo abfurd as to fay, he has the positive Idea of an actual infinite Number; the Infinity whereof lies only in a power ftill of adding any Combination of Units to any former Number, and that as long and as much as one will; the like also being in the Infinity of Space and Duration, which power leaves always to the Mind room for end lefs lefs Additions; yet there be thofe, who imagine they have pofitive Ideas of infinite Duration and Space. It would, I think, be enough to deftroy any fuch pofitive Idea of Infinite, to ask him that has it, whether he could add to it or no; which would eafily fhew the mistake of such a pofitive Idea. We can, I think, have no pofitive Idea of any Space or Duration which is not made up, and commenfurate to repeated numbers of Feet or Yards or Days and Years, which are the common Measures, whereof we have the Ideas in our Minds, and whereby we judg of the greatness of these fort of Quantities. And therefore, fince an Idea of infinite Space or Duration must needs be made up of infinite Parts, it can have no other Infinity than that of Number, capable ftill of farther Addition, but not an actual pofitive Idea of a Number infinite. For, I think, it is evident that the Addition of finite things together (as are all Lengths, whereof we have the pofitive Ideas) can never otherwise produce the Idea of Infinite,than as Number does; which, confifting of Additions of finite Units one to another, fuggefts the Idea of Infinite, only by a power we find we have of still increafing the Sum, and adding more of the fame kind, without coming one jot nearer the end of fuch Progreffion. J ить §. 14. They who would prove their Idea of Infinite to be pofitive, feem to me to do it by a pleasant Argument, taken from the Negation of an end; which being negative, the Negation of it is pofitive. He that confiders that the End is, in Body, but the Extremity or Superficies of that Body, will not perhaps be forward to grant that the End is a bare Negative: And he that perceives the end of his Pen is black or white, will be apt to think that the end is fomething more than a pure Negation. Nor is it, when apply'd to Duration, the bare Negation of Existence, but more properly the laft moment of it. But if they will have the End to be nothing but the bare Negation of Existence, I am fure they cannot deny but the Beginning is the firft inftant of Being, and is not by any body conceiv'd to be a bare Negation; and therefore by their own Argument, the Idea of Eternal, a parte ante, or of a Duration without a Beginning, is but a negative idea. Does this mean the such an idea to pass live weard 1. 15. The Idea of Infinite has, I confefs, fomething of pofitive in all thofe What is p things we apply to it. When we would think of infinite Space or Duration, we tive, what ne at firft ftep usually make fome very large Idea, as perhaps of Millions of Ages, gative in our "Idea of Infi: or Miles, which poffibly we double and multiply feveral times. All that we nite. thus amals together in our Thoughts is pofitive, and the affemblage of a great number of pofitive Ideas of Space or Duration. But what ftill remains beyond this, we have no more a positive diftin& Notion of, than a Mariner has of the depth of the Sea; where having let down a large portion of his Sounding-line, he reaches no bottom: Whereby he knows the depth to be fo many Fathoms, and more; but how much that more is, he hath no diftin& Notion at all: And could he always fupply new Line, and find the Plummet always fink, without ever stopping, he would be fomething in the pofture of the Mind reaching after a compleat and pofitive Idea of Infinity. In which cafe let this Line be to, or 10,000 Fathoms long, it equally difcovers what is beyond it; and gives only this confus'd and comparative Idea, that this is not all, but one may yet go farther. So much as the Mind comprehends of any Space, it has a pofitive Idea of: But in endeavouring to make it Infinite, it being always enlarging, always advancing, the Idea is ftill imperfect and incompleat. So much Space as the Mind takes a view of in its Contemplation of Greatness, is a clear Picture and pofitive in the Understanding: but Infinite is ftill greater. 1. Then, the Idea of fo much, is pofitive and clear. 2. The Idea of Greater is alfo clear, but it is but a comparative Idea. 3. The Idea of fo much greater as cannot be comprehended; and this is plain negative, not pofitive. For he has no pofitive clear Idea of the largeness of any Extenfion, (which is that fought for in the Idea of Infinite) that has not a comprehenfive Idea of the Dimenfions of it: And fuch no body, I think, pretends to in what is Infinite. For to fay a Man has a pofitive clear Idea of any Quantity, without knowing how great it is, is as reasonable as to fay, he has the pofitive clear idea of the Number of the Sands on the Sea-shore, who knows not how many they be; but only that they are more than twenty. For juft fuch a perfect and pofitive Idea has he of an infinite Space or Duration; who fays it is larger than the Extent or Duration of 10, too, iooo, or any Vol. I: N other |