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Show 102- . Infinity. Bqok U. Space by farther Additions, remaining frill the fame, he hence takes th, Jd,~ of infnit• Spa«. . . 4- !lis, I think, is the way whereby the Mtnd gm the Idea of inf ;te s}ae<. 'Tis a quite different Confideranon to examme,. whether the Mind has the Idea offuch a ~ouwdlefs Space atlually extjlmg, fi nce our IdeaJ are not always Proofs of the Exifience of Things; but yet Iince this comes here in our way, I fuppofe I may fay, that we areaptto think, that Space in it felf is athlally boundlefs, to which Imagination, the Idea of Space or Expanfion of its felf naturally leads us. For it being confidered by us, either as the Extenfion of Body, or as exifling by it tetf, withoutany folid Matter taking it up, (for of fuch a void Space, we have not only the Idea, but l have proved, as I think, from the Motion of Body, its neceifary exiflence,) it is impollible the Mind !hould be ever able to lind or fuppofe any end of it, or be flopp' d any where, in its progrefs in this Space, how far (oever it extends its Thoughts. Any Bounds made with Body, ev~n Adamantine Walls, are fo far from putting a fiop to the Mind in its f.1rther progrefs in Space and Extenfion, that it rather facilitates and enlarges it: Forfo far as that Body reaches, fo far no one can doubt of Extenfion; and when weare come to the utmofi elttremity of Body, what is there that can there put a fiop and fatisfie the Mind, that it is at the end of Space, when it perceive it is not; nay, when it is fatislied that BoPY it.felf can move into it? For il it benecelfary for the matron of Body, that there !hould be an empty Space, though never fo little hereamongfl Bodies, and it!><'. pollible for Body to r_nove in or through that empty Space; nay,tt IS 1mpoilible for any parttcle of Matter to move but into an empty Space, the fame pollibility of a Bodies moving into a void Spac;e, beyond the utmofi Bounqs of Body, as well as into a void Space interfperfed amongfi Bodies, will ah~ays remain clear and evident, the Idea of empty pure Saace, whether within or beyond the confines of all Bodies, being exactly the fame, differing not in Nature, though in Bulk; and there being nothing to hinder Body from moving into it: So that wherever the Mind places it fclfby any thought, either amongfi or remote from all Bodies, it can in this uniform Idea of Space no-where lind any bounds, any end; and fomufi necelfarily conclude it by the very Nature and Idea of each part of it to be actually infinite. .. _§. 5. As by the power we lind in our felves of rcpeatinij, as often as we WtiJ, any Idea of Space, we get the Idea ofimmenfity"; to by being able to repeat the Idea of any length of Duration we have in our Minds with all the endl~fs addition of Number, we come by the Idea of Et;rnity. For we lind m our felves we can no more come to an end of fitch repeated Ideas, than we can come to the ~nd, of Number, which every one perceives he cannot. But here agam tts another quefi10n, quite different from our havmg an (de a of Eternity, to know whether there were any rtal Bemg, :-vhofe Duratton has. been eternal. He ~hat confiders fomething now extfimg~ mull neceifanly come to fomethmg eternal, but having fpoke of thts 10 another plac~, I !hall fay here no more of it, but proc;eed <;>n to fom~ other Confiderattons of our Idea of Infinity .• §.6. If tt be fo, that our Idea ofinlinity be got from the Power we obfervc m our felves, of repeating without end our own IdeaJ; It may be demanded , Why we do not attri~ute InjiniiJ to other Ideas as well aJ tbofe of Sface and Duration; fmce they may be as cafily, a~d as ofre~ rc~eatcd m our Mmds as the other ; and yet no body ever thinks of in· fimte fweetn~fs, or infinite whitenefs, though he can repeat the Idea of SwectorWhtte, asfrequentlyasthofeofaYard, or a Day ? To which l Chap. XIV . Infinity. I anfwe~, All the IdtaJ that are conftdered as having jxlrts, and are ca• pable ofincreafe by the addition of any equal or leis parts, afford us by their repetition the Idea of lnlimty; becau!e With this endletS repetition, there is connnued an enlargement, of wluch there can be no end. But in other Ideas it is not fo; lor to the largefi Id•a df Exrenfion ·or Duration that I at prefent have, the addition of any the leafl part mokes an inl: reafe; but to the perfect en Idea I have oft he whitefi Whitenefs, if I add another of a letS or equal whitenefs, (and of a whiter than I have, I cannor add the Idea,) it makes no increafe, and enlarges not my Idea at all · and therefore the different IdeaJ of Whitenefs, f.!Jc. are called Degrees: ,for thofe Ideas that confifl of Parts, are capable of being augmented by every addition of the leafi pare ; but if you take rhe Idea ofW hite, which one parcel of Snow yielded yefierday to our Sight, and another Idea of White from another parcel of Snow you fee to day, and put thetn together in your Mind, they embody, as it were, and run into one, and the Idea of Whitene!S is not at all increafed; and if we add a lcfs degree of Whitenefs to a greater, weare fo far from increafing, that we diminilh it. Thofe Ideas that con fill: not of Pans, cannot be augmented to whor proportion Men pleafe, or be firetched beyond what they have received by their Senfes; but Space, Duratton, and Number, betng capable of mcrea!e by repetition, leave in the Mind an Idea of an endtefs room for,more; nor can we concetveany where a fiop to a farther Addttton or Progref.. fion, and fo thofe UeaJ alone lead our Minds towards the Thought of Infinity. . . . . §.7. Though our Id~a oflnlimry a~1fe from the contemplatton <>fQ.tlarttity, and the endlefs mcreafe the ~md 1s able to make m Qyanttty by the repeated additions of what Pornons theteof 1t pleafes ; yet I gue& we caufe greatconfufion in our Thoughts, when we join Infinity to any fup ·pofed Idea of Qgantity the Mind can be thought to have, and fo difcourf~ or reafon about an infinite quantity :is an infinite Space, or an infinite Duration : For ·our Idea of IH./inity being, as I think, an end/eft growing Idea but the Idea of any Q)Jantity the Mind has, being at that time terrn'inated in tl1at Idea, lfor be it as great as it will, it can be no greater than it is,) to join Infinity t~ it, i~ to adjufl a fianding meafure. to a growing bulk · and therefore I dunk 1t IS not an mfignilicant fubnlty tl I fay, that we ;re carefully to difiingui!h between the !d.- of the Infinity of Space, and the Idea of aSpace infinite: The lirfi is nothing but a fuppofed -endlefs Progrellion of the Mind, over what repeated Ideas of Space It pleafes ; but to have actually in the Mind the Idea of a Space mfimte, IS to fuppofe the Mind already paired over, and actually to have a View of a)l thofe repeated Idw ofSpace, _which an end!efs repetition can never totally reprefent to it, whtcll carnes 1i1 tt a plam contrndtctwn: . §. 8. This, perhaps, will be a little.plaiher, if we confider tt m Num. bers. The infinity of Numbers, to the end of whofe addttton every one perceives there is no approach, eaft!y appears to any one that reflect. on it : But how clear foevcr this Idea of the Infimty of Number be, there IS nothing yet more evident than the abfurdity of the actual Jd,a of an Infi· nite Number, whatfoevcr pofitive IdeaJ we have m our Mmds of any Space, Duration, or Number, let them be never f~ great, they are lhtl fin ite- but when we fuppofe an mexhaufltble remamder, from whtch we remo~e allloounds, and wherein we allow the Mind an endlefs progref/ ion of Thought, without ever cnmpleating the Idea, there we have our Idea of Infinity; wluch though tt feem to be pretty clear, when we contid or nothina elfe in it, but the Negation of an end, yet when we would ~ frame |