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Show lnftnity. Book II. frame in our Minds the Idea of an Infinite Space or Duration, that Idea is very dbfcure, and confufed, becaufe it is made up_ of two Parts, very different, if. not inconfifrent. For let a Man frame m Ius Mmd an Idea of any Space or Number, as great as he will ; 'tis plain, the Mind refrs and terminates in that Idea, which is contrary to the Idea of In.(intty, _wh1ct1 conjij/r in a Juppofod endlefr Progrcffion. And therefore, I thmk, It IS, that we are fo eafily confounded, when we come to argue, and reafon about infinite Space or Duration, &c. Becaufe the parts of fuch an Idta, not being perceived to be, a.• they are,inconfifrent, the one fide or other a!" ays perplexes, whatever Confequences we draw from the other, as an Idea of Motion not paffing{)n, would perplex any one, wh? fl10uld argue from fuch an ldea which is not better fhan an Idta of monon at refr; and fuch ano1her feeJ~s to me to be theJd_,, of a Space,or( which is the fame thing) a Number infinite, i.e. of a Space or Number, wluch the Mmd actually has and fo views, and terminates in; and of a Space or Number, which in a c~nfrant and endlefs Progref!ion, and enlarging it, can in Thought never attain to. For how large foever an Idea of Space I have in my Mind, it is no larger than it is that infrant that I have it, though I be capablethe next infrant to double it; and fo on in infinitum: For that alone IS mfinite, w!tich has no Bounds, and that the Idta of Infinity; in which our Thoughts can find none. ~. 9· But of all other Idear,it is Numbrr, as I have faid, which, I think, furni{htr ur witb tbe clearcf1 and moj/ dij/infl Idea of Injinity we are capable of. For even in Space aad Duration, when the Mind purfues the Idea of Infinity, it there makes ufes of the /dear and Repetitions ofNumbers, as of millions ol millions of Miles, or Years, which are as fo many difrinCl: I dear, kept belt by Number from running into a confufed heap; wherein. the Mind lofes it felf; and when it has added together as many millions, &c. as it pleafes,ofknown lengths of Space or Duration, theclcarefr Idea it can get of Infinity, is the confufed incomprchenfible remainder of endlefs addible Numbers, which affords no profpeCl: of Stop or Boundary. ~· Io. It -will, perhaps, give us a little farther light into th~ Idea we have of Infinity, and difcover to us, that it is nQtbiwg hut th~ Infnity of Numha applied to determinatt parrr, of which we have in our Minds the difrinCl Mear, if we confider that Number is not generally thought by us infinite, whereas Duration and Extenfion is apt to be fo; which arifes from hence, That in Number we are at one end, as it were: for there being in Number nothing lefs than an Unite, we there frop, and arc at an end ; but in addition, or increafe of Number, we can fet no Bounds: and fo it is like a Line, whereof one end terminating with us, the orh" is extended frill forwards beyond all that we can conceive ; but in Space and Duration it is otherwife. For in Duration, we confider it, as if this Line of Number were extended both ways to an unconceivable, undeterminate, and infinite length; which is evident to any one, that will but refleCl: on what Confideration he hath of Eternity; which, I fuppofe, he will lind to be nothing elfe, but the turning this Infinity of Number both ways, a partt ante, and il parte pof/, as they fpeak For when we would confider Eternity, a parte ante, what do we but beginning from our felves, and the prefent time we are in, we repeat in our Minds the !dear of Years o~ Ages, or any other a(Jignable Portion of Duration pafr, with a prof peel: of proceedmg m fuch Addition, with all the Infinity of Num· ber; and when we would confider Eternity, a parte po./1, we jult after the fame rate begm from our felves, and reckon by multiplied Periods yet to come Chap. XVII. !l')ftniiy. come ftill, extending that Line of Number, as before; and thefc two bemg put togt ther, are that mfimte Duration we call Eternity. which eve~ y "':"Y we confider, appears infinite, becaufe we ftil! turn tl;at wa the mfimteend ofNurnber, t.e. the Power ftill of adding more. y ~. I L The fame happens alfo m Space, wherein conceiving our fe!ves to be as .'t were m the Centre, we d? on all fides purfue thofe indetenninabl~ Lmes of Number; and reckonmg any way from our felves, a Yard M1le, D~ameter of the Earth, or Orhu magma, by the infinity of Number: we add others to them as often a. we will; and having no more Reaton to fct Bounds to thofe repeated Ideas, than we have tofet Bounds to Number, we have that tndetermmable Idea of Immen/ity. ~-I~- And fince in any bulk of Matter,our Thoughts can never arrive at the utmofr Dtvijibtltty, therefore there is an apparent Infinity to us alfo in that, winch has the Infimty alfo of Number, but with this diiTerence, That m the former Confideranons of the Infinity of Space and Duration, we onl_y ufeAdd•uon of Numbers; whereas this is like the divifion of an Umte mt~ tts FraCl:10ns, wh~rem the Mind alfo can proceed i• in.finit•m, as well as m the former Ad:huons, it !J:ing indeed but the Addition frill of new Numbers: though m the Addmon qf the one, we can have no more the pofiuve Idea of a Space mfinttely great, than in the Divifion of the ~ther, .we can have the Idta of a Body infinitely little; our Idea of Infimty bemg, os I may fo fay, a growmg and fugitive Idea ft'll · boundlefs Progreflion that can frep no where. ' 1 J.l1 a §. '3· Though it be hard, I think,to lind any one foabfurd as to fay he ~as the P?littve Idea of an aCl:ual infinite Number; the Infinity whereof ltes only 10 a Power ftill of addmg any Combi!lation ofUnites to any former Number, and that as long, and as much as one will ; the like alfo bemg 10 the Infimt_y of Space and Dutation, which Power leaves always to the Mmd room /orendlefs Additions; yet there be thofe who imag·ne they have po/iti-ve Ideas of i•finite Duration and Space. It :vould I thil~k be enough to deftroy any iuch pofinve Idea of infinite, to ask ftlm tha~ has It, whether he could add to it or no; which would eaiily ihew themifiake. of fuch a pofiuve Idea: We can, I tlunk, have no potitive Idea of any Space or DuratiOn, wfllch JS not made up of, and commenfurate to repeated Numbers of Feet or Yards, or Days and Years, which are the common meafures whereof we have the !dear in our Minds, and wf1ercby we Judge of the greatnefs of thefe fort of quantities. And therefore, Iince a~ Idta .or mfimte Space or Duration mufr needs be made up of infinite I arts, It can have no other Infinity, than that of Number capable fitll of farther Addmo.n i but not an aCl:ual pofitive Idea of a Number inlimte. For, I thmk, It IS ev1dent, that the Addition of finite things together (as ore all lengths, wher~of we have the pofitive Ideas) can nevrr otherw1fe produce the Idea of mfimte, than as Number does; which coniilt• n!' of Add1t1ons of fin1te Unites one to another, fuggefts the Idea of Infimte,_ only by a Power we. find we have, of frill increafing the Sum, and addmg more of the fame k10d,w1thout commg one jot nearer the end of fuch Progreflion. ~- q. They who would prove their Ide. of ln./i•itc to he pojitivt, feem to me to dolt b_y a pleafant Argument, taken li·om the Negation of an end ; wh1ch bemg neganve, the Negation of it is pofitive. He that confiders that the end 1s m Body, but the extremity or fuperficies of that Body wdl not, perhaps, be forward to grant, that the end is a bare neganve: 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 Neg;tion; P nor |
