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Show too Number. Book II. cdfary d(il:inct Names are to Numbering, without pretending to introduce neW ones of my irtvention. §. 7. Thus Children, either for Want of Na11les to mark the feveral Ptqgieffiorts of Numbers, or not havtngyet the faculty to collect fc:rtterecJ JdedJ into complex ones, and range them to a regular Order, and fo retain them in their Memories, as is neceflary to reckoning, do not begin to number very early, nor proceed ir: it very far or il:eadily, till a good while after they are well furmfi1ed With good il:ore of other Idem ; and ()Oe may often obferve them in difcourfe and reafon pretty well, and have very clear conceptions of feveral ot~er things., before they can tell' io. Arid fome, through the default of thelf Memones, who cannot retain the feveral Combinations of Numbers, with their Names annexed in their difiinct orders, and the dependence of fo long a train of numeral Progrcf.. lions, and their relation one to another, are not able all their life-time, td reekon or regularly go over any moderate Series of Numbers. For he that \Viii count Twenty, or have any Idea of that Number, mull: know that Nineteen went before, with the diil:inct Name or Sign of every one of them, as they il::!nd marked in their order; for where-ever this fails, a gap is made, the CHain breaks, and the Progrefs in numbering can go no farther. So that to reckon rigbt, it it required, x. That the Mind diil: ingttifli C!r~fiilly two Jde~s; wh.iclt are ~iffe~ent one fr~m anoth<:t only by the udd1ftdn or fobtraClwil of one Unite. 2.. That 1t retam m memory tile Names, or Marks, · of tbe fevernl Combinations from an Unite to tHat Nllrl'lber; atid that not' ~ohfllfedly, and at random, but in tlxat exaefoil!er, thattheNlimbers follow one' another; ih either of which if it ~ip~,' tfte whole bulinefs 6f 'Mu'dibring •Will be difiurbed, and there ,will 'tehlaib ohly tile confufed Ided of multitude, but the IdedJ necefiiuY to difii~ httm~rtldoil~ will Mt be .ittained to. '. · • §!•8. This fatt!'ret iS bbfer\la!Jle in 'Numher, That it is 'thit which the Mind make~ llfe of,' in1meaforiHg' oil thingr that by us are meafurable, which J;nncipally.at:fJ!xpawfon~hd <Dur'atioH 1 and our Idea. of Infinity, even·wln:n applied td tijofe, kertl~ to'be nothiftgbut the Infinity ofNum· ber, ' Fotwllat elfChte our Ideas of Eternity and Immenfity but then:peated additl~ms'of ce_rtain Idear ~f iinag~ned .parts of Space' and ExpanlioH,, br ~fitton, .w1th the Infi~1ty ~f NumiJe_r, m which we can come to rlo-eM·bf Addlbont For fucli lin mexhaufi1ble fiock, {'\lumber, of all othe~ idtlr Jdeat,mnll.Cleat!yfurnif!Je5 Us with,as is obviou~ to every one! For lh h Man coiled: mto'oneSUni as' great a Number as he pleafes, this Mult_itude,, ho~v great 'foever, lelfens not one' jot the power of adding to It, ot bnngs hun any nearer the end of the mexhau!hble frock of Number, Where frill there telnaihs as touch to be added, as if none \A• ere taken our. And this end!efs addition of Numbers, fo apparent to the Mind, is that, I thmk, wluch gtves us the cleaxeft and moil: diil:inct Ide• of Infinity· of wlli~h more in the following Chapter. . · ' ~1o .,,·, · lJJirf I .u !1 itO!H <J:'J")' "uL r .. \.1 L.1 1 Jli ,/ ,.: ..... .-.. l " I /1' • :: J ~.- I I' CH.AP· l' l l u j . , . I I\ - Chap. VXII· Infinity. ------------------ CHAP. XVII. 0 J Infinity. §. t. HE that would know what kind of Idea it is to which we give the name of Injinity, cannot do it better than by confidering to what Infinity is by the Mind more immediately attributed, and then how the Mind comes to frame it. Fi,ite, and bjinite, feem to me to be looked upon by the Mind, as the Modes of'2!Jantity, and to be attributed primarily in their firil: delignation only to thofe things wh!ch have parts? and are capable of increafe or dimmunon,by the addmon or fubtrafr1on of any the leail: part ; and fuch are the Ideas of Space, Duration, ond Number, which we have confidered in the foregoing Chapters. 'Tis true, that we cannot but be affurcd, That the Great GOD, of whom, and from whom are all things, is incomprehenf1bly Infimte; but yet, when we apply to thot firft and !upream Be.ing,. ou_r Idea of Infinite in o.ur weak and n.arrow Thoughts, we do it pnmanlym refpefrofh1s DuratiOn and Ub1qu1ty; and, I tlunk, more figuratively to his Power, Wifdom, and Goodnefs, ant\ other At· tributes which are properly inexhauil:ible and incomprehenfible, &r. For wh;n we call them Infinite, we have no other Idea of this Infinity, ~ut what carries with it fome refleCtion on, and. imitation of that 'Number or Extent of the Acts or Objects of God's Power, Wifdom, an~ Good. nelS which can never be fuppofed fo great, or fo many, which thefe At· trib~tes will not always furlnount and. exceed, let us multiply them in our Thoughts with all theinfinity of endlefsnu'?~r. I do ,n?t pretend to fay how thefe Attributes arc m G,OD, who IS mfimtely lieyond the reach of our narrow Capacities: They do without doubt contain in them all poflible perfection; but this, I fay, is our way of conceiving them, and thefe our Ideas of their Infinity. · §. 2.. Finite then, and Infinite, being by the Mind looked on as modifications of Expanfion and Duration, the next thing to be confidered is, Horv the Mind comer /;y them. As for the Idea of Finite, there is no great c\ifliculty ; the obviou.s portions ofExte~fion,that affect our Senfes? carry with them toto the Mmd the IJea of F1mte, and the ordmary perwds of ~cceffion whereby we meafure Time and Duration ; as Hours, Days, and y cars' are bounded Lengths: the difficulty is, how we come by thofe t<>umtlefs Ideas of Eternity and Immenjty, Iince the 9bjeCts we converfe ~vith, come fo much fhort of any approach or proportwn to that Largepefs. .' ·§. 3. Every one that has any Idea of any il:oted lengths of Space, as a foot finM ~hat he can repeat that Idea; and joining it to the former, lnak;the1 !JeJ ofrwof'oot; and by the addition of a. third, three Foot; and fo on without ever coming to an end of hls.add1t1ons, whether oft he fame Idea of a Foot or if he pleafe of doubling It, or any other Idea he )t:ls of ariy length, ;sa Mile, or Diametre of the Earth, or of the Orbis f1·•r.nw ; for which-ever ofthefe hetakes,and how often foever he doubles, or any ocherwife multiplies it, he finds t!J~t after he has contmued tlus doub'ling in his Thoughts, and enlarged Ius Idea as much as he pleafes, he has no more reafon to ftop, nor is one jot nearer the end of fuch AdLlition, than he was at firft·fetting out; the power of enlarging his Idea of C Space l OI |