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Show 274 Extent of Hum4ne Knowledge. Book IV. --~~-------------~--------------~~------------ that are ignorant of Algfbra cannot imagine the Wonders in this kind are to be done by it; and what farther Im provements and Helps, advantageous to otl~e,r parts ofKnowledg~, the fagaci~us Mind of Man may yet find our, t!s not,ealie to determme. Th1s at leafi I believe, that the '/deaspf~anmx ~re not thofe alone that are capable of Dcmonflration ~uc\ Kn~~>ledge ; and that other, and perhaps more ufeful parts of Con~ em~latwn, would .afford us Certainty, if Vices, Pailions, and domineenng Jnterefis did not oppofe, or menace fuch Endeavours. The Idea of a fupreme Being, infinite in PO\I'er and Wifdom. wltofc Workmanflup we are, and on whom we depenJ ; and the [J,; of our felves, as underfiandmg,ratlonnl Creatures, being fuch as are clear in u ~ould, I fuppofe, if duly confidered, and purfued, afford fuch Found~: twns of our Duty and Rules of 1\.Clion, as might place Morality amo11gfl. th• SCieNCes car;al/, of Demonjfration; wherc.n I doubt not, but from Pnnc1ples, as mcontefiable as thofe of the Mathematicl<s, by ncceffiry Confequcnces, the .meafures of nght and wrong mi<>l1t be made out to ouy one that will apply himfelf with the fame Ind1!fer~Jcy and Arten;ion to the one, as he d?es t.o the other of thefe Sciences. The Relation of other Modes may certainly be perceived, as well as thofe of Number and Ex-· tenfi?n; ~nd I cannot fee why they lhould not alfo be capable of Demon-' firauon, 1f due Methods were thooght on to examine, or purfue rhcir J\.greement or D1fagreement. Where there is no Propriety, there is 1.0 I•J•flJCe, 1s a Propolit1o~ as cer.ram as any Demonfiration in E11clid : For ~~e Idea ofProJ'Crty, bemg a r!ght to any thing; and the lclea to w!1ich !"!~name lnJUfilce IS gtven, bemg the Invafion or Violation of that right. It IS ev1denr, thatthefe Idear being thus efiablifl1ed, and rhefc names an: lexed to them, I • can gs certainly know this Propolition to be true as t Jat a Tnangle has three J\.ngles equal to two right ones. 1\.gain, No Go' li~r.ment allows a6Jolu" Li/;erty? the Idea of Government being the efla~ it.lhment of Soc1ety upon cert31!1 Rules or Laws, which require Conformity to them; and the Idea of abfolute Liberty, being for any one to do ;hatevfie~ he pleaffes; I .am as capable of being certain of the Truth of this ro\'0 1t1on, as o any m Mathematicks. . f ~.~ 9· That which in this refped has given the advantage to rite Ideas 0 X!!fiuant!ty, ~nd made them thought more capable of Certainty and Demon rat10n, ts, l F11'rfl1, That they can be fer down, and reprefented by fenfible marl<s, nWy u cw 1 Jda ve a greater and 0~ Co fi d . 5, d "rer rre pon ence With them than a- CO ieso~f 'rhO: ld~un. s whatfocvcr. Dia~rams drawn on· Paper are wtrds c · I •.s 1S. th'fi Mmd, and not !table to the Uncertainty that in L' ar[Y 10 t letr lgnt cation. An Angle, Circle, or Square d~J\1'11 ch mes, les open to the v~ew, and cannot be miftaken: it r~m~ins un· an~eably, ~d Il"!ay at le1fure beconfidered, and examined ond theDf" moo rat10n rev1fed, and all the parts of it may be gone o~c; more rhan :c~ Wdthour aay dan~er of the leafi change in the ideas. Tllis cann,ot wh~r~by c;;:: ~~nmfu;al: ead we ~ave nofenji61e marks that rej'emMe them, them b . which t em own' we have nothmg but Words to exprefs IJ, thy' fi d fcthough, when Wntten, they remain the fame yet the t!Jaeat st heye y an do·rl r: may .c han. ~e 1. 0 tl le Jra me 'M a n; and ,t is ver'y feldom, are not lnerent m d1 erent Perfons. . STiondly, J\.nother thing that makes the greater difficulty in Ethicks :,res ~~mor~ Ideas are commonly more complex than thofe of the Fi: conve : mar fc conlidered in Mathematicks: from whence thefe two ln-mences ollow : FITjl, That their names are of more uncertain ~ig-nification, (:hap. III. Extent of Humane Knowledge. nification, the precife ColleCtion of limple !dear they fiand for not being fo eafily agreed on , and fo the Sign that is ufed for them in Communication, always, and in Thinking, often, does not always carry with it the fame !dea. Upon which the lame Diforder, Confulion, and Error follows, as would if a Man, going to demonflrate fomething of an Heptagon, fi10uld in the DiagrJm he took to do it, leave out one of the J\.ngles, and by over~ght make rl1e Figure with one J\.ngle lefs than the name ordinarily imported, or he intended it lhould, when at firft he thought of his Demonfiration. This often happens, and is hardly avoidable in very complex moralltleas, where the fame name being retained, one 1\.ngle, 1. e. one fimple Idea is left out or put in, in the complex one, (fiill called by the fame name,) more at one time than another. Seco11dly, From the Complexednefs ofthefe moral Ideas the~e follows another lnconvt;nience, (vii.) that the Mmd cannot ealily retam thofe prec1fe Combmattons, ·fo enClly and perfeCtly, as is nece/Tary in the Examination of the Habitudes and Correfpondencies, Agreements or Difagrcements, of feveral of them one with another; efpecially where it is to be judged of by long DeduCtions, and the Intervention offeveral other complex !dea r, to thew the 1\.greement, or D1fagreemcnt of two remote ones. l11e great help againfi this, which Mathematicians find in Diagrams :md Figures, which remain unalterable in their Draughts,is very apparent, and the memory would often have great difficulty otherwife to retain. them fo exaCtly, whilfi the Mind went over the parts of them, fiep by fiep, to examine their feveral Corref}>andencies: J\.nd though in cafling up a long Summ, either in 1\.ddition, Multiplication, or Divifion, every part be only a Progretlion of the Mind, taking a view of its own fd_.s, and Co!! (idering their Agreement or.Di1agreement, and the Refolution of the ~efiion be nothing but the Refult of the whole, made up of fue~ parttogl~rs; whereof the Mind has a clear Perception ; yet wuhout fettmg down the feveral Pans by marks, whofe precife Signir.cations are known, avd by; marks, that !aft and remain in view, when the memory had let them go ; it would be almofi impotlible to carey fo many different ld-.s in ·Mind, without confounding, or letting llip [orne parts of the Reckoning, and thereby making all our Reafonings about it ufelefs. In wh1ch Cafe, the Cyphers or Marks help not the Mind at all to perceive the. J\.greement of any two, or more Numbers, their Equalities or Proporttons. That the Mind has only by Intuition of its own Ideas of the Numbers themfe!ves. But the numerical CharaCters are helps to the memory, to record andretain the feveral/d,as about which the Demonfiration is made, whereby a man may know how far his intuitive Knowledge, in furveying feveral of the particulars, has proceeded; that fo he may withm~t Confufion .&o on to what is yet unknown ; and, at lafi, have 1ll one v1ew Qefore h1m the Refult of oil his Perceptions and Reafonings. · . §,tO One part of theft Uifadvaotagp, in moral Ideas, wh1ch has made them be thought not capable of Demonftration, !J1a]' il) a good rneafure be remedud bv Definitions, fetting down that Col!echon of limpltt !d~as, which every-Term lhall fiand for; and then u(ingt!Je Termsfiedily and confiqntly for that precife ColleB:ion, And Wlj~.~method~ A.lil•h•, or fomething of that kind,may hereafter fuggefi,to te111pve the orJwr: d1ffi• cultics, is not calie to foretell. Confi.dent I am, that if Men would 10 the fame method, and with the fame inditferency, fear~h ~fter moral, as they, do mathematical Truths, they would find them tO !Jave a JlrongerCon• 9ex1on one with another, and a. more necelfary Confequence [rom our ~lear and diflin 1 !deas, and to come nearer perfeCt !Je!liOnfil'lltlOOj than N n,. i> |