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Show 'vegrkr of ~norvledge ... Book I V. 10, that yet would need a Probf. Sinte without the Perception of fuch Agreement or Difagreement, there is no Knowledge produced : If it be perceived by it felf, it is intuitive Knowledge: If it cannot be perceived by it (elf, there is need of fome intervening !Jea, as a common meafure to fhew their Agreement or Difagreement, by which it is plain, that every O:ep in Reafoning, that produces Knowledge, has intuitive Certainty , which when the Mind perceives, there is no more required but t~ remember it to make the Agreement or Difagreement of th~ Ideas concer~ing \l'hich we enqui.re. vilible and certain_. So ~hat to mak; ~ny thtng a Dem.onfrratt~n, It IS nece/Tary to percetve the tmmediate Agreement of !he tntervenmg Ideas, whereby the Agreement or Difagreement of \he two /Jeas und~r Examination ('vherethe on~ i~ always the lirfr, and the other the!afl: m the Account) IS found. This tntuitive Perception of the Agreement or Difagreement of the intermediate Idea1 in tach Step ahd Progre(lidh oft he Demonfiration,mufl: alfo be carried ex;[!. ly in the,M:ind,ancf a Man mufl: be fore that no part is left out; which bctaufe in long DeduCl:ions, and the ufe of many Proofs, the Memory does hot always fo readily and exaCl:ly retain: therefore it comes to pafs that this is IJ\ore imperfeCl: than intuitive Knowledge, and Men embrace 'often l'alfhoods for Demdnfrrtttions. ~. 8. The nl::ce~ry of this !ntuitive ffnowledge, in each fl:ep of fcientiAcal dr .demonO:rattve Reafonmg, gave occafi~~· I imagine, to that mifla- 1reH Axzom, tbat all Reqfonzng was ex pra:cogrutts & prxconceais . which how far it is :1. mifu.ke, 1 fl~all have occafion to fl1ew more at larg;, where t come to confider Pro~olittons, and parttcularly thofe Propofitions which are called Maxims; and to !hew th~t'tis by a mifiake, that they ; re fuppofed to ~ the foundations of all our Knowledge and Reafonings. §, 9· It ts 11~t only Mathematicks, or the ld<as ~/on< of Nurn!Jer, ExttnjioH, and FJg«r<, that ar; 'capable of DttnOHj/ration, no more than it is [hefe Ideas alone, and th~tr Modes, that are capable of Intuition : For whatever ldtas We have, wh'erem the Mtnd can perceive the immediate ,Agrfem~nt o.r _Difagreement tha~ is between them, there the Mind is ca· pabl~ of,mtUlttve ffnowledge; and \vhere it.'can perceive the Agreement or Oifagreement of any two ldtas, by an mt~llttve Perception of the Agree- 1n~t o/ Difagl'eement they ha~e Wtth any .mtermediate Ideas, rJ1ere the _Mtnd ts caJ)ali1e of Demonfl:ratton, \vhtch IS not limited to Idw of Extetlfion, orf)gure, or Number, or tbeir N!odes. _ §. l o. T!!e Reafon ~hy i.t haS been generally fought for, and fuppofed to be only m thofe, I tmagm~, has bten not only the general ufefulneiS of 'thofe Sctences: But becaufe, m comparing their Equality or Exce(s, the M~es of Number~ have every the leafl: difference very clear and.perc~iva: t>Ie . 1And though 10 Elctenfion, eVery 'the !eafi Excefs is not fo perceptible; ~etthe. Mmd has found out ways, to examme and dtfcover demonfirative_ IY the Juft Equahty of two Angles, or Extenfions, or Figures, and both thefe, '·e. Numbers and Ftgures; can be fet down by vifible and Jailing marks. ' §. r'r. 'But in other liinple fdeas,who(e Modes and differences are made, ,nnd counted by d"&ree~, a~d not quantity, we have not (o nice and accurate a dtfl:~ncbon ot .thetr differences, as to perceive, or lind ways to meafore thetr )Ufi Equality, or the leafl: Differences. For thofe other limplc Ideas, bcwg A~;pearaoce~ or Scnfations, produced in us by the Size, f i~~ c, Number, and Mouon of minute Corpufcles fingly infenfible, their ' erent deJ!;r~ alfo .depend upon the variation of fome, or all of thofe Caufes; wh1~:-h Iince ttcannot be obferved by ·us in Particles of Matter, whereof Chap. H. whereof ea<h is too fub!ile to be perceived, it is impojljble for its to have wy exad: Meafures of the different d~gr.¢es of. thefe lim pie Jdtas. lior fuppoling the Senfation or ldta we ~arne WhitcnefS, be . produced in liS by a certain. number of Globules, wbtch. havmg a verttctty abput thetli own Centres fl:ril<e upon the Retina of the Eye, with a certam degree of Rotation ~swell as progtciiive Swifen~fs ; it willdJence eafily follow, that -he m~re the fupcrficial parts of any Body arc fo .ordered; :Is to re~ ed: the greater n~mbet o~ Globules of ~lg~t, and to give the~ that pr~ per Rotation, wluch ts fit to produce th;siSenfatiOn •ot Whtte m us,. the more White will that Body appear, that, from ? n ~q_!Jai fpace fends to. the Retina the greater number of fuch Corpufcles, With that peculiaf forn of Molion. ' J do not fay, that the na1ur~ of Light ~onlills iit very. f"!al! round Globules, nor of Whitenefs, in fueh a teXtJ\~C ofi• parts as g1ves a certain Rotation to thefe Globules, when tt refleCts-them ; f?tt I am ,not now treating phJ iically 6f Light, or Colours: Q~t· ~hiSI I tht.nk, I ~ay Jay, that I cannot .(and I W6uld be g!ad 3ny one would make mtelhgtble that he did) aoncetve how Bodtes Wltllaut/ us , can an¥ ways affeCl: our Senfes, but by the immediate con.ta& of the fenlible &dtes the~felves, as in Tafiing and Feeling; or the tmp1ilfb offome mfenlible Parndes coming from fhern, as in Seeing, Hearin~, and Smelhng ; by the dtfferent impulfe df-'which Parts, cal\fed by thetr dt!ferep~ SIZe, Ftgure, and Mer. tion the variety of Senfations is produced m us. ' . §! 1,, Whether then they ~ Globules, or no ; or whether they have. a Verticity about -their own Centres, t)1at produc_e. the Idea of Wlutenefs m lis, this is certain, that the more Parncles ~f Ltght. are refleCl:ed from a Body, fitted to give them that peculiar Mottpn, ,WJ!tch produces the Senfation of Whitenefsin us; and potlibly too, the qUicker the p.ecu!tar Motion is the whiter does the Body appear, from whtch the greater number ard reflected, ,as is evident in the lame ptece of J.>jlper ~ut ".' the Sun. beams, in the Shade, and in a dark ljole ; 111 each of whtch, It wdl produce in us the U ta of Whiten~IS in far different degrees. . § N t knowing therefore what number of PartiCles , nor what Mo~i~~ ·of rl1em is fit to produce any precife d~gree ofWhitenefs, we cannot demonfirate the certain Equality of any two de!lrees of Whttenefs, booaufe we have no certain Standard ,to theafure ,them by, nor Means: to di!lin uifh every the leafi real difference; the only help we have bemg fro g ur Senfes which in this point• fail us. But where the dtfferen.ce ts fo ~;.,t as to produce in the Mind clearly dillint'): Ideas, whole dtfferencesgcan be perfeCl:ly retained, there thefe ld•as of Colours, liS w~ fee lD dit!Crent kinds , as Blue and Red, are as capable of Demonfl:ratt~, ad Idea< of Number and Extenlion. What·l have /ler~ _fatd of Wluten an Colours, 1 think, holds true in all fecuhdones Q!lahttes and thetr Modes. § T hefe two (viz.) Intuition· .and Demonllt'luon, are the degffies of 0~~knowledge ; ~vhatever comes fl1ort of one of thefe, Wtth what a u· ranee foever embraced, is but Faith, or Optmon, but not Knowledge, at lea!t in nil general Truths. There is, indeed, another PerceptloH •[1 the Mind employ'd about the particular exij/eHce of ji11Jte Be!Hf!,S w1;f t us. _.:hich going beyond bare probability, and yet not reachmg per ~ to ~ither of the tore-going degrees of Certainty, paifes under the nameo . \{now ledge. There can be nothi~g more certain,th~n tha.t .the Idea f.d re-> cc~ve from an external ObjeCl: ism our Mmds; thts IS mtumve Kno\;,f ~e: Butwhetherthcre be any thing more than barely that Idea 'tn. our .'In i, whether we can thence certam· 1y t·n Jce t. tl Je ex·tn ence of af % t 11M11g w11 tt hJo' ukt us, which correfponds to t ha. t'T'd e M,~· s ; 1la t whereo orne e tt h1e0t e |