520

METAPHYSICS.

several ways wherein the mind is possessed of truth, each of whichis called Knowledge. 1st, There is actual know ledge, when themind has a present view of the agreement or disagreement of anyof its ideas, or of the relation they have one with another. 2dly.A man is said to know any proposition, when having once evi-dently perceived the agreement or disagreement of the ideaswhereof it consists, and so lodged it in his memory, that, wheneverit comes to be reflected on again, the mind assents to it withoutdoubt or hesitation, and is certain of the truth of it. And thismay.be called habitual knowledge. And thus a man may besaid to know all those truths which are lodged in his memory by aforegoing, clear, and full perception.

Of habitual knowledge there are two sorts: the one is of suchtruths laid up in the memory, as whenever they occur to the mind,it actually perceives the relation that is between those ideas. Andthis is in all those truths, where the ideas themselves, by an im-mediate view, discover their agreement or disagreement one withanother. The other is of such truths, whereof the mind havingbeen convinced, it retains the memory of the conviction, withoutthe proofs. Thus a man that remembers certainly, that lie onceperceived the demonstration, that the three angles of a triangle areequal to two right ones, knows it to he true, when that demonstra-tion is gone out of his mind, and possibly cannot be recollected :but he knows it in a different way from what he did before, name-ly, not by the intervention.of those intermediate ideas, wherebythe agreement or disagreement of those in the proposition was atlirst perceived, but by remembering, i. e. knowing that lie wasonce certain of the truth of this proposition, that the three angles ofa triangle are equal to two right ones. The immutability of thesame relations between the same immutable tilings, is now the ideathat shews him, that if the three angles of a triangle were onceequal to two right ones, they will always he so. And lienee liecomes to be certain, that what was once "true, is always true ; whatideas once agreed will always agree; and consequently, what heonce knew to be true, he will always know to be true, as long ashe can remember, that he once knew it.

Of the Degref.s of Human Knowledge.

All our knowledge consisting in the view the mind has of itsown ideas, which is the utmost light and greatest certainty we arecapable of, the different clearness of our knowledge seems to liein the different way of perception the mind lias of the agreementor disagreement of any of its ideas. When the mind perceivesthis agreement or disagreement of two ideas immediately by them-selves, without the intervention of any other, we may call it intui-tive knowledge ; in which cases the mind perceives truth as theeye does light, only by being directed towards it. Thus themind perceives, that white is not black ; that three are more thantwo, and equal to one and two. This part of knowledge is irre-sistible, and, like the bright sunshine, forces itself immediately tobe perceived as soon as ever the mind turns its view that way. llis on tliis intuition that depends all the certainty and evidence ofour other knowledge; which certainty every one finds to be sogreat, that he cannot imagine, and therefore cannot require, agreater. The next degree of knowledge is, where the mind per-ceives not this agreement or disagreement immediatelv, or by thejuxla-position, as it were, of the ideas, because those ideas con-cerning whose agreement or disagreement the inquiry is made,cannot oy the mind in- so put together as to shew it. fn this casethe mind is found to discover the agreement or disagreementwhich it searches, by tire intervention of other ideas: and this iswhat we call reasoning. Thus, if we would know the agreementor disagreement in bigness between the three angles of a triangleand two right angles, we cannot by an immediate view and com-paring them do it; because the three angles of a triangle cannotbe brought at once, and be compared with any other one or twoangles. And so of this the mind iias no immediate or intuitiveknowledge. But we must find out some other angles to which thethree angles of a triangle have equality ; and li tilling those equalto two right ones, w e come to know the equality of these threeangles to two right ones. These intervening ideas which serve toshew the agreement of any two others - , are called proofs: andwhere the agreement or disagreement is bv this means plainly ainiclearly perceived, it is f ailed demonstration. A quickness in the«i;ud to bud those proofs, and to apply them right, is called saga-

city. This knowledge, though it be certain, is not so clear a” 1 'evident as intuitive knowledge. It requires pains and attention*and steady application of mind, to discover the agreement or dis-agreement of the ideas it considers; and there must be a progres-sion by steps and degrees before the mind can in this way arrive a*certainty. Before demonstration there was a doubt, which, 111intuitive knowledge, cannot happen to the mind that lias its (acuityof perception left to a degree capable of distinct ideas, non’ 01 ?than it can he a doubt to the eye, that can distinc tly see white an‘‘black, whether this ink and paper be all of a colour. Now, 1(1every step that reason makes in demonstrative knowledge, thereis an intuitive knowledge of that agreement or disagreement l(seeks with the next immediate idea, which it uses as a proof:if it were not so, that would still require a proof : since withoutthe perception of such agreement or disagreement, there isknowledge produced. By which it is evident, that every step "Jreasoning llial produces knowledge has intuitive certainty; hu*when the mind perceives, there is no more required hut to re-member it, to make tlie agreement or disagreement of the ideas*concerning which we inquire, visible and certain. This intuit" -0perception of the agreement or disagreement of the intermedia* 11ideas, in each step and progression of the demonstration, must alsobe exactly carried in the mind : and a man must be sure that »°part is left out; which because in long deductions tin: memorycannot easily retain, this knowledge becomes more imperfect that*intuitive, and men often embrace falsehoods for demonstrations-It has been generally taken for granted, that mathematics alone arecapable of demonstrative certainty. But to have such an agree-ment or disagreement as may ire intuitively percehecl, being n°‘(he privilege of the ideas of number, extension, and figure aion f *it may possibly be tire want of due method and application in us,and not of sufficient evidence in tilings, that demonstration l' ;lSbeen thought to have so little to do in oilier parts of knowledge-for, in whatever ideas tire mind can perceive the agreement o'disagreement immediately, there it is capable of intuitive know-ledge: and where it can perceive the agreement or disagreeiiH'i’*of any two ideas, by an intuitive perception of the agreement ° rdisagreement they have with any intermediate ideas, there tb emind is capable of demonstration, which is not limited to ti'°ideas of figure, number, extension, or their modes. The reason*why it has been generally supposed to belong to them only, 15because in comparing their equality or excess the modes of nil tu-bers have every the least difference very clear and perceivable-And in extension, though every the least excess is not so percepti-ble, yet the mind lias found out ways to discover the just equallyof two angles, extensions, or figures; and both, that is, number*and figures, can lie set down by visible anil lasting marks. lb"in other simple ideas, whose modes and differences are made an®counted by degrees, and not quantity, we have not so nice a' 1accurate a distinction of their differences, as to perceive or f |,|(ways to measure their just equality or least differences: for tho?°other simple ideas being appearances or sensations produced iff 1|Sby the si/e, figure, motion, &c. of minute corpuscles singlysensible, their different degrees also depend on the variation 0 ,some or all of those causes J which, since it cannot he observe 1 -by us in particles of matter, whereof each is too subtile to ba ]> ercr-ived, it is impossible for us to have any exact measures of t*'°different degrees of these simple ideas. Thus, for instance, i'?:knowing what number of pat tides, nor what motion of them, i s 1to produce any precise degree of whiteness, we cannot di m oirstrate the certain equality 01 any two degrees of whiteness, becau sCwe haw no certain standard to measure them by, nor means *°distinguish every the least difference ; the only help we have be’ 11 '?from'onr senses, which in this point fail us. But wln-re (lie‘1'.ferencc- is so great as to produce in the mind ideas clearly distil' 0 *’there ideas ot colours, as we see in different kinds (blueand >' l< ’for instaiiee,) areas capable ot demonstration as ideas of numb 1and cxleii ion. What is line said of colours holds true in all i -1 *condary qualities. These two then, intuition and demoiislrati 01 ^are the degrees of our knowledge ; whatever comes short of onethese is but faith or opinion, not knowledge, at least in all gener-^truths. There is, indeed, another perception of the mind i 1,1 _ployed about tin- particular existence of finite beings without llS *which going beyond probability, but not reaching to either ol • ^foregoing degrees of certainty, passes under the-name ofkno''

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