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$9. Demonftration not limited to Quantity. It has been generally taken for granted, that mathematics alone are capable of demonftrative certainty; but to have fuch an agreement or difagreement as may intuitively be perceived, being, as I imagine, not the privilege of the ideas of number, extenfion and figure alone; it may poffibly be the want of due method and application in us, and not of fufficient evi, dence in things, that demonftration has been thought to have fo little to do in other parts of knowledge, and been scarce so much as aimed at by any but mathematicians. For whatever ideas we have, wherein the mind can perceive the immediate agreement or difagreement that is between them, there the mind is capable of intuitive knowledge; and where it can perceive the agreement or disagreement of any two ideas, by an intuitive perception of the agreement or disagreement they have with any intermediate ideas, there the mind is capable of demonftration, which is not limited to ideas of extenfion, figure, number, and their modes.

10. Why it has been so thought.

THE reafon why it has been generally fought for, and fuppofed to be only in thofe, I imagine has been not only the general usefulness of thofe fciences, but becaufe, in comparing their equality or excefs, the modes of numbers have every the least difference very clear and perceivable; and though in extenfion, every the leaft excefs is not fo perceptible, yet the mind has found out ways to examine and difcover demonftratively the juft equality of two angles, or extenfions, or figures; and both thefe, i. e. numbers and figures, can be fet down by visible and lasting marks, wherein the ideas under confideration are perfectly determined; which for the most part they are not, where they are marked only by names and words.

§ II.

Bur in other fimple ideas, whofe modes and differences are made and counted by degrees, and not quantity, we have not so nice and accurate a distinction of

their differences, as to perceive or find ways to meafure their juft equality, or the leaft differences. For those other fimple ideas, being appearances or fenfations, produced in us by the fize, figure, number and motion of minute corpufcles fingly infenfible, their different degrees alfo depend upon the variation of fome, or all of those causes; which fince it cannot be obferved by us in particles of matter, whereof each is too fubtle to be perceived, it is impoffible for us to have any exact measures of the different degrees of thefe fimple ideas. For fuppofing the fenfation of idea we name whiteness be produced in us by a certain number of globules, which having a verticity about their own centres, ftrike upon the retina of the eye, with a certain degree of rotation, as well as progref five swiftness, it will hence eafily follow, that the more the fuperficial parts of any body are fo ordered, as to reflect the greater number of globules of light, and to give them that proper rotation which is fit to produce this fenfation of white in us, the more white will that body appear, that from an equal space fends to the retina the greater number of fuch corpufcles, with that peculiar fort of motion. I do not fay, that the nature of light confifts in very small round glo. bules, nor of whitenefs in fuch a texture of parts, as gives a certain rotation to these globules when it reflects them; for I am not now treating phyfically of light or colours: But this, I think, I may fay, that I cannot (and I would be glad any one would make intelligible that he did) conceive how bodies without us can any ways affect our fenfes, but by the immediate contact of the fenfible bodies themselves, as in tafting and feeling, or the impulfe of fome infenfible particles coming from them, as in feeing, hearing, and smelling; by the different impulse of which parts, caused by their different fize, figure and motion, the variety of fenfations is produced in us.

§ 12.

WHETHER then they be globules, or no; or whether they have a verticity about their own centres, that

produce the idea of whitenefs in us, this is certain, thatthe more particles of light are reflected from a body, fitted to give them that peculiar motion which produces the fenfation of whiteness in us, and poffibly too, the quicker that peculiar motion is, the whiter does the body appear, from which the greater number are reflected, as is evident in the fame piece of paper put in the fun-beams, in the fhade, and in a dark hole; in each of which it will produce in us the idea of whiteness in far different degrees.

13. Why it has been fo thought.

NoT knowing therefore what number of particles, nor what motion of them is fit to produce any precife degree of whiteness, we cannot demonftrate the certain equality of any two degrees of whiteness, because we have no certain standard to measure them by, nor means to diftinguish every the leaft real difference, the only help we have being from our fenfes, which in this point fail us. But where the difference is fo great, as to produce in the mind clearly distinct ideas, whofe differences can be perfectly retained, there these ideas of colours, as we fee in different kinds, as blue and red, are as capable of demonstration, as ideas of number and extenfion. What I have here faid of whiteness and colours, I think, holds true in all fecon dary qualities, and their modes.

$14. Senfitive Knowledge of particular existence. THESE two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of thefe, with what affurance foever embraced, is but faith, or opinion, but not knowledge, at leaft in all general truths. There is, indeed, another perception of the mind, employed about the particular exiftence of finite beings without us, which going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, paffes under the name of knowledge. There can be nothing more certain, than that the idea we receive from an external object is in our minds; this is intuitive knowledge. But whether there be any thing more than

barely that idea in our minds, whether we can thence certainly infer the existence of any thing without us, which correfponds to that idea, is that, whereof some men think there may be a question made; because men may have fuch ideas in their minds, when no fuch thing exifts, no fuch object affects their fenfes. But yet here, I think, we are provided with an evidence, that puts us paft doubting; for I ask any one, whether he be not invincibly confcious to himself of a different perception, when he looks on the fun by day, and thinks on it by night; when he actually taftes wormwood, or smells a rofe, or only thinks on that favour or odour? We as plainly find the difference there is between any idea revived in our minds by our own memory, and actually coming into our minds by our fenfes, as we do between any two diftinct ideas. If any one fay, a dream may do the fame thing, and all thefe ideas may be produced in us without any external objects, he may please to dream that I make him this anfwer: 1. That it is no great matter, whether I remove his fcruple, or no; where all is but a dream, reafoning and arguments are of no use, truth and knowledge nothing. 2. That I believe he will. allow a very manifeft difference between dreaming of being in the fire, and being actually in it. But yet if he be refolved to appear fo fceptical, as to maintain that what I call being actually in the fire is nothing but a dream, and that we cannot thereby certainly know, that any fuch thing as fire actually exists without us I anfwer, that we certainly finding that pleafure or pain follows upon the application of certain objects to us, whose existence we perceive, or dream that we perceive by our senses; this certainty is as great as our happinefs or mifery, beyond which we have no concernment to know, or to be. So that I think, we may add to the two former forts of knowledge this alfo, of the existence of particular external objects, by that perception and confcioufnefs we have of the actual entrance of ideas from them, and allow these three degrees of knowledge, viz. intuitive, de

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monftrative, and fenfitive; in each of which, there are different degrees and ways of evidence and certainty.

$15. Knowledge not always clear, where the Ideas

are fo.

BUT fince our knowledge is founded on, and employed about our ideas only, will it not follow from thence, that it is conformable to our ideas; and that where our ideas are clear and distinct, or obfcure and confufed, our knowledge will be fo too? To which I anfwer, No: For our knowledge confifting in the perception of the agreement or difagreement of any two ideas, its clearness or obfcurity confifts in the clearness or obfcurity of that perception, and not in the clearnefs or obfcurity of the ideas themselves; v. g. a man that has as clear ideas of the angles of a triangle, and of equality to two right ones, as any mathematician in the world, may yet have but a very obfcure perception of their agreement, and so have but a very ob. fcure knowledge of it. But ideas, which by reason of their obfcurity or otherwife, are confufed, cannot produce any clear or diftinct knowledge; because as far as any ideas are confused, so far the mind cannot perceive clearly whether they agree or disagree: Or, to exprefs the fame thing in a way lefs apt to be mifunderstood, he that hath not determined the ideas to the words he uses, cannot make propofitions of them, of whose truth he can be certain.

K

CHAP. III.

OF THE EXTENT OF HUMAN KNOWLEDGE.

§ I.

NOWLEDGE, as has been faid, lying in the perception of the agreement or disagreement of any of our ideas, it follows from hence, that,

1. No farther than we have Ideas.

FIRST, We can have knowledge no farther than we have ideas.

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