first; till at last, after many removes, it has a great mixture of dimness, and is not at first sight so knowable, especially to weak eyes. Thus it is with knowledge, made out by a long train of proofs.

§. 7. Each step must have intuitive evidence.-Now, in every step reason makes in demonstrative knowledge, there is an intuitive knowledge of that agreement or disagreement, it seeks with the next intermediate idea, which it uses as a proof: for if it were not so, that yet would need a proof; since without the perception of such agreement or disagreement, there is no knowledge produced. If it be perceived by itself, it is intuitive knowledge; if it cannot be perceived by itself, there is need of some intervening idea, as a common measure to show their agreement or disagreement. By which it is plain, that every step in reasoning, that produces knowledge, has intuitive certainty : which when the mind perceives, there is no more required, but to remember it, to make the agreement or disagreement of the ideas, concerning which we enquire, visible and certain. So that to make any thing a demonstration, it is necessary to perceive the immediate agreement of the intervening ideas, whereby the agreement or disagreement of the two ideas under examination (whereof the one is always the first, and the other the last, in the account) is found. This intuitive perception of the agreement or disagreement of the intermediate ideas, in each step and progression of the demonstration, must also be carried exactly in the mind, and a man must be sure that no part is left out; which, because in long deductions, and the use of many proofs, the memory does not always so readily and exactly retain; therefore it comes to pass, that this is more imperfect than intuitive knowledge, and men embrace often falsehood for demonstrations.

§. 8. Hence the mistake, ex præcognitis et præconcessis.— The necessity of this intuitive knowledge, in each step of scientifical or demonstrative reasoning, gave occasion, I imagine, to that mistaken axiom, that all reasoning was ex præcognitis et præconcessis; which how far it is mistaken, I shall have occasion to show more at large, when I come to consider propositions, and particularly those propositions which are called maxims; and to show that it is by a mistake, that they are supposed to be the foundations of all our knowledge and reasonings.

§. 9. Demonstration not limited to quantity.-It has been generally taken for granted, that mathematics alone are capable of demonstrative certainty; but to have such an agreement or disagreement, as may intuitively be perceived, being, as I imagine, not the privilege of the ideas of number, extension, and

figure alone, it may possibly be the want of due method and application in us, and not of sufficient evidence in things, that demonstration has been thought to have so 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 disagreement 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 demonstration, which is not limited to ideas of extension, figure, number, and their modes. §. 10. Why it has been so thought.-The reason why it has been generally sought for, and supposed to be only in those, I imagine has been not only the general usefulness of those sciences; but because, in comparing their equality or excess, the modes of numbers have every the least difference very clear and perceivable; and though in extension, every the least excess is not so perceptible; yet the mind has found out ways to examine and discover demonstratively the just equality of two angles, or extensions, or figures; and both these, i. e. numbers and figures, can be set down by visible and lasting marks, wherein the ideas under consideration are perfectly determined, which, for the most part, they are not, where they are marked only by names and words.

§. 11. But in other simple ideas, whose 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 and find ways to measure their just equality, or the least differences. For those other simple ideas being appearances or sensations, produced in us by the size, figure, number, and motion of minute corpuscles singly insensible, their different degrees also depend upon the variation of some or all of those causes; which, since it cannot be observed by us in particles of matter, whereof each is too subtile to be perceived, it is impossible for us to have any exact measures of the different degrees of these simple ideas. For supposing the sensation or idea we name whiteness, be produced in us by a certain number of globules, which having a verticity about their own centres, strike upon the retina of the eye, with a certain degree of rotation, as well as progressive swiftness; it will hence easily follow, that the more the superficial parts of any body are so ordered, as to reflect the greater number of globules of light, and to give them the proper rotation, which is fit to produce this sensation of white in us, the more white will that body appear, that from

an equal space sends to the retina the greater number of such corpuscles, with that peculiar sort of motion. I do not say, that the nature of light consists in very small round globules, nor of whiteness, in such a texture of parts as gives a certain rotation to these globules, when it reflects them; for I am not now treating physically of light or colours: but this, I think, I may say, 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 senses, but by the immediate contact of the sensible bodies themselves, as in tasting and feeling, or the impulse of some insensible particles coming from them, as in seeing, hearing, and smelling; by the different impulse of which parts, eaused by their different size, figure, and motion, the variety of sensations is produced in us.

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§. 12. Whether then they be globules, or no; or whether they have a verticity about their own centres, that produces the idea of whiteness in us; this is certain, that the more particles of light are reflected from a body, fitted to give them that peculiar motion, which produces the sensation of whiteness in us; and possibly, too, the quicker that peculiar motion is, the whiter Hoes the body appear, from which the greater number are reflected, *s is evident in the same piece of paper put in the sun beams, on the shade, and in a dark hole; in each of which, it will proluce in us the idea of whiteness in far different degrees.

§. 13. Not knowing therefore what number of particles, nor what motion of them, is fit to produce any precise degree of whiteness, we cannot demonstrate the certain equality of any two degrees of whiteness, because we have no certain standard to measure them by, nor means to distinguish very the least real difference, the only help we have, being from our senses, which in this point fails us. But where the difference is so great, as to produce in the mind clearly Histinct ideas, whose differences can be perfectly retained, there these ideas of colours, as we see in different kinds, es blue and red, are as capable of demonstration, as ideas of number and extension. What I have here said of whiteness and colours, I think, holds true in all secondary qualities, and their modes.

§. 14.

Sensitive knowledge of particular existence.-These o, viz., intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with what aurance soever embraced, is but faith, or opinion, but not knowledge, at least in all general truths. There is, indeed, another perception of the mind, employed about the particular existence of finite beings without us; which going beyond

bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, passes 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 than intuitive knowledge. But whether there be any thing more barely that idea in our minds, whether we can thence certainly infer the existence of any thing without us, which corresponds to that idea, is that, whereof some men think there may be a question made, because men may have such ideas in their minds, when no such thing exists, no such object affects their senses. But yet here, I think, we are provided with an evidence, that puts us past doubting: for I ask any one, whether he be not invincibly conscious to himself of a different perception, when he looks on the sun by day, and thinks on it by night; when he actually tastes wormwood, or smells a rose, or only thinks on that savour, or odour? We as plainly find the difference there is between an idea revived in our minds by our own memory, and actually coming in our minds by our senses, as we do between any two distinct ideas. If any one say, a dream may do the same thing, and all these ideas may be produced in us without any external objects, he may please to dream that I make him this answer: First, That it is no great matter, whether I remove this scruple, or no: where all is but dream, reasoning and arguments are of no use; truth and knowledge nothing. Secondly, That I believe he will allow a very manifest difference between dreaming of being in the fire, and being actually in it. But yet if he be resolved to appear so sceptical, as to maintain, that what I call being actually in the fire, is nothing but a dream; and we cannot thereby certainly know, that any such thing as fire actually exists without us; I answer, that we certainly finding, that pleasure or pain follows upon the application of certain objects to us, whose existence we perceive, or dream that we perceive, by our senses: this certainly is as great as our happiness or misery, beyond which, we have no concernment to know, or to be. So that, I think, we may add to the two former sorts of knowledge, this also, of the existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas from them, and allow these three degrees of knowledge, viz., intuitive, demonstrative, and sensitive: in each of which, there are different degrees and ways of evidence and certainty.

§. 15. Knowledge not always clear, where the ideas are so.→ But since our knowledge is founded on, and employed about, our ideas only, will it not follow from thence, that it is conform

able to our ideas; and that where our ideas are clear and distinct, or obscure and confused, our knowledge will be so too? To which I answer, No: for our knowledge consisting in the perception of the agreement or disagreement of any two ideas, its clearness or obscurity, consists in the clearness or obscurity of that perception, and not in the clearness or obscurity 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 obscure perception of their agreement, and so have but a very obscure knowledge of it. But ideas which, by reason of their obscurity or otherwise, are confused, cannot produce any clear or distinct knowledge; because as far as any ideas are confused, so far the mind cannot perceive clearly, whether they agree or disagree. Or to express the same thing in a way less apt to be misunderstood. He that hath not determined ideas to the words he uses, cannot make propositions of them, of whose truth he can be certain.

CHAPTER III.

OF THE EXTENT OF HUMAN KNOWLEDGE.

§. 1. Knowledge, as has been said, lying in the perception of the agreement or disagreement of any of our ideas, it follows from hence, that,

First, no farther than we have ideas.-First, We can have knowledge no farther than we have ideas.

§. 2. Secondly, no farther than we can perceive their agreement or disagreement.-Secondly, That we can have no knowledge farther than we can have perception of their agreement, or disagreement: which perception being, 1, Either by intuition, or the immediate comparing any two ideas; or, 2, By reason, examining the agreement or disagreement of two ideas, by the intervention of some others: or, 3, By sensation, perceiving the existence of particular things. Hence it also follows,

§. 3. Thirdly, intuitive knowledge extends itself not to all the relations of all our ideas.-Thirdly, That we cannot have an intuitive knowledge, that shall extend itself to all our ideas, and all that we would know about them; because we cannot examine and perceive all the relations they have one to another by juxta-position, or an immediate comparison one with another. Thus having the ideas of an obtuse and an acute angled triangle, both drawn from equal bases, and between parallels, I can, by