ment 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.

Why it has been so thought.

§. 10. The reason why it has been generally sought for, and supposed to be only in those, I imagine has been not only the ge

neral 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 of 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 of all 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 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, caused by the different size, figure, and motion, the variety of sensations is produced in us.

§. 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 does the body appear, from which the greater number are reflected, as is evident in the same piece of paper put in the sun-beams, in the shade, and in a dark hole; in each of which it will produce 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 every the least real difference, the only help we have being from our senses, which in this point fail us. But where the difference is so great, as to produce in the mind clearly distinct ideas, whose differences can be perfectly retained, there these ideas or colours, as we see in different kinds, as 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.

Sensitive §. 14. These two, viz. intuition and deknowledge monstration, are the degrees of our knowof particular ledge; whatever comes short of one of these, existence. with what assurance 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 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 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 into 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; 1. 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. 2. 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 applica tion of certain objects to us, whose existence we perceive or dream that we perceive by our senses; this certainty 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. But since our knowledge is foundKnowledge ed on, and employed about our ideas only, not always will it not follow from thence, that it is clear, where conformable to our ideas; and that where the ideas are our ideas are clear and distinct, or obscure so. 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 be can be certain.

CHAP. 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,

1. No farther First, we can have knowledge no farther

than we have than we have ideas.

ideas.

than we can

perceive

their agree

§. 2. Secondly, that we have no know2. No farther ledge farther than we can have perception of their agreement or disagreement. Which perception being, 1. Either by intuition, or ment or dis- the immediate comparing any two ideas; or, agreement. 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. Intuitive knowledge extends it

of all our

§. 3. Thirdly, that we cannot have an intuitive knowledge, that shall extend itself to all our ideas, and all that we would know about self not to all them; because we cannot examine and perthe relations ceive all the relations they have one to anideas. other by juxtaposition, 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 intuitive knowledge, perceive the one not to be the other, but cannot that way know whether they be equal or no; because their agreement or disagreeinent in equality can never be perceived by an immediate comparing them the difference of figure makes their parts incapable of an exact immediate application; and therefore there is need of some intervening qualities to measure them by, which is demonstration, or rational knowledge. §. 4. Fourthly, it follows also, from what is above observed, that our rational knowknowledge ledge cannot reach to the whole extent of our ideas; because between two different

4. Nor demonstrative