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 Reasoning.

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 scarcely 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.

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 [1.] the general usefulness of those sciences, but [2.] because, in com

paring equality or excess, the Modes of Numbers have every—the least-difference very clear and perceivable: and though in Extension 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 [3.] 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.

But in other simple ideas, whose modes and differences are made and counted by degrees, and not [by] quantity, we have not so nice and accurate a distinction of their differences as to perceive or 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 subtle to be perceived, it is impossible for us to have any exact measures of the different degrees of these simple ideas.

Sensitive knowledge of particular existence.—These two, viz. Intuition and Demonstration, are the Degrees of our Knowledge; whatever comes short of one of these, 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 that we receive from an external object is in our minds; this is Intuitive Knowledge. But whether there BE any thing more than barely that ideain-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 any rived 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 his scruple or not: 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

idea re

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 that we cannot thereby certainly know that any such thing 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 [which] we have of the actual entrance of ideas from them-and [may] 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.

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 conformable 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 disagreeemnt 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 agree

ment, 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 has not determined the 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.

KNOWLEDGE, as has been said, lying in the Perception of the agreement or disagreement of any of our Ideas, it follows from hence, that,

No farther than we have ideas.-First, We can have Knowledge no farther than we have Ideas.

No farther than we can perceive their agreement or disagreement. Secondly, That we can have no Knowledge farther than we can have Perception of that 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,

Intuitive knowledge extends itself not to all the relations of all our ideas.-Thirdly, That we cannot have an In