Reasoning was ex Præcognitis et Præconcessis," the falsity of which I shall have occasion to shew when I consider propositions, especially those called maxims.

It has generally been taken for granted that Mathematics alone are capable of demonstration; possibly from want of due method and application, and not of evidence in other parts of knowledge: for wherever the mind can by an intuitive perception of the agreement of intermediate ideas discover the agreement of two remote ideas, there is demonstration; and this privilege is not limited to ideas of Extension, Figure, Number, and their Modes.

The reason of this opinion is not only the general usefulness of that science; but because the minutest differences in numbers are so clear: and though this is not the case in Extension, yet our marks for the ideas of number and figure are clearer and more perfectly determined than ideas marked only by words. In other simple ideas, whose differences are counted by degrees, and not by quantity, the minutest variations cannot be measured, because we have no exact signs of the degrees of our sensations. Not knowing what number or motion of the particles of any body is necessary to produce a precise degree of whiteness, we cannot demonstrate the certain equality of any two degress. Whatever falls short of

intuition or demonstration, with whatever assurance embraced, is but Faith or Opinion, at least in all general truths.

There is indeed another perception of the mind, concerning the particular existence of finite beings without us, which exceeding probability, but not amounting to certainty, passes under the name of knowledge: for some men doubt whether from the idea in our minds we can certainly infer the existence of any thing external corresponding to it, because men may have such ideas in their minds, without objects either existing or affecting their senses. But I think we have evidence that puts this past doubt: for I ask any one if he is 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 only thinks on its savour. There is as plain a difference between an idea revived by memory, and one immediately perceived by sense, as between any two distinct ideas.

If any one say, that in a dream ideas may arise without external objects; he may please to dream that I make him this answer-1st, No matter whether or no I remove his scruple; where all is a dream, reasoning is useless, knowledge nothing. 2dly, I believe he will allow a manifest difference between dreaming of being in the fire, and actually being in it but should he say that this last state is

mere supposition, there being no such thing as fire without us; I reply that we certainly find pleasure or pain follow the application of certain objects whose existence we perceive, or dream that we perceive, by the senses; and this certainty is as great as our happiness or misery, beyond which we have no concern to know or to be. So that I think to the two former degrees of knowledge may be added this of the existence of particular external objects, by our consciousness of ideas derived from them; which I call Sensitive.

Our knowledge may not always be clear, even where our ideas are clear; because the clearness or obscurity of our knowledge consists not in that of the ideas themselves, but in our perception of their agreement or disagreement: a man may have the clearest ideas of the angles of a triangle, and of equality to two right ones, and yet but a very obscure perception of their agreement. In short, he that hath not determined ideas to the words he uses, cannot make propositions of them, of whose truth he can be certain.

CHAP. III.

OF THE EXTENT OF HUMAN KNOWLEDGE.

OUR knowledge cannot exceed our ideas either in extent or perfection: and frequently it falls short of the extent of our ideas; because we cannot find intuitive propositions to serve as proofs of the agree ment or disagreement of two different ideas. It would indeed be well with us if there were not many doubts about our ideas, of which I believe we never shall be resolved. Nevertheless I do not doubt that human knowledge might be carried much farther, if men would employ as much labour about the means of discovering truth, as they do for the support of falsehood, to maintain a system, or party, they are once engaged in.

We have the ideas of a square, a circle, and equality, and yet shall perhaps never be able to find a circle equal to a square, and certainly know that it is so:-We have the ideas of matter and thinking, but shall possibly never know whether any material being thinks or not; it being impossible for us, merely by the contemplation of our own ideas, to discover whether Omnipotency has not given to some systems of matter a power to perceive and think, or joined a thinking immaterial substance to matter: for, not know

ing wherein thinking consists, we can almost as easily conceive matter endued with that faculty, as any other substance; at least I see no contradiction in the supposition: though I think I have proved (chap. x. book iv.) that it is no less than a contradiction to suppose matter (which is evidently in its own nature void of sense and thought) to be the first eternal thinking being.

How can any one know that some perceptions, as Pleasure and Pain, do not belong to some bodies, or that they can only belong to an immaterial substance, being produced by the motion of the parts of body. As far as we can conceive, body can only affect body, and motion produce motion; so that when we allow that motion produces pleasure or pain, or any idea of colour or sound, we quit our reason, and attribute it to the good pleasure of our maker.

I mean not to lessen the belief of the soul's immateriality: nor am I speaking here of Probability, but of Knowledge; and I think that it becomes the modesty of philosophy not to pronounce magisterially, where we want that evidence that can produce knowledge; that it is of use also to discern how far our knowledge does reach; for the present not being a state of vision, we must in many things be content with faith and probability. We need not think it strange that we are unable to attain philosophical proofs of the soul's immateriality, since all the great"