actually in view, and poffibly cannot be recollected : but he knows it in a different way from what he did before. The agreement of the two ideas joined in that propofition is perceived, but it is by the intervention of other ideas than those which at first produced that perception. He remembers, i. e. he knows (for remembrance is but the reviving of fome paft knowledge) that he was once certain of the truth of this propofition, that the three angles of a triangle are equal to two right ones. The immutability of the fame relations between the fame immutable things, is now the idea that fhows him, that if the three angles of a triangle were once equal to two right ones, they will always be equal to two right ones. And hence

he comes to be certain, that what was once true in the cafe, is always true; what ideas once agreed, will always agree; and confequently what he once knew to be true, he will always know to be true, as long as he can remember that he once knew it. Upon this ground it is, that particular demonftrations in mathematics afford general knowledge. If then the perception that the fame ideas will eternally have the fame habitudes and relations, be not a fufficient ground of knowledge, there could be no knowledge of general propofitions in mathematics; for ro mathematical demonftration would be any other than particular and when a man had demonftrated any propofition concerning one triangle or circle, his knowledge would not reach beyond that particular diagram. If he would extend it farther, he must renew his demonftration in another inftance, before he could know it to be true in another like triangle, and fo on by which means one could never come to the knowledge of any general propofitions. Nobody, I think, can deny that Mr. Newton certainly knows any propofition, that he now at any time reads in his book, to be true; though he has not in actual view that admirable chain of intermediate ideas, whereby he at firft difcovered it to be true. Such a memory as that, able to retain fuch a train of particulars, may

be well thought beyond the reach of human faculties; when the very difcovery, perception, and laying together that wonderful connection of ideas, is found to furpafs most readers comprehenfion. But yet it is evident, the author himself knows the propofition to be true, remembering he once faw the connection of those ideas, as certainly as he knows fuch a man wounded another, remembering that he faw him run him. through. But because the memory is not always fo clear as actual perception, and does in all men more or lefs decay in length of time, this amongst other differences is one, which fhows that demonftrative knowledge is much more imperfect than intuitive, as we fhall fee in the following chapter.

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CHAP. II.

OF THE DEGREES OF OUR KNOWLEDGE.

1. Intuitive.

LL our knowledge confifting, as I have faid, in the view the mind has of its own ideas, which is the utmost light and greateft certainty we with our faculties, and in our way of knowledge, are capable of, it may not be amifs to confider a little the degrees of its evidence. The different clearness of our knowledge feems to me to lie in the different way of perception the mind has of the agreement or difagreement of any of its ideas. For if we will reflect on our own ways of thinking, we fhall find that fometimes the mind perceives the agreement or difagreement of two ideas immediately by themselves, without the intervention of any other: and this, I think, we may call intuitive knowledge. For in this, the mind is at no pains of proving or examining, but perceives the truth, as the eye doth light, only by being directed toward it. Thus the mind perceives, that white is not black, that a circle is not a triangle, that three are more than two, and equal to one and two. Such kind of truths the mind perceives at the first fight of the ideas together, by bare intuition, without the inter

vention of any other idea; and this kind of knowledge is the clearest and most certain that human frailty is capable of. This part of knowledge is irrefiftible, and, like bright fun-fhine, forces itself immediately to be perceived, as foon as ever the mind turns its view that way; and leaves no room for hefitation, doubt, or examination, but the mind is prefently filled with the clear light of it. It is on this intuition that depends all the certainty and evidence of all our knowledge; which certainty every one finds to be fo great, that he cannot imagine, and therefore not require a greater: for a man cannot conceive himfelf capable of a greater certainty, than to know that any idea in his mind is fuch as he perceives it to be; and that two ideas, wherein he perceives a difference, are different, and not precifely the fame. He that demands a greater certainty than this, demands he knows not what, and fhows only that he has a mind to be a fceptic, without being able to be fo. Certainty depends fo wholly on this intuition, that in the next degree of knowledge, which I call demonftrative, this intuition is neceffary in all the connections of the intermediate ideas, without which we cannot attain know. ledge and certainty.

§ 2. Demonftrative.

THE next degree of knowledge is, where the mind perceives the agreement or difagreement of any ideas, but not immediately. Though wherever the mind perceives the agreement or disagreement of any of its ideas, there be certain knowledge, yet it does not always happen, that the mind fees that agreement or difagreement which there is between them, even where it is discoverable; and in that cafe remains in ignorance, and at most gets no farther than a probable conjecture. The reafon why the mind cannot always perceive presently the agreement or disagreement of two ideas, is, because those ideas, concerning whofe agreement or difagreement the inquiry is made, cannot by the mind be fo put together as to fhow it. In this cafe then, when the mind cannot fo bring its ideas to

gether, as by their immediate comparison, and as it were juxta-pofition or application one to another, to perceive their agreement or difagreement, it is fain, by the intervention of other ideas (one or more, as it happens) to discover the agreement or difagreement which it fearches; and this is that which we call reaJoning. Thus the mind being willing to know the agreement or difagreement in bignefs, between the three angles of a triangle and two right ones, cannot by an immediate view and comparing them do it; because the three angles of a triangle cannot be brought at once, and be compared with any one or two angles; and so of this the mind has no immediate, no intuitive knowledge. In this cafe the mind is fain to find out fome other angles, to which the three angles of a triangle have an equality; and finding those equal to two right ones, comes to know their equality to two right ones.

§3. Depends on Proofs.

THOSE intervening ideas which ferve to fhow the agreement of any two others, are called proofs; and where the agreement or difagreement is by this means plainly and clearly perceived, it is called demonftration, it being shown to the understanding, and the mind made fee that it is fo. A quickness in the mind to find out these intermediate ideas (that shall discover the agreement or difagreement of any other) and to apply them right, is, I fuppofe, that which is called fagacity.

§ 4. But not fo eafy.

THIS knowledge by intervening proofs, though it be certain, yet the evidence of it is not altogether fo clear and bright, nor the affent fo ready, as in intuitive knowledge. For though in demonftration, the mind. does at laft perceive the agreement or difagreement of the ideas it confiders, yet it is not without pains and attention: there must be more than one tranfient view to find it. A fteady application and pursuit is required to this discovery; and there must be a progreffion by steps and degrees, before the mind can in this

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way arrive at certainty, and come to perceive the agreement or repugnancy between two ideas that need proofs and the ufe of reafon to show it.

$5. Not without precedent Doubt.

ANOTHER difference between intuitive and demonftrative knowledge, is, that though in the latter all doubt be removed, when by the intervention of the intermediate ideas the agreement or difagreement is perceived; yet before the demonftration there was a doubt, which in intuitive knowledge cannot happen to the mind, that has its faculty of perception left to a degree capable of diftin&t ideas, no more than it can be a doubt to the eye (that can diftinctly fee white and black) whether this ink and this paper be all of a colour. If there be fight in the eyes, it will at firft glimpse, without hefitation perceive the words printed on this paper different from the colour of the paper; and fo if the mind have the faculty of diftinct perceptions, it will perceive the agreement or difagreement of thofe ideas that produce intuitive knowledge. If the eyes have loft the faculty of seeing, or the mind of perceiving, we in vain inquire after the quickness of fight in one, or clearness of perception in the other. $6. Not fo clear.

Ir is true, the perception produced by demonftration is alfo very clear, yet it is often with a great abatement of that evident luftre and full affurance, that always accompany that which I call intuitive; like a face reflected by feveral mirrors one to another, where, as long as it retains the fimilitude and agreement with the object, it produces a knowledge; but it is fill in every fucceffive reflection with a leffening of that pesfect clearness and diftinctnefs, which is in the first, till at laft, after many removes, it has a great mixture of dimness, and is not at first fight fo knowable, efpecially 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 reafon makes in demonftrative knowledge, there is an intuitive knowledge of that agree