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 molt readers comprehenfion. But yet it is evident, the author himself knows the propofition to be true, remembering he once faw the connection of thofe ideas, as certainly as he knows fuch a man wounded another, remembering that he faw him run him through. But becaufe 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 shall fee in the following chapter.

A

CHAP. II.

OF THE DEGREES OF OUR KNOWLEDGE.

$r. Intuitive.

LL our knowledge confifting, as I have faid, in the view the mind has of its own ideas, which is the utmoft light and greatest 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 disagreement 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 themfelves, 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 firft fight of the ideas together, by bare intuition, without the inter

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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 itfelf im. mediately 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 precisely the fame. He that demands a greater certainty than this, demands he knows not what, and shows 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 demonstrative, this intuition is neceffary in all the connections of the intermediate ideas, without which we cannot attain knowledge and certainty.

$2. Demonftrative.

THE next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately. Though wherever the mind perceives the agreement or difagreement 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 difagreement of two ideas, is, becaufe thofe ideas, concerning whofe agreement or difagreement the inquiry is made, cannot by the mind be fo put together as to how it. In this cafe then, when the mind cannot so 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 fo 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 thofe 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 fhall difcover 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 steady application and pursuit is required to this discovery; and there must be a progreffion by steps and degrees, before the mind can in this

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

5. Not without precedent Doubt.

ANOTHER difference between intuitive and demonstrative 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 diftinct 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 first glimpfe, without hesitation perceive the words printed on this paper different from the colour of the paper; and fo if the mind have the faculty of diftinct percep tions, it will perceive the agreement or difagreement of thofe ideas that produce intuitive knowledge. If the eyes have loft the faculty of feeing, or the mind of perceiving, we in vain inquire after the quickness of fight in one, or clearnefs of perception in the other. 6. Not fo clear.

It is true, the perception produced by demonftration is also 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 still in every fucceffive reflection with a leffening of that per fect clearness and diftinctnefs, which is in the first, till at last, after many removes, it has a great mixture of dimnefs, and is not at firft 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 flep reafon makes in demonstrative know ledge, there is an intuitive knowledge of that agree

ment or difagreement it feeks with the next intermediate idea, which it ufes as a proof; for if it were not fo, that yet would need a proof; fince without the perception of fuch agreement or difagreement, there is no knowledge produced. If it be perceived by itself, it is intuitive knowledge; if it cannot be perceived by itfelf, there is need of fome intervening idea, as a common measure to show their agreement or disagreement: By which it is plain that every step in reafoning 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 difagreement of the ideas, concerning which we inquire, vifible and certain. So that to make any thing a demonftration, it is neceffary to perceive the immediate agreement of the intervening ideas, whereby the agreement or difagreement 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 difagreement of the intermediate ideas, in each step and progreffion of the demonftration, muft alfo 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 al ways fo readily and exactly retain; therefore it comes to pafs, that this is more imperfect than intuitive. knowledge, and men embrace often falfehood for de. monstrations.

$8. Hence the miftake, Ex præcognitis et præconceffis. THE neceflity of this intuitive knowledge, in each flep of scientifical or demonstrative reasoning, gave occafion, I imagine, to that mistaken axiom, that all reafoning was ex præcognitis et præconceffis; which how far it is mistaken, I fhall have occafion to fhow more at large, when I come to confider propofitions, and particularly those propofitions which are called maxims; and to fhow that it is by a mistake, that they are fuppofed to be the foundation of all our know ledge and reasonings.