§ 9.

Habitual Knowledge twofold.

Or habitual knowledge, there are alfo, vulgarly speaking, two degrees:

First, The one is of fuch truths laid up in the memory, as whenever they occur to the mind, it actually perceives the relation is between thofe ideas. And this is in all thofe truths, whereof we have an intuitive knowledge; where the ideas themselves, by an immediate view, difcover their agreement or disagreement one with another.

Secondly, The other is of fuch truths, whereof the mind having been convinced, it retains the memory of the conviction without the proofs. Thus a man that remembers certainly that he once perceived the de monstration, that the three angles of a triangle are equal to two right ones, is certain that he knows it, because he cannot doubt of the truth of it. In his adherence to a truth, where the demonstration by which it was at first known is forgot, though a man may be thought rather to believe his memory than really to know; and this way of entertaining a truth feemed formerly to me like fomething between opinion and knowledge; a fort of affurance which exceeds bare belief, for that relies on the teftimony of another : yet upon a due examination I find it comes not short of perfect certainty, and is in effect true knowledge. That which is apt to mislead our first thoughts into a mistake in this matter, is, that the agreement or difagreement of the ideas in this cafe is not perceived, as it was at first, by an actual view of all the intermediate ideas, whereby the agreement or difagreement of thofe in the propofition was at firft perceived; but by other intermediate ideas, that fhow the agreement or difagreement of the ideas contained in the propofition whose certainty we remember. For example, in this propofition, that the three angles of a triangle are equal to two right ones, one who has feen and clearly perceived the demonftration of this truth, knows it to be true, when that demonstration is gone out of his mind; fo that at prefent it is not

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 shows 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 no ma thematical demonftration would be any other than particular and when a man had demonstrated 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 first discovered it to be true. Such a memory as that, able to retain such a train of particulars, may

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be well thought beyond the reach of human faculties; when the very discovery, perception, and laying together that wonderful connection of ideas, is found to furpass most 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 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 amongit. other differences is one, which fhows that demonftrative knowledge is much more imperfect than intuitive, as we fhall fee in the following chapter.

A

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 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 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 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 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 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 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 difcoverable; and in that cafe remains in ignorance, and at most gets no farther than a probable conjecture. The reason why the mind cannot always perceive presently the agreement or difagreement of two ideas, is, because those ideas, concerning whofe agreement or disagreement the inquiry is made, cannot by the mind be fo put together as to fhow it. In this ease then, when the mind cannot fo bring its ideas tó

gether, as by their immediate comparison, and as it were juxta-pofition or application one to another, to perceive their agreement or disagreement, it is fain, by the intervention of other ideas (one or more, as it happens) to discover the agreement or disagreement which it fearches; and this is that which we call reafoning. 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 flow the agreement of any two others, are called proofs; and where the agreement or disagreement 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 disagreement of any other) and to apply them right, is, I fuppofe, that which is called. fagacity.

§4. But not fo easy.

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 last 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