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1. Identity, or diverfity.
2. Relation.

3. Co-existence, or necessary connection.
4. Real exiflence.

§ 4. 1. Of Identity or Diverfity. FIRST, AS to the firft fort of agreement or difagreement, viz. identity or diverfity, It is the first act of the mind, when it has any fentiments or ideas at all, to perceive its ideas; and fo far as it perceives them, to know each what it is, and thereby alfo to perceive their difference, and that one is not another. This is fo abfolutely neceffary, that without it there could be no knowledge, no reafoning, no imagination, no diftinct thoughts at all. By this the mind clearly and infallibly perceives each idea to agree with itself, and to be what it is; and all diftin&t ideas to disagree, . e. the one not to be the other: and this it does without pains, labour or deduction, but at first view, by its natural power of perception and diftinction. And though men of art have reduced this into those general rules, What is, is; and it is impoffible for the fame thing to be, and not to be; for ready application in all cafes, wherein there may be occafion to reflect on it; yet it is certain, that the firft exercife of this faculty is about particular ideas. A man infallibly knows, as foon as ever he has them in his mind, that the ideas he calls white and round, are the very ideas they are, and that they are not other ideas which he calls red or fquare: Nor can any maxim or propofition in the world make him know it clearer or furer than he did before, and without any fuch general rule. This then is the firft agreement or difagreement, which the mind perceives in its ideas; which it always perceives at first fight: and if there ever happen any doubt about it, it will always be found to be about the names, and not the ideas themfelves, whofe identity and diverfity will always be perceived, as foon and as clearly as the ideas themfelves are, nor can it pofiibly be otherwife.

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§ 5. 2. Relative.

SECONDLY, The next fort of agreement, or difagree ment, the mind perceives in any of its ideas, may, 1 think, be called relative, and is nothing but the percep tion of the relation between any two ideas, of what kind foever, whether fubftances, modes, or any other. For fince all diftin&t ideas muft eternally be known not to be the fame, and fo be univerfally and conftantly denied one of another, there could be no room for any pofitive knowledge at all, if we could not perceive any relation between our ideas, and find out the agreement or difagreement they have one with another, in feveral ways the mind takes of comparing them.

§ 6. 3. Of Co-existence.

THIRDLY, The third fort of agreement, or difagreement, to be found in our ideas, which the perception of the mind is employed about, is co-existence, or nonco-exilence in the fame fubje&t; and this belongs particularly to fubftances. Thus, when we pronounce concerning gold that it is fixed, our knowledge of this truth amounts to no more but this, that fixedness, or a power to remain in the fire unconfumed, is an idea that always accompanies and is joined with that particular fort of yellownefs, weight, fufibility, malleablenefs, and folubility in aqua regia, which make our complex idea, fignified by the word gold.

$7. 4. Of real Existence.

FOURTHLY, The fourth and laft fort is that of actual real existence agreeing to any idea. Within thefe four forts of agreement or difagreement, is, I fuppofe, contained all the knowledge we have, or are capable of: For all the inquiries that we can make concerning any of our ideas, all that we know or can affirm concerning any of them, is, that it is, or is not, the fame with fome other; that it does, or does not, always co-exist with fome other idea in the same subject; that it has this or that relation to fome other idea; or that it has a real exiftence without the mind. Thus blue is not yellow, is of identity: Two triangles upon equal bafes between

two parallels are equal, is of relation: Iron is fufceptible of magnetical impreffions is of co-exiflence: God is, is of real exiftence. Though identity and co-exiftence are truly nothing but relations, yet they are fo peculiar ways of agreement or difagreement of our ideas, that they deferve well to be confidered as diftinct heads, and not under relation in general; fince they are fo different grounds of affirmation and negation, as will eafily appear to any one, who will but reflect on what is faid in feveral places of this effay. I should now proceed to examine the feveral degrees of our knowledge, but that it is necessary first to confider the different acceptations of the word knowledge.

8. Knowledge actual or babitual.

THERE are several ways wherein the mind is poffeffed of truth, each of which is called knowledge.

1. There is actual knowledge, which is the prefent view the mind has of the agreement or difagreement of any of its ideas, or of the relation they have one to another.

2. A man is faid to know any propofition, which having been once laid before his thoughts, he evidently perceived the agreement or disagreement of the ideas whereof it confifts; and fo lodged it in his memory, that whenever that propofition comes again to be reflected on, he, without doubt or hesitation, embraces the right fide, affents to, and is certain of the truth of it. This, I think, one may call habitual knowledge and thus a man may be faid to know all those truths which are lodged in his memory, by a foregoing clear and full perception, whereof the mind is affured pait doubt, as often as it has occafion to reflect on them. For our finite understandings being able to think clearly and diftinctly. but on one thing at once, if men had no knowledge of any more than what they actually thought on, they would all be very ignorant; and he that knew moft would know but one truth, that being all he was able to think on at one time.

$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 baving been convinced, it retains the memory of the conviction without the proofs. Thus a man that remembers certainly that he once perceived the demonftration, 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 those in the propofition was at first perceived; but by other intermediate ideas, that fhow the agreement or difagreement of the ideas contained in the propofition whofe 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 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 no ma thematical 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 fartaer, 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

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