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two parallels are equal, is of relation : Iron is fufcep. tible of magnetical imprespons is of co-exiftence : God is, is of real existence. Though identity and co-ex. istence are truly nothing but relations, yet they are so peculiar ways of agreement or disagreement of our ideas, that they deserve well to be considered as diftinct heads, and not under relation in general; fince they are so different grounds of affirmation and nega. tion, as will easily appear to any one, who will but reflect on what is said in several places of this essay. I should now proceed to examine the several degrees of our knowledge, but that it is necessary first to consider the different acceptations of the word knowledge.
5 8. Knowledge actual or habitual. THERE are several ways wherein the mind is possessed of truth, each of which is called knowledge.
I. There is actual knowledge, which is the present view the mind has of the agreement or disagreement of any of its ideas, or of the relation they have one to another.
3. A man is said to know any proposition, 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 proposition comes again to be reflected on, he, without doubt or hesitation, embraces the right side, allents to, and is certain of the truth of it. This, I think, one may call habitual knowledge : and thus a man may be said to know all those truths which are lodged in his memory, by a foregoing clear and full perception, whereof the mind is assured pait doubt, as often as it has occafion to reflect on them. For our finite understandings being able to think clearly and diflinctly. 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 most would know but one truth, that being all he was able to think on at one time.
8 9. Habitual Knowledge twofold. Of habitual knowledge, there are also, vulgarly speaking, two degrees :
First, The one is of such truths laid up in the me. mory, as whenever they occur to the mind, it actually perceives the relation is between those ideas. And this is in all those truths, whereof we have an intuitive knowledge; where the ideas themselves, by an immediate view, discover their agreement or disagreement one with another.
Secondly, The other is of such truths, whereof the mind having been convinced, it retains the memory of the conviétion without the proofs. Thus a man that remembers certainly that he once perceived the dem monftration, 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 ad. herence 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 seemed formerly to me like something between opinion and knowledge ; a sort of assurance which exceeds bare belief, for that relies on the testimony 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 case is not perceived, as it was at first, by an actual view of all the intermediate ideas, whereby the agreement or disagreement of those in the proposition was at first perceived; but by other intermediate ideas, that show the agree. ment or disagreement of the ideas contained in the proposition whofe certainty we remember. For ex. ample, in this proposition, that the three angles of a triangle are equal to two right ones, one who has seen and clearly perceived the demonstration of this truth, knows it to be true, when that demonstration is gone out of his mind ; so that at present it is not actually in view, and poflibly cannot be recoilected : but he knows it in a different way from what he did before. The agreement of the two ideas joined in that proposition is perceived, but it is by the intervention of other ideas than those which at first produced that perception. He remembers, i. a. he knows (for remembrance is but the reviving of fome paft knowledge) that he was once certain of the truth of this proposition, that the three angles of a triangle are equal to two right ones. The immutability of the fame relations between the same 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 case, is always true; what ideas once agreed, will always. agree ; and consequently 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 demonstrations in mathematics afford general knowledge. If then the perception that the same ideas will eternally have the same habitudes and relations, be not a sufficient ground of knowledge, there could be no knowledge of general propositions in mathematics ; for no man thematical demonítration would be any other than particular : and when a man had deinonstrated any propofition concerning one triangle or circle, his knowledge would not reach beyond that particular diagram. If he would extend it fartner, he muit renew his demonstration in another instance, before he could know it to be true in another like triangle, and so on : by which means one could never come to the knowledge of any general propositions. 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, inay
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 comprehension. But yet it is evident, the author himself knows the proposition to be true, remembering he once saw the connection of those ideas, as certainly as he knows such a man wounded another, remembering that he saw him run him through. But because the memory is not always so clear as actual perception, and does in all men more or less decay in length of time, this amongst other differences is one, which shows that demonstrative knowledge is inuch more imperfect than intuitive, as we ihall see in the following chapter.
1. Intuitive. A LL our knowledge consisting, as I have said, in A the view the mind has of its own ideas, which is the utmost light and greatest certainty we with our faculties, and in our way of knowledge, are capable of, it may not be amiss to consider a little the dea grees of its evidence. The different clearness of our knowledge seems to me to lie in the different way of perception the mind has of the agreement or disagree. ment of any of its ideas. For if we will reflect on our own ways of thinking, we fhall find that sometimes the mind perceives the agreement or disagreement 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 påins 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 sight 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 irre. fiftible, and, like bright sun-fhine, forces itself im. mediately to be perceived, as soon as ever the mind turns its view that way; and leaves no room for he. fitation, 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 so great, that he cannot imagine, and therefore not require a greater: for a man cannot conceive him, self capable of a greater certainty, than to know that any idea in his mind is such as he perceives it to be ; and that two ideas, wherein he perceives a difference, are different, and not precisely the same. He that demands a greater certainty than this, demands he knows not what, and shows only that he has a mind to be a sceptic, without being able to be fo. Certainty depends fo wholly on this intuition, ihat in the next degree of knowledge, which I call demonstrative, this intuition is necessary in all the connections of the intermediate ideas, without which we cannot attain knowa ledge and certainty.
. .. 2. Demonstrative. Tuệ 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 disagreement of any of its ideas, there be certain knowledge, yet it does not always happen, that the mind sees that agreement or disagreement which there is between them, even where it is discoverable ; and in that case 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 disagreement of two ideus, is, because those ideas, concerning whose agreement or disagreement the inquiry is made, cannot by the mind be so put together as to show it. In this case then, when the mind cannot so bring its ideas to