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does, or does not, always co-exist with some other idea in the same subject; that it has this or that relation with some other idea: or that it has a real existence without the mind. Thus blue is not yellow; is of identity: two triangles upon equal bases between two parallels are equal; is of relation: iron is susceptible of magnetical impressions; is of co-existence: God is; is of real existence. Though identity and co-existence are truly nothing but relations, yet they are such peculiar ways of agreement or disagreement of our ideas, that they deserve well to be considered as distinct heads, and not under relation in general; since they are so different grounds of affirmation and negation, as will easily appear to any one, who will but reflect on what is said in

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That which your lordship is afraid it may be dangerous to, is an article of faith that which your lordship labours and is concerned for, is the certainty of faith. Now, my lord, I humbly conceive the certainty of faith, if your lordship thinks fit to call it so, has nothing to do with the certainty of knowledge. As to talk of the certainty of faith, seerns all one to me, as to talk of the knowledge of believing, a way of speaking not easy to me to understand.

Place knowledge in what you will; start what new methods of certainty you please, that are apt to leave men's minds more doubtful than before; place certainty on such grounds as will leave little or no knowledge in the world: (for these are the arguments your lordship uses against my defi. nition of knowlege) this shakes not at all, nor in the least concerns the assurance of faith; that is quite distinct from it, neither stands nor falls with knowledge.

Faith stands by itself, and upon grounds of its own; nor can be removed from them, and placed on those of knowledge. Their grounds are so far from being the same, or having any thing common, that when it is brought to certainty, faith is destroyed; it is knowledge then, and faith no longer.

With what assurance soever of believing I assent to any article of faith, so that I stedfastly venture my all upon it, it is still but believing. Bring it to certainty, and it ceases to be faith. I believe that Jesus Christ was crucified, dead, and buried, rose again the third day from the dead, and ascended into heaven: let now such methods of knowledge or certainty be started, as leave men's minds more doubtful than before; let the grounds of knowledge be resolved into what any one pleases, it touches not my faith; the foundation of that stands as sure as before, and cannot be at all shaken by it; and one may as well say, that any thing that weakens the sight, or casts a mist before the eyes, endangers the hearing; as that any thing which alters the nature of knowledge (if that could be done) should be of dangerous consequence to an article of faith.

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several places of this essay. I should not proceed to examine the several degrees of our knowledge, but that it is necessary first to consider the different acceptations of the word knowledge.

Knowledge actual or ha. bitual.

§. 8. There are several ways wherein the mind is possessed of truth, each of which is called knowledge.

1. 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.

2. 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 consists; and so lodged it in his memory, that whenever that proposition comes again to be reflected on, he, without doubt or hesitation, embraces the right side, assents 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 past doubt, as often as it has occasion to reflect on them. For our finite understandings being able to think clearly and distinctly 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.

Whether then I am or am not mistaken, in the placing certainty in the perception of the agreement or disagreement of ideas; whether this account of knowledge be true or false, enlarges or straitens the bounds of it more than it should; faith still stands upon its own basis, which is not at all altered by it; and every article of that has just the same unmoved foundation, and the very same credibility, that it had before. So that, my lord, whatever I have said about certainty, and how much soever I may be out in it, if I am mistaken, your lordship has no reason to apprehend any danger to any article of faith from thence; every one of them stands upon the same bottom it did before, out of the reach of what belongs to knowledge and certainty. And thus much of my way of certainty by ideas; which, I hope, will satisfy your lordship how far it is from being dangerous to any article of the christian faith whatsoever.

§. 9. Of habitual knowledge, there are also, vulgarly speaking, two degrees:

Habitual knowledge

First, the one is of such truths laid up in twofold. the memory, 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 conviction, without the proofs. Thus a man that remembers certainly that he once perceived the demonstration, that the three angles of a triangle are equal to two right ones, is certain that he knows it, because he cannot doubt 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 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 disagreement 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 agreement or disagreement of the ideas contained in the proposition whose certainty we remember. For example, 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 possibly 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 proposition is per

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ceived, 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 some past 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 same 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 mathematicks 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 mathematicks; for no mathentical demonstration would be any other than particular: and when a man had demonstrated any proposition concerning one triangle or circle, his knowledge would not reach beyond that particular diagram. If he would extend it further, he must 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 pro positions. Nobody, I think, can deny that Mr. Newton certainly knows any proposition, 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 be well thought beyond the reach of human faculties; when the very discovery, perception, and laying together that wonderful connexion of ideas, is found to surpass most readers comprehension. But yet it is evident, the author himself knows the proposition to be true, remembering he once saw the connexion 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 much more imperfect than intuitive, as we shall see in the following chapter.

С НА Р. II.

Of the Degrees of our Knowledge.

§. 1. ALL our knowledge consisting, as

I have said, in the view the

Intuitive.

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 degrees 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 disagreement of any of its ideas. For if we will reflect on our own ways of thinking, we shall find that sometimes the mind perceives the agreement or disagreement 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 sight of the ideas together, by bare intuition, without the intervention 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 irresistible, and like bright sun-shine forces itself immediately to be perceived, as soon as ever the mind turns its view that way;

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