that are lodged in his memory: for if men had no knowlege of any thing more than they actually thought on, they would be very ignorant; and he that knew most would know but one truth at a time.

There are two sorts of habitual knowlege: the one is of such truths laid up in the memory, as whenever they occur to the mind, it actually perceives the relation between the ideas; and 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 remembering 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. Though, in adherence to a truth, where the demonstration is forgotten, a man may be thought to believe his memory, rather than to know; yet, on due examination, I find it comes not short of certainty, and is in effect true knowlege. That which is apt to lead to a mistake is, that the agreement or disagreement of the ideas in this case is not perceived as it was at first, by actual view, but by other intermediate ideas. For example, in the proposition that the three angles of a triangle are equal to two right ones—one who has seen the demonstration of this truth knows it to be true, when the demonstration is gone out of his mind; but he knows it in a different way. He remembers, i. e. he knows, that he was once certain of the truth of the proposition. The immutability of the same relation 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 so. On this ground particular demonstrations in mathematics afford general knowlege. 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 knowlege is much more im

perfect than intuitive, as we shall see in the following chapter.

CHAPTER II.

Of the Degrees of our Knowlege.

All our knowlege consisting in the view the mind. has of its own ideas, which is the utmost light and greatest certainty we are capable of, the different clearness of our knowlege seems to lie in the different way of perception the mind has of the agreement or disagreement of any of its ideas.

When the mind perceives this agreement or disagreement of two ideas immediately by themselves, without the intervention of any other, we may call it intuitive knowlege, in which cases the mind perceives truth as the eye does light, only by being directed towards it. Thus the mind perceives that white is not black, that three are more than two, and equal to one and two. This part of knowlege is irresistible, and, like the bright sunshine, forces itself immediately to be perceived, as soon as ever the mind turns its view that way. It is on this intuition that depends all the certainty and evidence of our other knowlege; which certainty every one finds to be so great, that he cannot imagine, and therefore not require a greater.

The next degree of knowlege is, where the mind perceives not this agreement or disagreement immediately, or by the juxtaposition, as it were, of the ideas, 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 the mind is fain to discover the agreement or disagreement which it searches, by the intervention of other ideas; and this is that which we call reasoning. And thus, if we would know the agreement or disagreement in bigness, between the three angles of a triangle and two right angles, we cannot by an im

mediate view and comparing them do it; because the three angles of a triangle cannot be brought at once and be compared with any other one or two angles; so of this the mind has no immediate or intuitive knowlege. But we must find out some other angles; to which the three angles of a triangle have equality, and finding those equal to two right ones, we come to know the equality of these three angles to two right ones. Those intervening ideas which serve to show 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 demonstration. A quickness in the mind to find those proofs, and to apply them right, is, I suppose, that which is called sagacity.

This knowlege, though it be certain, is not so clear and evident as intuitive knowlege. It requires pains and attention, and steady application of mind, to discover the agreement or disagreement of the ideas it considers, and there must be a progression by steps and degrees before the mind can in this way arrive at certainty. Before demonstration there was a doubt which in intuitive knowlege cannot happen to the mind, that has its faculty of perception left to a degree capable of distinct ideas, no more than it can be a doubt to the eye, that can distinctly see white and black, whether this ink and paper be all of a color.

Now in every step that reason makes in demonstrative knowlege there is an intuitive knowlege of that agreement or disagreement it seeks with the next intermediate idea, which it uses as a proof; for if it were not so, that yet would need a proof; since, without the perception of such agreement or disagreement, there is no knowlege produced. By which it is evident that every step in reasoning that produces knowlege has intuitive certainty; which, when the mind perceives, there is no more required but to remember it, to make the agreement or disagreement of the

ideas concerning which we inquire visible and certain. This intuitive perception of the agreement or disagreement of the intermediate ideas in each step and progression of the demonstration must also be exactly carried in the mind: and a man must be sure that no part is left out; which, because in long deductions the memory cannot easily retain, this knowlege becomes more imperfect than intuitive, and men often embrace falsehoods for demonstrations.

It has been generally taken for granted that mathematics alone are capable of demonstrative certainty. But to have such an agreement or disagreement as may be intuitively perceived, being as I imagine, not the privilege of the ideas of number, extension, and figure alone, it may possibly be the want of due method and application in us, and not of sufficient evidence in things, that demonstration has been thought to have so little to do in other parts of knowlege. For in whatever ideas the mind can perceive the agreement or disagreement immediately, there it is capable of intuitive knowlege: and where it can perceive the agreement or disagreement of any two ideas, by an intuitive perception of the agreement or disagreement they have with any intermediate ideas, there the mind is capable of demonstration, which is not limited to the ideas of figure, number, extension, or their modes. The reason why it has been generally supposed to belong to them only, is because, in comparing their equality or excess, the modes of numbers have every the least difference, very clear and perceivable; and in extension, though every the least excess is not so perceptible, yet the mind has found out ways to discover the just equality of two angles, extensions, or figures; and both, that is, numbers and figures, can be set down by visible and lasting marks.

But in other simple ideas, whose modes and differences are made and counted by degrees, and not quantity, we have not so nice and accurate a distinction of

their differences, as to perceive or find ways to measure their just equality, or the least differences. For those other simple ideas being appearances or sensations produced in us, by the size, figure, motion, &c. of minute corpuscles singly insensible, their different degrees also depend on the variation of some or all of those causes; which, since it cannot be observed by us in particles of matter, whereof each is too subtile to be perceived, it is impossible for us to have any exact measures of the different degrees of those simple ideas. Thus, for instance, not knowing what number of particles, nor what motion of them is fit to produce any precise degree of whiteness, we cannot demonstrate the certain equality of any two degrees of whiteness, because we have no certain standard to measure them by, nor means to distinguish every the least difference; the only help we have being from our senses, which in this point fail us.

But where the difference is so great as to produce in the mind ideas clearly distinct, there ideas of colors, as we see in different kinds, blue and red, for instance, are as capable of demonstration, as ideas of number and extension. What is here said of colors, I think holds true in all secondary qualities. These two, then, intuition and demonstration, are the degrees of our knowlege. Whatever comes short of one of these is but faith or opinion, not knowlege, at least in all general truths.

There is indeed another perception of the mind employed about the particular existence of finite beings, without us, which, going beyond probability, but not reaching to either of the foregoing degrees of certainty, passes under the name of knowlege. Nothing can be more certain, than that the idea we receive from an external object is in our minds. This is intuitive knowlege; but whether we can thence certainly infer the existence of any thing without us, corresponding to that idea, is that whereof some men