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

But

think there may be a question made, because men may have such an idea in their minds, when no such thing exists, no such object affects their senses. it is evident that we are invincibly conscious to ourselves of a different perception, when we look on the sun in the day, and think on it by night; when we actually taste wormwood, and smell a rose, or only think on that savour or odour. So that I think we may add to the two former sorts of knowlege this also of the existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas from them, and allow these three degrees of knowlege, viz. intuitive, demonstrative, and sensitive.

But since our knowlege is founded on, and employed about our ideas only; will it follow thence that it must be conformable to our ideas, and that where our ideas are clear and distinct, obscure and confused, there our knowlege will be so too? I answer, No. For our knowlege consisting in the perception of the agreement or disagreement of any two ideas, its clearness or obscurity consists in the clearness or obscurity of that perception, and not in the clearness or obscurity of the ideas themselves. A man, for instance, that has a clear idea of the angles of a triangle and of equality to two right ones, may yet have but an obscure perception of their agreement; and so have but a very obscure knowlege of it. But obscure and confused ideas can never produce any clear or distinct knowlege, because as far as any ideas are obscure or confused, so far the mind can never perceive clearly whether they agree or disagree; or, to express the same thing in a way less apt to be misunderstood, he that hath not determined ideas to the words he uses cannot make propositions of them, of whose truth he can be certain.

CHAPTER III.

Of the Extent of Human Knowlege.

1. From what has been said concerning knowlege, it follows, first, that we can have no knowlege farther than we have ideas.

2. Secondly, that we have no knowlege farther than we can have perception of that agreement or disagreement of our ideas, either by intuition, demonstration,

or sensation.

3. Thirdly, we cannot have an intuitive knowlege that shall extend itself to all our ideas, and all that we would know about them; because we cannot examine and perceive all the relations they have one to another, by juxtaposition, or an immediate comparison one with another. Thus we cannot intuitively perceive the equality of two extensions, the difference of whose figures makes their parts incapable of an exact immediate application.

4. Fourthly, our rational knowlege cannot reach to the whole extent of our ideas; because between two different ideas we would examine, we cannot always find such proofs as we can connect one to another, with an intuitive knowlege in all the parts of the deduction.

5. Fifthly, sensitive knowlege reaching no farther than the existence of things actually present to our senses, is yet much narrower than either of the former.

6. From all which it is evident, that the extent of our knowlege comes not only short of the reality of things, but even of the extent of our own ideas. We have the ideas of a square, a circle, and equality, and yet perhaps shall never be able to find a circle equal to a square.

7. We have the ideas of matter and thinking,1 but

Against that assertion of Mr. Locke, that possibly we shall never be able to know, whether any mere material being think or no,' &c. the bishop of Worcester argues thus: If this be

possibly shall never be able to know whether any mere material being thinks or no; it being impossible for us, by the contemplation of our own ideas, without

true, then, for all that we can know by our ideas of matter and thinking, matter may have a power of thinking: and, if this hold, then it is impossible to prove a spiritual substance in us from the idea of thinking: for how can we be assured by our ideas, that God hath not given such a power of thinking to matter so disposed as our bodies are? especially since it is said, That, in respect of our notions, it is not much more remote from our comprehension to conceive that God can, if he pleases, superadd to our idea of matter a faculty of thinking, than that he should superadd to it another substance, with a faculty of thinking. Whoever asserts this, can never prove a spiritual substance in us from a faculty of thinking, because he cannot know, from the idea of matter and thinking, that matter so disposed cannot think : and he cannot be certain that God hath not framed the matter of our bodies so as to be capable of it.'

To which Mr. Locke answers thus: Here your lordship argues, that on my principles it cannot be proved that there is a spiritual substance in us. To which, give me leave, with submission, to say, that I think it may be proved from my principles, and I think I have done it; and the proof in my book stands thus: First, we experiment in ourselves thinking. The idea of this action, or mode of thinking, is inconsistent with the idea of self-subsistence, and, therefore, has a necessary connexion with a support or subject of inhesion: the idea of that support is what we call substance; and so from thinking experimented in us, we have a proof of a thinking substance in us, which in my sense is a spirit. Against this your lordship will argue, that, by what I have said of the possibility that God may, if he pleases, superadd to matter a faculty of thinking, it can never be proved that there is a spiritual substance in us, because, on that supposition, it is possible it may be a material substance that thinks in us. I grant it; but add, that the general idea of substance being the same every where, the modification of thinking, or the power of thinking joined to it, makes it a spirit, without considering what other modifications it has, as whether it has the modification of solidity or no; as, on the other side, substance, that has the modification of solidity, is matter, whether it has the modification of thinking, or no and, therefore, if your lordship means by a spiritual, an immaterial substance, I grant I have not proved, nor on my prin. ciples can it be proved (your lordship meaning, as I think you do, demonstratively proved), that there is an immaterial substance in us that thinks. Though, I presume, from what I have said about this supposition of a system of matter, thinking (which there demonstrates that God is immaterial) will prove it in the highest degree probable that the thinking substance in us is immaterial: but your lordship thinks not probably enough; and by charging