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and each of those simple ideas, which are the ingredients of our complex ones, should be clear and distinct in our minds. For it being evident, that our knowledge cannot exceed our ideas; as far as they are either imperfect, confused, or obscure, we cannot expect to have certain, perfect, or clear knowledge.

Secondly, the other is the art of finding out those intermediate ideas which may show us the agreement or repugnancy of other ideas, which cannot be immediately compared. Mathema

$ 15. That these two (and not the retics an in lying on maxims, and drawing consestance of it.

quences from some general propositions) are the right methods of improving our knowledge in the ideas of other modes besides those of quantity, the consideration of mathematical knowledge will easily inform us. Where first we shall find, that he that has not a perfect and clear idea of those angles or figures of which he desires to know any thing, is utterly thereby incapable of any knowledge about them. Suppose but a man not to have a perfect exact idea of a right angle, a scalenum, or trapezium; and there is nothing more certain than that he will in vain seek any demonstration about them. Farther, it is evident, that it was not the influence of those màxims, which are taken for principles in mathematics, that have led the masters of that science into those wonderful discoveries they have made. Let à man of good parts know all the maxims generally made use of in mathematics ever so perfectly, and

contemplate their extent and consequences as much as he pleases, he will by their assistance, I suppose, scarce ever come to know that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two other sides. The knowledge, that the whole is equal to all its parts, and if you take equals from equals, the remainder will be equal, &c. helped him not, I presume, to this demonstration: and a man may, I think, pore long enough on those

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axioms without ever seeing one jot the more of mathematical truths. They have been discovered by the thoughts otherwise applied : the mind had other objects, other views before it, far different from those maxims, when it first got the knowledge of such truths in mathematics, which men well enough acquainted with those received axioms, but ignorant of their method who first made these demonstrations, can never sufficiently admire. And who knows what methods, to enlarge our knowledge in other parts of science, may hereafter be invented, answering that of algebra in mathematics, which so readily finds out the ideas of quantities to measure others by; whose equality or proportion we could otherwise very hardly, or, perhaps, never come to know?

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Some farther Considerations concerning our Know

ledge. $ 1. Our knowledge, as in other things, Our knowso in this, has so great a conformity with ledge partly our sight, that it is neither wholly necessary, nor wholly voluntary. If our know- partly vo

luntary. ledge were altogether necessary, all men's knowledge would not only be alike, but every man would know all that is knowable: and if it were wholly voluntary, some men so little regard or value it, that they would have extreme little, or none at all. Men that have senses cannot choose but receive some ideas by them; and if they have memory, they cannot but retain some of them; and if they have any distinguishing faculty, cannot but perceive the agreement or disagreement of some of them one with another : as he that has eyes, if he will open them by day, cannot but see some objects, and perceive a dif

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92 Considerations concerning our Knowledge. Book 4. ference in them. But though a man, with his eyes open in the light, cannot but see; yet there be certain objects, which he may choose whether he will turn his eyes to; there may be in his reach a book containing pictures and discourses, capable to delight or instruct him, which yet he may never have the will to open, never take the pains to look into. The applica- $ 2. There is also another thing in a tion volun

mans power, and that is, though he turns tary; but we

his eyes sometimes towards an object, yet know as things are,


may choose whether he will curiously

survey it, and with an intent application please. endeavour to observe accurately all that is visible in it. But yet what he does see, he cannot see otherwise than he does. It depends not on his will to see that black which appears yellow; nor to persuade himself, that what actually scalds him feels cold. The earth will not appear painted with flowers, nor the fields covered with verdure, whenever he has a mind to it: in the cold winter he cannot help seeing it white and hoary, if he will look abroad. Just thus is it with our understanding; all that is voluntary in our knowledge is the employing or withholding any of our faculties from this or that sort of objects, and a more or less accurate survey of them: but, they being employed, our will hath no power to determine the knowledge of the mind one way or other; that is done only by the objects themselves, as far as they are clearly discovered. And therefore, as far as men's senses are conversant about external objects, the mind cannot but receive those ideas which are presented by them, and be informed of the existence of things without: and so far as men's thoughts converse with their own determined ideas, they cannot but, in some measure, observe the agreement or disagreement that is to be found amongst some of them, which is so far knowledge: and if they have names for those ideas which they have thus considered, they

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must needs be assured of the truth of those pro-
positions which express that agreement or disagree-
ment they perceive in them, and be undoubtedly con-
vinced of those truths. For what a man sees, he can-
not but see; and what he perceives, he cannot but
know that he perceives.
§ 3. Thus he that has got the ideas of

Instance, in
numbers, and hath taken the pains to com- numbers.
pare one, two, and three to six, cannot
choose but know that they are equal : he that hath got
the idea of a triangle, and found the ways to measure
its angles, and their magnitudes, is certain that its
three angles are equal to two right ones; and can as
little doubt of that as of this truth, “that it is im-
possible for the same thing to be, and not to be."
He also that hath the idea of an intelli-

In natural gent, but frail and weak being, made by religion. and depending on another, who is eternal, omnipotent, perfectly wise and good, will as certainly know that man is to honour, fear, and obey God, as that the sun shines when he sees it. For if he hath but the ideas of two such beings in his mind, and will turn his thoughts that way, and consider them, he will as certainly find that the inferior, finite, and dependent, is under an obligation to obey the supreme and infinite, as he is certain to find that three, four, and seven are less than fifteen, if he will consider and compute those numbers; nor can he be surer in a clear morning that the sun is risen, if he will but


his eyes, and turn them that way. But yet these truths, being ever so certain, ever so clear, he may be ignorant of either, or all of them, who will never take the pains to employ his faculties, as he should, to inform himself about them.

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$ 1. The understanding faculties being ledge being given to man, not barely for speculation, short, we but also for the conduct of his life, man

would be at a great loss if he had nothing thing else.

to direct him but what has the certainty of true knowledge. For that being very short and scanty, as we have seen, he would be often utterly in the dark, and, in most of the actions of his life, perfectly at a stand, had he nothing to guide him in the absence of clear and certain knowledge. He that will not eat till he has demonstration that it will nourish him,-he that will not stir till he infallibly knows the business he goes about will succeed will have little else to do but to sit still and perish. What use to

$ 2. Therefore as God has set some

things in broad day-light; as he has given this twilight us some certain knowledge, though limited

to a few things in comparison, probably, as a taste of what intellectual creatures are capable of, to excite in us a desire and endeavour after a better state; so in the greatest part of our concernments he has afforded us only the twilight, as I may so say, of probability; suitable, I presume, to that state of mediocrity and probationership he has been pleased to place us in here; wherein, to check our over-confidence and presumption, we might by every day's experience be made sensible of our short-sightedness and liableness to error; the sense whereof might be a constant admonition to us, to spend the days of this our pilgrimage with industry and care, in the search and following of that way, which might lead us to a state of greater perfection: it being highly rational to think, even were revelation silent in the case, that as men employ those talents


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