consider and improve our Knowledge in, or reason about. And if they be specific ideas of Substances, we should endeavour also to make them as complete as we can; whereby I mean that we should put together as many simple ideas as, being constantly observed to coexist, may perfectly determine the species; 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, [or 'proofs'] which may show us the agreement or repugnancy of other ideas, which cannot be immediately compared.

Mathematics an instance of it.—That these two (and not the relying on Maxims, and drawing consequences 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 anything, is utterly thereby incapable of any knowledge about them. Farther [secondly], it is evident, that it was not the influence of those Maxims which are taken for 'principles' in Mathematics, that led the masters of that science into those wonderful discoveries [that] they have made. Let a 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, scarcely ever come to know that the square of the hypotenuse in a rightangled 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[s] will be equal,' &c., helped him not, I presume, to this demonstration: and a man may, I think, pore long enough on those axioms without ever seeing one jot the more of Mathematical Truths.

CHAPTER XIII.*

SOME FARTHER CONSIDERATIONS CONCERNING OUR

KNOWLEDGE.

1. Our knowledge partly necessary, partly voluntary.— Our Knowledge, as in other things, so in this, has so great a conformity with our sight, that it is neither wholly necessary, nor wholly voluntary. If our Knowledge 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 extremely little, or none at all. Men that have Senses cannot choose but receive some ideas by them; and if they

*This Chapter is properly a corollary easily deducible from the principles laid down in previous Chapters, and closes one department of the Fourth Book.-ED.

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 difference in them. But though a man with his eyes open in the light cannot but see, yet [1.] there [are] 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 and instruct him, which yet he may never have the will to open, never take the pains to look into.

The application voluntary; but we know as things are, not as we please.—There is also another thing in a man's power; and that is, though he turns his eyes sometimes towards an object, yet [2.] he may choose whether he will curiously survey it, and with an intent application 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 Knowlege is—the employing or withholding any of our faculties from this or that sort of objects, and a more or less accurate survey f them: but, they being employed, our Will has 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 must needs be assured of the truth of those Propositions which express that agreement or disagreement [which] they perceive in them, and be undoubtedly convinced of those truths. For what a man sees he cannot but see; and what he perceives he cannot but know that he perceives.

Instance in numbers. Thus he that has got the ideas of numbers, and has taken the pains to compare one, two, and three, to six, cannot choose but know that they are equal. He that has got the idea of a triangle, and found the ways to measure its angles and their magni- . tudes, 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 impossible for the same thing to be and not to be."

In natural religion. He also that has the idea of an intelligent but frail and weak being, made by, 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 has 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 open his eyes and turn them that way. But yet, these truths being ever so certain, ever so clear, he may be ignorant of [any] or all of them, who will never take the pains to employ his faculties, as he should, to inform himself about them.

CHAPTER XIV.

OF JUDGMENT.

Our knowledge being short, we want something else.— The understanding faculties being given to man, not barely for speculation, but also for the conduct of his life, man would be at a great loss if he had nothing to direct him but what was 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 [food] will nourish him, he that will not stir till he infallibly knows [that] the business he goes about will succeed, will have little else to do but to sit still and perish.

What use to be made of this twilight state. Therefore,