13.  The true Use of Hypotheses.

Not that we may not, to explain any phenomena of nature, make use of any probable hypothesis whatsoever:  hypotheses, if they are well made, are at least great helps to the memory, and often direct us to new discoveries.  But my meaning is, that we should not take up any one too hastily (which the mind, that would always penetrate into the causes of things, and have principles to rest on, is very apt to do) till we have very well examined particulars, and made several experiments, in that thing which we would explain by our hypothesis, and see whether it will agree to them all; whether our principles will carry us quite through, and not be as inconsistent with one phenomenon of nature, as they seem to accommodate and explain another.  And at least that we take care that the name of principles deceive us not, nor impose on us, by making us receive that for an unquestionable truth, which is really at best but a very doubtful conjecture; such as are most (I had almost said all) of the hypotheses in natural philosophy.

14.  Clear and distinct Ideas with settled Names, and the finding of those intermediate ideas which show their Agreement or Disagreement, are the Ways to enlarge our Knowledge.

But whether natural philosophy be capable of certainty or no, the ways to enlarge our knowledge, as far as we are capable, seems to me, in short, to be these two:—­

First, The first is to get and settle in our minds [determined ideas of those things whereof we have general or specific names; at least, so many of them as we would 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 co-exist, 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, which may show us the agreement or repugnancy of other ideas, which cannot be immediately compared.

15.  Mathematics an instance of this.

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.  Suppose but a man not to have a perfect exact idea