15.  Knowledge not always clear, where the Ideas that enter into it are clear.

But since our knowledge is founded on and employed about our ideas only, will it not follow from thence that it is conformable to our ideas; and that where our ideas are clear and distinct, or obscure and confused, our knowledge will be so too?  To which I answer, No:  for our knowledge 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:  v. g. a man that has as clear ideas of the angles of a triangle, and of equality to two right ones, as any mathematician in the world, may yet have but a very obscure perception of their agreement, and so have but a very obscure knowledge of it. [But ideas which, by reason of their obscurity or otherwise, are confused, cannot produce any clear or distinct knowledge; because, as far as any ideas are confused, so far the mind cannot 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 knowledge.

1.  Extent of our Knowledge.

Knowledge, as has been said, lying in the perception of the agreement or disagreement of any of our ideas, it follows from hence, That,

First, it extends no further than we have Ideas.

First, we can have knowledge no further than we have ideas.

2.  Secondly, It extends no further than we can perceive their Agreement or Disagreement.

Secondly, That we can have no knowledge further than we can have perception of that agreement or disagreement.  Which perception being:  1.  Either by intuition, or the immediate comparing any two ideas; or, 2.  By reason, examining the agreement or disagreement of two ideas, by the intervention of some others; or, 3.  By sensation, perceiving the existence of particular things:  hence it also follows: 

3.  Thirdly, Intuitive Knowledge extends itself not to all the relation of all our Ideas.

Thirdly, That we cannot have an intuitive knowledge 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 juxta-position, or an immediate comparison one with another.  Thus, having the ideas of an obtuse and an acute angled triangle, both drawn from equal bases, and between parallels, I can, by intuitive knowledge, perceive the one not to be the other, but cannot that way know whether they be equal or no; because their agreement or disagreement in equality can never be perceived by an immediate comparing them:  the difference of figure makes their parts incapable of an exact immediate application; and therefore there is need of some intervening qualities to measure them by, which is demonstration, or rational knowledge.