e memory, just as it is; and the mind must be sure that
no part of what is necessary to make up the demonstration is omitted or
overlooked. This makes some demonstrations long and perplexed, and too
hard for those who have not strength of parts distinctly to perceive,
and exactly carry so many particulars orderly in their heads. And even
those who are able to master such intricate speculations, are fain
sometimes to go over them again, and there is need of more than one
review before they can arrive at certainty. But yet where the mind
clearly retains the intuition it had of the agreement of any idea with
another, and that with a third, and that with a fourth, &c., there the
agreement of the first and the fourth is a demonstration, and produces
certain knowledge; which may be called RATIONAL KNOWLEDGE, as the other
is intuitive.

16. Secondly, to supply the narrowness of Demonstrative and Intuitive
Knowledge we have nothing but Judgment upon probable reasoning.

Secondly, There are other ideas, whose agreement or disagreement can no
otherwise be judged of but by the intervention of others which have not
a certain agreement with the extremes, but an USUAL or LIKELY one:
and in these is that the JUDGMENT is properly exercised; which is the
acquiescing of the mind, that any ideas do agree, by comparing them with
such probable mediums. This, though it never amounts to knowledge,
no, not to that which is the lowest degree of it; yet sometimes the
intermediate ideas tie the extremes so firmly together, and the
probability is so clear and strong, that ASSENT as necessarily follows
it, as KNOWLEDGE does demonstration. The great excellency and use of the
judgment is to observe right, and take a true estimate of the force and
weight of each probability; and then casting them up all right together,
choose that side which has the overbalance.

17. Intuition, Demonstration, Judgment.

INTUITIVE KNOWLEDGE is the perception of the CERTAIN agreement or
disagreement of two ideas immediately compared together.

RATIONAL KNOWLEDGE is the perception of the CERTAIN agreement or
disagreement of any two ideas, by the intervention of one or more other
ideas.

JUDGMENT is the thinking or taking two ideas to agree or disagree,
by the intervention of one or more ideas, whose certain agreement or
disagreement with them it does not perceive, but hath observed to be
FREQUENT and USUAL.

18. Consequences of Words, and Consequences of Id