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 Ideas.

Though the deducing one proposition from another, or making inferences in words, be a great part of reason, and that which it is usually employed about; yet the principal act of ratiocination is the finding the agreement or disagreement of two ideas one with another, by the intervention of A third.  As a man, by a yard, finds two houses to be of the same length, which could not be brought together to measure their equality by juxta-position.  Words have their consequences, as the signs of such ideas:  and things agree or disagree, as really they are; but we observe it only by our ideas.

19.  Four sorts of Arguments.

Before we quit this subject, it may be worth our while a little to reflect on four sorts of arguments, that men, in their reasonings with others, do ordinarily make use of to prevail on their assent; or at least so to awe them as to silence their opposition.

First, Argumentum ad verecundiam.