For each agreement or
disagreement of the ideas must be observed and seen in each step of
the whole train, and retained in the 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. 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 it 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.
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