15. The next is got by reasoning. But though we have, here and
there, a little of this clear light, some sparks of bright
knowledge, yet the greatest part of our ideas are such, that we cannot
discern their agreement or disagreement by an immediate comparing
them. And in all these we have need of reasoning, and must, by
discourse and inference, make our discoveries. Now of these there
are two sorts, which I shall take the liberty to mention here again:-
Through reasonings that are demonstrative. First, Those whose
agreement or disagreement, though it cannot be seen by an immediate
putting them together, yet may be examined by the intervention of
other ideas which can be compared with them. In this case, when the
agreement or disagreement of the intermediate idea, on both sides,
with those which we would compare, is plainly discerned: there it
amounts to demonstration whereby knowledge is produced, which,
though it be certain, yet it is not so easy, nor altogether so clear
as intuitive knowledge. Because in that there is barely one simple
intuition, wherein there is no room for any the least mistake or
doubt: the truth is seen all perfectly at once. In demonstration, it
is true, there is intuition too, but not altogether at once; for there
must be a remembrance of the intuition of the agreement of the medium,
or intermediate idea, with that we compared it with before, when we
compare it with the other: and where there be many mediums, there
the danger of the mistake is the greater.
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