By which it
is plain that every step in reasoning that produces knowledge, has
intuitive certainty; which when the mind perceives, there is no more
required but to remember it, to make the agreement or disagreement
of the ideas concerning which we inquire visible and certain. So
that to make anything a demonstration, it is necessary to perceive the
immediate agreement of the intervening ideas, whereby the agreement or
disagreement of the two ideas under examination (whereof the one is
always the first, and the other the last in the account) is found.
This intuitive perception of the agreement or disagreement of the
intermediate ideas, in each step and progression of the demonstration,
must also be carried exactly in the mind, and a man must be sure
that no part is left out: which, because in long deductions, and the
use of many proofs, the memory does not always so readily and
exactly retain; therefore it comes to pass, that this is more
imperfect than intuitive knowledge, and men embrace often falsehood
for demonstrations.
8. Hence the mistake, ex praecognitis, et praeconcessis. The
necessity of this intuitive knowledge, in each step of scientifical or
demonstrative reasoning, gave occasion, I imagine, to that mistaken
axiom, That all reasoning was ex pracognitis et praeconcessis:
which, how far it is a mistake, I shall have occasion to show more
at large, when I come to consider propositions, and particularly those
propositions which are called maxims, and to show that it is by a
mistake that they are supposed to be the foundations of all our
knowledge and reasonings.
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