7. Each step in demonstrated knowledge must have intuitive evidence.
Now, in every step reason makes in
demonstrative knowledge, there is an intuitive knowledge of that agreement or disagreement it seeks with the next
intermediate idea which it uses as a proof: for if it were not so, that yet would need a proof; since without the
perception of such agreement or disagreement, there is no knowledge produced: if it be perceived by itself, it is
intuitive knowledge: if it cannot be perceived by itself, there is need of some intervening idea, as a common
measure, to show their agreement or disagreement. 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.
