The reason why the mind
cannot always perceive presently the agreement or disagreement of
two ideas, is, because those ideas, concerning whose agreement or
disagreement the inquiry is made, cannot by the mind be so put
together as to show it. In this case then, when the mind cannot so
bring its ideas together as by their immediate comparison, and as it
were juxta-position or application one to another, to perceive their
agreement or disagreement, it is fain, by the intervention of other
ideas (one or more, as it happens) to discover the agreement or
disagreement which it searches; and this is that which we call
reasoning. Thus, the mind being willing to know the agreement or
disagreement in bigness between the three angles of a triangle and two
right ones, cannot by an immediate view and comparing them do it:
because the three angles of a triangle cannot be brought at once,
and be compared with any other one, or two, angles; and so of this the
mind has no immediate, no intuitive knowledge. In this case the mind
is fain to find out some other angles, to which the three angles of
a triangle have an equality; and, finding those equal to two right
ones. comes to know their equality to two right ones.
3. Demonstration depends on clearly perceived proofs. Those
intervening ideas, which serve to show the agreement of any two
others, are called proofs; and where the agreement and disagreement is
by this means plainly and clearly perceived, it is called
demonstration; it being shown to the understanding, and the mind
made to see that it is so.
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