9. Demonstration not limited to ideas of mathematical quantity. It
has been generally taken for granted, that mathematics alone are
capable of demonstrative certainty: but to have such an agreement or
disagreement as may intuitively be perceived, being, as I imagine, not
the privilege of the ideas of number, extension, and figure alone,
it may possibly be the want of due method and application in us, and
not of sufficient evidence in things, that demonstration has been
thought to have so little to do in other parts of knowledge, and
been scarce so much as aimed at by any but mathematicians. For
whatever ideas we have wherein the mind can perceive the immediate
agreement or disagreement that is between them, there the mind is
capable of intuitive knowledge; and where it can perceive the
agreement or disagreement of any two ideas, by an intuitive perception
of the agreement or disagreement they have with any intermediate
ideas, there the mind is capable of demonstration: which is not
limited to ideas of extension, figure, number, and their modes.
10. Why it has been thought to be so limited. The reason why it
has been generally sought for, and supposed to be only in those, I
imagine has been, not only the general usefulness of those sciences:
but because, in comparing their equality or excess, the modes of
numbers have every the least difference very clear and perceivable:
and though in extension every the least excess is not so
perceptible, yet the mind has found out ways to examine, and
discover demonstratively, the just equality of two angles, or
extensions, or figures: and both these, i.
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