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.
