e his memory than really to know, and this way of
entertaining a truth seemed formerly to me like something between
opinion and knowledge; a sort of assurance which exceeds bare belief,
for that relies on the testimony of another;--yet upon a due examination
I find it comes not short of perfect certainty, and is in effect true
knowledge. That which is apt to mislead our first thoughts into a
mistake in this matter is, that the agreement or disagreement of the
ideas in this case is not perceived, as it was at first, by an actual
view of all the intermediate ideas whereby the agreement or disagreement
of those in the proposition was at first perceived; but by other
intermediate ideas, that show the agreement or disagreement of the ideas
contained in the proposition whose certainty we remember. For example:
in this proposition, that 'the three angles of a triangle are equal
to two right ones,' one who has seen and clearly perceived the
demonstration of this truth knows it to be true, when that demonstration
is gone out of his mind; so that at present it is not actually in view,
and possibly cannot be recollected: but he knows it in a different way
from what he did before. The agreement of the two ideas joined in that
proposition is perceived; but it is by the intervention of other ideas
than those which at first produced that perception. He remembers, i.e.
he knows (for remembrance is but the reviving of some past knowledge)
that he was once certain of the truth of this proposition, that the
three angles of a triangle are equal to two right ones. The immutability
of the same relations between the same immutable things is now the idea
that shows him, that if the three angles of a triangle were once equal
to two right ones, they will always be equal to two right ones. And
hence he comes to be certain, that what was once true in the case, is
always true; what ideas once agreed will always agree; and consequently
what he once knew to be true, he will always know to be true; as long
as he can remember that he once knew it. Upon this ground it is, that
particular demonstrations in mathematics afford general knowledge. If
then the perception, that the same ideas will ETERNALLY have the same
habitudes and relations, be not a sufficient ground of knowledge, there
could be no knowledge of general propositions in mathematics; for no
mathematical demonstration would be any other than particular: and
when a man had demonstrated any propo