A quickness in the mind to find out these
intermediate ideas, (that shall discover the agreement or disagreement
of any other,) and to apply them right, is, I suppose, that which is
called sagacity.
4. As certain, but not so easy and ready as intuitive knowledge.
This knowledge, by intervening proofs, though it be certain, yet the
evidence of it is not altogether so clear and bright, nor the assent
so ready, as in intuitive knowledge. For, though in demonstration
the mind does at last perceive the agreement or disagreement of the
ideas it considers; yet it is not without pains and attention: there
must be more than one transient view to find it. A steady
application and pursuit are required to this discovery: and there must
be a progression by steps and degrees, before the mind can in this way
arrive at certainty, and come to perceive the agreement or
repugnancy between two ideas that need proofs and the use of reason to
show it.
5. The demonstrated conclusion not without doubt, precedent to the
demonstration. Another difference between intuitive and
demonstrative knowledge is, that, though in the latter all doubt be
removed when, by the intervention of the intermediate ideas, the
agreement or disagreement is perceived, yet before the demonstration
there was a doubt; which in intuitive knowledge cannot happen to the
mind that has its faculty of perception left to a degree capable of
distinct ideas; no more than it can be a doubt to the eye (that can
distinctly see white and black), Whether this ink and this paper be
all of a colour.
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