If there be sight in the eyes, it will, at first
glimpse, without hesitation, perceive the words printed on this
paper different from the colour of the paper: and so if the mind
have the faculty of distinct perception, it will perceive the
agreement or disagreement of those ideas that produce intuitive
knowledge. If the eyes have lost the faculty of seeing, or the mind of
perceiving, we in vain inquire after the quickness of sight in one, or
clearness of perception in the other.
6. Not so clear as intuitive knowledge. It is true, the perception
produced by demonstration is also very clear; yet it is often with a
great abatement of that evident lustre and full assurance that
always accompany that which I call intuitive: like a face reflected by
several mirrors one to another, where, as long as it retains the
similitude and agreement with the object, it produces a knowledge; but
it is still, in every successive reflection, with a lessening of
that perfect clearness and distinctness which is in the first; till at
last, after many removes, it has a great mixture of dimness, and is
not at first sight so knowable, especially to weak eyes. Thus it is
with knowledge made out by a long train of proof.
7. Each step in demonstrated knowledge must have intuitive evidence.
Now, in every step reason makes in demonstrative knowledge, there is
an intuitive knowledge of that agreement or disagreement it seeks with
the next intermediate idea which it uses as a proof: for if it were
not so, that yet would need a proof; since without the perception of
such agreement or disagreement, there is no knowledge produced: if
it be perceived by itself, it is intuitive knowledge: if it cannot
be perceived by itself, there is need of some intervening idea, as a
common measure, to show their agreement or disagreement.
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