Benedict de Spinoza, THE ETHICS
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and "knowledge of the second kind." Besides these two kinds of
knowledge, there is, as I will hereafter show, a third kind of
knowledge, which we will call intuition. This kind of knowledge
proceeds from an adequate idea of the absolute essence of
certain attributes of God to the adequate knowledge of the
essence of things. I will illustrate all three kinds of
knowledge by a single example. Three numbers are given for
finding a fourth, which shall be to the third as the second is
to the first. Tradesmen without hesitation multiply the second
by the third, and divide the product by the first; either
because they have not forgotten the rule which they received
from a master without any proof, or because they have often made
trial of it with simple numbers, or by virtue of the proof of
the nineteenth proposition of the seventh book of Euclid,
namely, in virtue of the general property of proportionals.

But with very simple numbers there is no need of this. For
instance, one, two, three being given, everyone can see that the
fourth proportional is six; and this is much clearer, because
we infer the fourth number from an intuitive grasping of the
ratio, which the first bears to the second.

XLI. Knowledge of the first kind is the only source of falsity,
knowledge of the second and third kinds is necessarily true.

>>>>>Proof--To knowledge of the first kind we have (in the
foregoing note) assigned all those ideas, which are inadequate
and confused; therefore this kind of knowledge is the only
source of falsity (II. xxxv.). Furthermore, we assigned to the
second and third kinds of knowledge those ideas which are
adequate; therefore these kinds are necessarily true (II.
xxxiv.). Q.E.D.

XLII. Knowledge of the second and third kinds, not knowledge of
the first kind, teaches us to distinguish the true from the
false.

>>>>>Proof--This proposition is self-evident. He, who knows how
to distinguish between true and false, must have an adequate
idea of true and false. That is (II. xl., note ii.), he must
know the true and the false by the second or third kind of