ETHICS(II, P43) 515
adequate knowledge of the essence of things. I shall illustrate all these kinds of
knowledge by one single example. Three numbers are given; it is required to find a
fourth which is related to the third as the second to the first. Tradesmen have no hesi-
tation in multiplying the second by the third and dividing the product by the first,
either because they have not yet forgotten the rule they learned without proof from
their teachers, or because they have in fact found this correct in the case of very sim-
ple numbers, or else from the force of the proof of Proposition 19 of the Seventh
Book of Euclid, to wit, the common property of proportionals. But in the case of very
simple numbers, none of this is necessary. For example, in the case of the given num-
bers 1, 2, 3, everybody can see that the fourth proportional is 6, and all the more
clearly because we infer in one single intuition the fourth number from the ratio we
see the first number bears to the second.
PROPOSITION 41:Knowledge of the first kind is the only cause of falsity; knowledge
of the second and third kind is necessarily true.
Proof: In the preceding Scholium we asserted that all those ideas which are inad-
equate and confused belong to the first kind of knowledge; and thus (Pr. 35, II) this
knowledge is the only cause of falsity. Further, we asserted that to knowledge of the sec-
ond and third kind there belong those ideas which are adequate. Therefore (Pr. 34, II),
this knowledge is necessarily true.
PROPOSITION 42:Knowledge of the second and third kind, and not knowledge of the
first kind, teaches us to distinguish true from false.
Proof: This Proposition is self-evident. For he who can distinguish the true from
the false must have an adequate idea of the true and the false; that is (Sch. 2 Pr. 40, II),
he must know the true and the false by the second or third kind of knowledge.
PROPOSITION 43:He who has a true idea knows at the same time that he has a true
idea, and cannot doubt its truth.
Proof: A true idea in us is one which is adequate in God insofar as he is explicated
through the nature of the human mind (Cor. Pr. 11, II). Let us suppose, then, that there
is in God, insofar as he is explicated through the nature of the human mind, an adequate
idea, A. The idea of this idea must also necessarily be in God, and is related to God in
the same way as the idea A (Pr. 20, II, the proof being of general application). But by
our supposition the idea A is related to God insofar as he is explicated through the
nature of the human mind. Therefore, the idea of the idea A must be related to God in
the same way; that is (Cor. Pr. 11, II), this adequate idea of the idea A will be in the
mind which has the adequate idea A. So he who has an adequate idea, that is, he who
knows a thing truly (Pr. 34, II), must at the same time have an adequate idea, that is, a
true knowledge of his knowledge; that is (as is self-evident), he is bound at the same
time to be certain.
Scholium: I have explained in the Scholium to Pr. 21, II what is an idea of an idea;
but it should be noted that the preceding proposition is sufficiently self-evident. For
nobody who has a true idea is unaware that a true idea involves absolute certainty. To
have a true idea means only to know a thing perfectly, that is, to the utmost degree.
Indeed, nobody can doubt this, unless he thinks that an idea is some dumb thing like a
picture on a tablet, and not a mode of thinking, to wit, the very act of understanding. And
who, pray, can know that he understands some thing unless he first understands it? That
is, who can know that he is certain of something unless he is first certain of it? Again,