riangle it cannot be conceived. It is the same
thing to say, that the concept A must involve the concept B, as
it is to say, that A cannot be conceived without B. Further,
this affirmation cannot be made (II. Ax. iii.) without the idea
of a triangle. Therefore, this affirmation can neither be nor be
conceived, without the idea of a triangle. Again, this idea of a
triangle must involve this same affirmation, namely, that its
three interior angles are equal to two right angles. Wherefore,
and vice versa, this idea of a triangle can neither be nor be
conceived without this affirmation, therefore, this affirmation
belongs to the essence of the idea of a triangle, and is nothing
besides. What we have said of this volition (inasmuch as we have
selected it at random) may be said of any other volition, namely,
that it is nothing but an idea. Q.E.D.

Corollary.--Will and understanding are one and the same.

Proof.--Will and understanding are nothing beyond the
individual volitions and ideas (II. xlviii. and note). But a
particular volition and a particular idea are one and the same
(by the foregoing Prop.); therefore, will and understanding are
one and the same. Q.E.D.

Note.--We have thus removed the cause which is commonly
assigned for error. For we have shown above, that falsity
consists solely in the privation of knowledge involved in ideas
which are fragmentary and confused. Wherefore, a false idea,
inasmuch as it is false, does not involve certainty. When we
say, then, that a man acquiesces in what is false, and that he
has no doubts on the subject, we do not say that he is certain,
but only that he does not doubt, or that he acquiesces in what is
false, inasmuch as there are no reasons, which should cause his
imagination to waver (see II. xliv. note). Thus, although the
man be assumed to acquiesce in what is false, we shall never say
that he is certain. For by certainty we mean something positive
(II. xliii. and note), not merely the absence of doubt.

However, in order that the foregoing proposition may be fully
explained, I will draw attention to a few additional points, and
I will furthermore answer the objections which may be advanced
against our doctrine. Lastly, in order to remove every scruple,
I have thought it worth while to point out some of the
advantages, which follow therefrom. I say "some," for they will
be better appreciated from what we shall set forth in the fifth
part.

I begin,