involves the conception or idea of a triangle, that is, without the idea of a triangle 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 versâ, 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