Note.--In the same way it is proved, that there is in the mind no absolute faculty of understanding, desiring, loving, &c. Whence it follows, that these and similar faculties are either entirely fictitious, or are merely abstract and general terms, such as we are accustomed to put together from particular things. Thus the intellect and the will stand in the same relation to this or that idea, or this or that volition, as "lapidity" to this or that stone, or as "man" to Peter and Paul. The cause which leads men to consider themselves free has been set forth in the Appendix to Part I. But, before I proceed further, I would here remark that, by the will to affirm and decide, I mean the faculty, not the desire. I mean, I repeat, the faculty, whereby the mind affirms or denies what is true or false, not the desire, wherewith the mind wishes for or turns away from any given thing. After we have proved, that these faculties of ours are general notions, which cannot be distinguished from the particular instances on which they are based, we must inquire whether volitions themselves are anything besides the ideas of things. We must inquire, I say, whether there is in the mind any affirmation or negation beyond that, which the idea, in so far as it is an idea, involves. On which subject see the following proposition, and II. Def. iii., lest the idea of pictures should suggest itself. For by ideas I do not mean images such as are formed at the back of the eye, or in the midst of the brain, but the conceptions of thought. PROP. XLIX. There is in the mind no volition or affirmation and negation, save that which an idea, inasmuch as it is an idea, involves. Proof.--There is in the mind no absolute faculty of positive or negative volition, but only particular volitions, namely, this or that affirmation, and this or that negation. Now let us conceive a particular volition, namely, the mode of thinking whereby the mind affirms, that the three interior angles of a triangle are equal to two right angles. This affirmation 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.