P48: In the Mind there is no absolute, or free, will, but the Mind is determined to will this or that by a cause which is also determined by another, and this again by another, and so to infinity.

Dem.: The Mind is a certain and determinate mode of thinking (by P11), and so (by IP17 C2) cannot be a free cause of its own actions, or cannot have an absolute faculty of willing and not willing. Rather, it must be determined to willing this or that (by IP28) by a cause which is also determined by another, and this cause again by another, etc., q.e.d.

Schol.: In this same way it is also demonstrated that there is in the Mind no absolute faculty of understanding, desiring, loving, etc. From this it follows that these and similar faculties are either complete fictions or nothing but Metaphysical beings, or universals, which we are used to forming from particulars. So intellect and will are to this or that idea, or to this or that volition as ‘stone-ness’ is to this or that stone, or man to Peter or Paul.

We have explained the cause of men’s thinking themselves free in the Appendix of Part I.

But before I proceed further, it should be noted here that by will I understand a faculty of affirming and denying, and not desire. I say that I understand the faculty by which the Mind affirms or denies something true or something false, and not the desire by which the Mind wants a thing or avoids it.

But after we have demonstrated that these faculties are universal notions which are not distinguished from the singulars from which we form them, we must now investigate whether the volitions themselves are anything beyond the very ideas of things. We must investigate, I say, whether there is any other affirmation or negation in the Mind except that which the idea involves, insofar as it is an idea—on this see the following Proposition and also D3—so that our thought does not fall into pictures. For by ideas I understand, not the images that are formed at the back of the eye (and, if you like, in the middle of the brain), but concepts of Thought {NS: or the objective Being of a thing insofar as it consists only in Thought}.