Marsilio Ficino’s Platonic Theology, Volume II

2Suppose, moreover, that the point receives that form so that it alone is the form’s seat and foundation, while the form remains separate from the body’s breadth. The point too must then be detached from the breadth, especially since nothing is properly an accident’s subject unless it exists in actuality in its own right. Such a point will be separated from the line; it will be neither anything belonging to the line nor the limit of its breadth, and the line will be bounded by some other point next to it. That other point will likewise exist in an actuality of its own, so that it too may become the seat of an accidental form; it too will therefore be severed from the line, especially since the same account applies to every point. It follows either that no point exists in a line—which is the height of folly, since the line would have no limits—or that the length of a line is made from points. That too is ridiculous, because adding point to point does not increase length. This appears as follows. Conceive three points in succession. We shall ask whether the middle point forces the two outer points so far apart that they do not touch, or instead fails to prevent them from coinciding. If it forces them apart, it certainly does not touch one with the same part of itself by which it touches the other; otherwise it would not separate them. But if one part of it faces one outer point and another part the other, the middle point itself consists of two parts and is no point at all, since it is divisible. We are therefore compelled to admit that the middle point does not prevent the others from coinciding. All the points will thus be in all the others, and by their coincidence they will produce no length, since the middle point creates no interval between the other points. If no bodily length is composed of points, no point is found within it that can ever come to exist by itself in actuality and become the subject of an intelligible form. Someone may perhaps say that a point exists in a body not in actuality but in potency, and by that very potency becomes the subject of the intelligible form. Although this has already been refuted, it may be refuted once more in this way. Because such points are in potency rather than actuality, and because they are infinite, nothing distinguishes them from one another so that one rather than another should receive the form. All of them therefore receive it. The intellect will consequently either receive in actuality infinitely many forms at once for each thing to be understood, or through infinitely many points understand the same thing infinitely many times at once. Both are impossible: there cannot be infinitely many forms in actuality, nor infinitely many acts of understanding at once.