ABSTRACT
This chapter discusses certain views about mathematical objects, especially numbers, held by the Pythagoreans, Plato, and certain Platonists, to which views Aristotle opposes his own. The remark that the Pythagoreans were induced to conclude that all things are numbers by the fact that they found numbers in the musical scale, in the heaven, and in many things besides. They held that numbers were not separable, that is they had no separate existence, but were the material out of which things are made. Aristotle goes on to say that he holds, as before stated, and that it is obvious, that the objects of mathematics are not separable from sensible things. Physics then is concerned with things that have in themselves a principle of motion; mathematics is theoretical and is a science dealing with things that are unchanging but have no separate existence. It is clear, therefore, that there are three kinds of theoretical science, physics, mathematics, and theology.
