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rigorous demonstration, and rejects the rest on philosophic as well as religious grounds.

The existence of separate intelligences he proves in the same way as Ibn Daud from the motions of the celestial spheres. These motions cannot be purely "natural," i. e., unconscious and involuntary like the rectilinear motions of the elements, fire, air, water and earth, because in that case they would stop as soon as they came to their natural place, as is true of the elements (cf. above, p. xxxiii); whereas the spheres actually move in a circle and never stop. We must therefore assume that they are endowed with a soul, and their motions are conscious and voluntary. But it is not sufficient to regard them as irrational creatures, for on this hypothesis also their motions would have to cease as soon as they attained the object of their desire, or escaped the thing they wish to avoid. Neither object can be accomplished by circular motion, for one approaches in this way the thing from which one flees, and flees the object which one approaches. The only way to account for continuous circular motion is by supposing that the sphere is endowed with reason or intellect, and that its motion is due to a desire on its part to attain a certain conception. God is the object of the conception of the sphere, and it is the love of God, to whom the sphere desires to become similar, that is the cause of the sphere's mo- tion. So far as the sphere is a body, it can accomplish this only by circular motion; for this is the only continuous act possible for a body, and it is the simplest of bodily motions.

Seeing, however, that there are many spheres having different kinds of motions, varying in speed and direction, Aristotle thought that this difference must be due to the difference in the objects of their con- ceptions. Hence he posited as many separate Intelligences as there are spheres. That is, he thought that intermediate between God and the rational spheres there are pure incorporeal intelligences, each one moving its own sphere as a loved object moves the thing that loves it. As the number of spheres were in his day thought to be fifty, he as- sumed there were fifty separate Intelligences. The mathematical sciences in Aristotle's day were imperfect, and the astronomers thought that for every motion visible in the sky there must be a sphere, not knowing that the inclination of one sphere may be the cause of a number of apparent motions. Later writers making use of the more