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Aristotle's Rewinding Spheres: Three Options and their Difficulties

Aristotle asserts at 1073blO-13 that he intends to give in Metaphysics 8 a definite conception about the multitude of the divine transcendent entities, which function as the movers of the celestial spheres. In order to do so, he describes several celestial theories. First Eudoxus', then the modifications of this theory propounded by Callippus, and finally his own suggestion, the introduction of yet further spheres which integrate the celestial spheres into a single overarching scheme. For this, after explaining the spheres providing the component motions of each planet, Aristotle introduces so-called rewinding spheres (anelittousai), which perform contrary revolutions to the ones performed by the spheres carrying the planet.