The discussion that revolved around the admissibility of eccentrics and epicycles lied at the core of this theoretical discussion, and those who would not allow such concepts took the position that such eccentrics and epicycles would then introduce a center of heaviness, other than the Earth, around which celestial simple bodies would then move. Ptolemy tried to resolve the debate by introducing the Apollonian theorem, which allowed for the replacement of an eccentric with a simple concentric sphere carrying an epicycle. But the problem could not be resolved so easily as the epicycle itself was also found objectionable for it also introduced a center of heaviness around which the epicycle itself revolved, and worse yet the epicycle had to be placed out there in the world of the Aristotelian ether which was defined as the ultimate simple element par excellence.
Andalusian astronomers such as Ibn Bāja (Avempace d. 1138/9), Ibn Ṭufayl (d. 1185/6), Ibn Rushd (Averroes d. 1198), and al-Biṭrūjī (c. 1200), each in his own style, expressed their dissatisfaction with Ptolemaic astronomy specifically because it harbored such appalling non-Aristotelian bodies as eccentrics and epicycles. Al-Biṭrūjī went farther than all of them by undertaking to construct a complete alternative configuration that avoided these eccentrics.[231]
Al-Biṭrūjī's success was spoiled by the inability of his configuration to account for the observations in a quantitative manner that would allow for the predictability of the planetary positions for any time and any place. That fundamental test of any astronomical proposition was the main hurdle against which al-Biṭrūjī's configuration collapsed. It was only an attempt to resuscitate the old Eudoxian spheres that had at one point enchanted Aristotle himself, but could not even then predict the position of any planet at any time, despite the fact that they could give a rather naive description of a planet's general behavior. And so was the case with Al-Biṭrūjī's construction, which also failed to account for the observable motions of the planets. For that reason alone Biṭrūjī's account remained to be a curious proposition that was not pursued any further by later astronomers. I suppose no practicing astronomer or astrologer, who needed to compute positions of planets, could take it seriously.
On more serious grounds, and for all those who wished to uphold the Aristotelian universe, at some point they had to admit that the Arsitotelian universe was not all that consistent anyway. Again we shall return to this philosophical issue later on. But in the context of this chapter, where we are focusing on the reception of the Greek scientific tradition into the Islamic civilization, let us complete the picture by indicating the range of objections the astronomers who worked in Islamic times were prepared to raise. According to Aristotle, all celestial bodies, spheres, stars and planets, were all supposed to have been made of the same Aristotelian simple element, ether. That element was supposed to be divine, thus the simplest of all elements, capable only of one motion: the circular motion that had no beginning, nor end. As a result the simple element ether did not partake of any composition or any generation or corruption, as was the case with the other sublunar elements that experienced linear contrary motions. If that Aristotelian proposition were to be taken literally, and there were some who did take it so, then one would wonder how could a sphere, say, that carried the sun, in the same fashion a ring carried a crown, emit such a bright light as the light of the sun, from only one part of it, where the sun is located, while the rest of its body acted like a crystalline transparent spherical substance that did not emit any light? This, when the sun and its carrying sphere were both assumedly made of the same element ether.
Ibn al-Shāṭir of Damascus confronted the Aristotelian universe along these very lines and with this exact understanding. In his own way though, he posed the question in the following manner: He said that since the stars, and the planets, were themselves different from the spheres that carry them, as in the case with the sun that emits light while the sphere that carries it does not, then Aristotle would have to admit that the celestial world was not all that simple and must admit of some type of composition. Now, since astronomers, Aristotelian ones included would know that some of the fixed stars were in fact considerably bigger than the largest epicycles of the planets, then if a composition is allowed for the fixed stars, the same composition must also be admitted for the much smaller epicycles as well. Ibn al-Shāṭir would then conclude that he was entitled to as much composition in the celestial spheres that would allow for the epicycles as Aristotle would allow for the fixed stars. He then went on to say, that while Aristotle and those who followed him could be right about the inadmissibility of the eccentrics, they were all wrong on the inadmissibility of the epicycles. The immediate consequence of this position led Ibn al-Shāṭir to construct very complicated mathematical models that would replace the Ptolemaic models, but at the same time they were all constructed without a single eccentric sphere. In his defense he simply changed the Aristotelian assumption to stipulate that the universe was not as simple and consistent as Aristotle had thought, but according to Ibn al-Shāṭir, that it admitted of some form of composition. In a real sense, Ibn al-Shāṭir's novel assumption was the only one I know of where an astronomer actually confronted the Aristotelian assumptions with a set of his own. This should have serious philosophical repercussions when taken in the context of the gradual collapse of the Aristotelian universe that culminated with the Newtonian final coup de grace.
In the context of the encounter with the Greek scientific tradition, and in the context of the relationship of the science of astronomy to the other sciences, a particular case should be made for mathematics. Not only because the astronomers used this discipline so profusely, nor because it was the demonstrative science par excellence, but because those same astronomers who went on to criticize Ptolemaic astronomy, and with their extensive proposals for alternative constructions, began to unravel the nature of the discipline of mathematics as well, by noticing that there were so many mathematical constructions that could explain the same observational results. The standard case in this regard was that of the Apollonius theorem which was used by Ptolemy himself to account for the same observations either by an eccentric construction or by an epicyclic one. Ptolemy was conscious of the fact that those two mathematical constructions depicted the same observational results, and opted to use the eccentric construction on account of its simplicity since it involved only one motion as he put it.
What Ptolemy did not say was that both constructions, the eccentric as well as the epicyclic, violated the Aristotelian cosmology. For in the first case, the eccentric assumed a fixed center of heaviness other than the Earth, which was inadmissible, and in the second case of the epicycle it assumed a center of heaviness out in the celestial realm as we just described.
Later astronomers who had no vested interest to defend the Aristotelian universe one way or another were at times ambivalent about those constructions and went along with the Ptolemaic choice of the eccentric constructions. As we have just said, only Ibn al-Shāṭir objected to the eccentrics and avoided using them in his reformulation of astronomy.
231
See, for example, Bernard Goldstein,