the Creator except by establishing that the world had a beginning, and it is impossible to establish that the world had a beginning except by establishing that bodies had a beginning.”

They said that the way to do this is to infer, from the origination of accidents, the origination of the things in which those accidents subsist. Some argued from motion and rest alone; others appealed to spatial states, which they define as combination, separation, motion, and rest. Still others appealed to accidents generally. Their proof rests on the premise that whatever is never devoid of events must itself have had a beginning, since events without a first are impossible.

Their opponents—adherents of religious traditions and others, including both those who hold that the heavens and the earth were brought into existence from nothing and those who hold that the celestial spheres are beginningless and eternal—say to them: “The occurrence of events after their previous nonexistence is itself an event. It must therefore have a newly arising cause; otherwise, one of the two alternatives of a contingent thing would be favored without a determining factor.”

Those among the adherents of religious traditions and others who hold that the celestial spheres had a beginning also say to them:

“You have established that the world had a beginning by a certain method, yet the world’s having a beginning is possible only if the contrary of what you have established is true. What you have presented as proof that the world had a beginning therefore does not prove that it had a beginning; indeed, it does not even entail this. A proof must necessarily entail what it proves, such that whenever the proof holds, what it proves must also hold. Rather, your proof is incompatible with the world’s having a beginning and contradicts it. It implies that the world could not have come into being—indeed, that there could be no coming into being of