Aristotle and Aquinas' Third Way

Aristotle seems to have thought that the earth and the species inhabiting it are eternal. This seems extremely implausible for reasons that should have been available to Aristotle.

It is difficult to wipe out a species, but surely not possible: all it takes is to kill each of the finitely many individuals. Given a species s that cannot have more than n members, and given a long enough time, we would expect there to be a very high probability that all the members of s would have died out during some hour due to random events. Given any finite number of species each with a bound on how many members it can have, and given a long enough time, we would expect with very high probability that all the members would die off.

Now there is a finite limit on how many species there are on earth (as Aristotle knew, the earth is finite), and a finite limit on how many members the species can have (again, the earth is finite). So we should have expected all the species that existed some long amount of time ago to have died out.

The above provides an argument that if the world is eternal, new species can arise. For if new species can’t arise and the world is eternal, then by now there should have been no species left.

How could Aristotle have gotten out of this worry without rejecting his thesis about the eternity of the earth?

One way be to suppose a powerful protector of our ecosystem that would make sure that the species-destroying random events never happen. This protector would either itself have to be sufficiently powerful that it would not be subject to the vicissitudes of chance, or there would have to be an infinite (probably uncountably infinite!) number of such protectors.

Another option would be for Aristotle to reject his thesis that there is only one earth (which was based on theory of gravitation as attraction to the center of the universe: if there were more than one earth they would have both collapsed into the center of the universe by now).

If there were infinitely many earths, then it’s perhaps not so crazy to think that some earth would have lucked out and not had its species die out. Of course, this would not only require Aristotle to reject his thesis that there is only one earth, but also the finitist thesis that there cannot be an infinite number of co-actual things. (Interestingly, given the plausibility that any given species has probability one of dying out given infinite time, and given the countable additivity of probabilities, this way out would require not merely infinitely many earths, but an uncountable infinity of earths. Assuming an Archimedean spacetime for our universe, it would require a multiverse.)

In any case, Aristotle’s commitment to new species not coming into existence (or at least new species of interesting critters; he may be OK with worms coming into existence) is in tension with what he says about the earth’s eternity.