The classical versions of eternal recurrence say that recurrence occurs within our universe. Those classical versions say that there is a cyclical pattern of events in our space-time. Since the classical theory of eternal recurrence makes claims about our universe, it is open to scientific study. And it is almost certainly false. There is no recurrence within our universe. However, that does not refute the theory of eternal recurrence.
Here is a multiverse version of eternal recurrence that is consistent with science: (1) our universe exists; (2) for every universe, there exists an exactly similar predecessor universe; and (3) for every universe, there exists an exactly similar successor universe. This theory says nothing about the events in our universe. Perhaps our universe starts with a Big Bang and then runs through its entire history until all entropy is maximal. If that’s right, then that same pattern occurs in every predecessor and successor universe. This theory says that there is a two-way infinite series of exactly similar universes.
Since all these universes are exactly similar, their contents are exactly similar. Your life exists in our universe; but if something exists in some universe, then it is a member of a two-way infinite series of exactly similar counterparts in the other universes. The term “counterpart” signifies a technical philosophical concept, developed most extensively by the recent American philosopher David Lewis (1986: ch. 4). Counterpart theory is deeply fascinating, but there’s no need to get into it too deeply here.
The multiverse version of the eternal return entails that your life is a member of a two-way infinite series of exactly similar lives in exactly similar universes. For every one of your lives, there exists an exactly similar predecessor life. For every one of your lives, there exists an exactly similar successor life. You will be reborn over and over again, to live your life over and over again. However, this rebirth is not reincarnation – there is no immaterial thinking substance (no Cartesian soul) that travels from counterpart to counterpart. There is no transmigration of souls. Nor is there any continuity of memory – you do not remember your past lives in any meaningful way. Of course, you do remember your past lives in the entirely trivial sense that remembering what you did yesterday is the same as remembering what you did on the corresponding day of every one of your past lives.
And there is no personal identity across all your counterparts. Taken together, your counterparts don’t make up the stages in the life or career of some big person. You are not identical with any one of your past or future selves. They are distinct people who are exactly similar to you in every way. To use some logical jargon, they are qualititatively identical to you, but they are not numerically identical to you. Your life does not persist through recurrence; you do not survive into the next cycle. Your life is merely repeated, and the form of your life is exactly re-instantiated. Your biography is the singlel universal shared in common by all your lives. But that universal is not you.
This theory of eternal recurrence does not involve any theistic deities. On the contrary, it says that nature is fully self-sufficient. Since nature is uncreated, it needs no creator. It always has been and it always will be. So this theory of eternal recurrence is entirely compatible with the most rigorous atheism. And the thesis that you have infinitely many counterparts does not involve any immaterial thinking substance that passes from each previous counterpart to its next counterpart. It is entirely consistent with the most puritanical materialism. Of course, this theory agrees with the Aristotelian doctrine that the soul is the form of the body. Your body has a form – it runs a biological program. And that program will run over and over again.
This theory of eternal recurrence is also consistent with naturalism. It does not involve any super-natural agencies. It is an entirely natural theory. It is even a purely mechanistic theory. Nature is just a big loop. It is a looping process that has always been running and always will be running. The ultimate natural pattern, the logos of natural creative power, is a big looping program. It always has and always will be running.
This theory of eternal recurrence is consistent with atheism, with materialism, and with naturalism. But what about rationalism? Rationalism permits the existence of any objects that are found in empirically justified theories. Rationalism doesn’t guarantee that these things exist; it merely states that it is rational to say that they exist. Unfortunately for the eternal return, it doesn’t seem like there are any good arguments for it. Unless some good evidence-based argument for it is found, it’s not rational to believe in the theory of eternal recurrence. And eternal recurrence, with its sterile repetition of the same, probably isn’t what an advocate of rebirth wants anyway.
Despite its failures, the eternal return is a good illustration of a theory of rebirth that is consistent with atheism (as well as most other doctrines that inspire atheists). It suggests that there may be good lines of reasoning for more desirable types of rebirth. There may be types of rebirth that can be included in an atheistic nature-religion.
Lewis, D. (1986) On the Plurality of Worlds. Cambridge, MA: Blackwell.