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I have encountered the concept of eternal return e.g. in reading about Friedrich Nietzsche (1844 – 1900) and Pythagoras (c. 570 – c. 495 BC). This is one formulation from Nietzsche's The Will To Power:

If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force - and every other representation remains indefinite and therefore useless - it follows that, in the great dice game of existence, it must pass through a calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combinations conditions the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game ad infinitum.

I have noticed that the Wikipedia article on eternal return cites only a single (brief) argument against eternal return in Georg Simmel's (1858 – 1918) formulation: he seems to be arguing that time may run into "local loops", so not everything is bound to repeat infinitely often. But more than this counter-attempt must have accumulated during the concept's long history (also in Eastern philosophy).

What (substantially) other argument's have philosopher's (and others) put forward against the concept of eternal return? What is seen as its main fallacy and can account for the fact that it is (apparently) absent from contemporary discourse.

  • This whole concept is dealt with in the Vedas and is the crux of the Vedic belief of the eternity of the existence. Simply put, if you throw a pair of dice a number of times you may get a sequence of 8-4-9. Continue to throw, and sooner or later, the same combination comes up. There have been an infinite number of universes before and an infinite number in the future, so the same sequence of events will repeat sooner or later. – Swami Vishwananda Mar 19 '15 at 6:01
  • @SwamiVishwananda I think some have countered this (roughly) with reference to probability distribution. If it's uniform you have the situation of a dice. If not, then other patterns (with"local loops") may emerge. So yes, the idea of eternal return is of course present in the Vedas (and elsewhere in Eastern philosophy), but are arguments against the concept (as the question asks) as well? – Drux Mar 19 '15 at 8:11
  • Yes understand the difference. I have seen both interpretations by commentators of the Vedas. The more classical is the eternal 'local loop', but some more modern (last 130 years) commentators have suggested the more uniform interpretation. I lean towards the latter... And that does not even bring in the interpretation of the Vedas as whether there is one 'universe' or multiple 'verses'. There is scripture to support both. – Swami Vishwananda Mar 19 '15 at 10:26
  • The classical method of Indian scriptural commentary is for the commentator to make objections with arguments to his interpretation and to answer those objections with a counter argument. So, yes, there are arguments against the concept of eternal return that are presented and refuted. There are also some ancient commentators who followed a materialistic philosophy and made arguments against it as well. – Swami Vishwananda Mar 19 '15 at 10:30
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    A Hindu philosopher by the name of Gaudapada wrote a commentary on the Mandukya Upanishad called Gaudapada's Karika. It is a defense of the Hindu Advaita (non-dual) philosophy. Chapters 2, 3, and 4 specifically are arguments defending the non-dual Brahman using reasoning and logical argumentation alone, no scriptural references. In those chapters he gives opposing arguments of nihilists and materialists and defends his arguments against those opposing views. – Swami Vishwananda Mar 22 '15 at 4:56
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The existence of 'strange attractors' undermines the physical assumptions behind eternal return. The math does not work: previous centuries have just not understood how complex prediction really is.

The standard cheezy example is that as you zoom in on a point on the boundary of the Mandelbrot set, the image really can be proved to continually produce motifs not present in earlier images.

The fact it might look the same on many occasions does not mean it is repeating, because it can be moving through the same state in a different evolutionary direction. Even if there is infinite time, there are also infinitely many derivatives of any function, so infinite subtlety in its variation, and constant capacity to escape repetition.

A simpler example that even the Pythagoreans knew about, is that digit expansions of pi do not repeat, so a circular object rolling infinitely around a square whose side is an even multiple of its radius will, in fact, not ever fall into a perfect, repeating pattern. The position on the rim where it starts down the next side will always be a tiny bit different from what it was on every previous occasion.

If something that simple and clean never repeats, why would anything as complex as a universe?

The classical answer here is that the difference is always shrinking and at some point the difference is small enough not to matter. But from parts of math like bifurcation theory, we see tiny differences can have huge effects over long periods, if they somehow eventually affect a point where the system is very touchy.

Previous generations of mathematicians did not really take that to heart. There is strong human bias to presume convergent behavior. But given computers, we can see by observation that repeating systems of any high complexity almost always have points where some of the derivatives grow very, very large, so a very small difference can make a big bump. This was the ultimate death knell of high-powered analog computers, and the reason everything is digital now.

From an entirely different direction, the level of determinacy presumed simply is not consistent with our observations of the world. We really do observe quantum indeterminacy. So if you have any faith in modern science, this is just not realistic or likely.

  • Tx. I Esp. the argument around digit expansion of pi was of interest to me. – Drux Mar 20 '15 at 9:09
  • I should point out the general modern counterargument: We keep finding out more and more of our reality is discrete, rather than continuous. If in the end we discover that absolutely everything, including space and time are quantized then the very notion of a circle, or of a derivative is an illusion that exists only for our computational convenience, and this argument, which assumes some aspect of space is continuous, falls apart. The transcendence of pi vanishes if pi can exist only as an abstraction. – jobermark Mar 20 '15 at 16:06
  • Also interesting. Do you have a general reference (other than Physics textbooks) which goes into more, e.g. book-length, depth? Reminds me of an argument of Alain Connes where he sees the physical world as a struggle between the discrete and the continuum. – Drux Mar 21 '15 at 7:38
  • There are a lot of folks here attached to the 'simulation' argument. They might be sources for better arguments for a finite universe, if you do a search. I am an idealist of a sort, and a mathematician, so I firmly believe math is real in some sense internal to humans and not just an approximation of the outside world. I am just pointing out the potential future weakness in the argument I actually believe. If the 'quantum foam' people are right, and space is quantized, then the universe must end or loop. I personally I don't think they are. – jobermark Mar 21 '15 at 15:29
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Everything in the universe is periodic. Every object takes birth, grows to a maturity, and then dies. It then remains dead for some time and again reincarnates. This cycle continues for eternity. However it is not exactly periodic. By law of nature, every life is controlled by different destiny. Destiny never repeats for any object.

If we combine two such periodic waves, corresponding to two objects, the resultant will be periodic also. A time will come, when two objects will start almost at same time again and again. However the waveforms will never be exact. Consider the examples of Ramayan and Mahabharat stories in Vedic literature. At some high level both stories are identical. At many detail levels also they are identical. But still there are significant differences between them. Take a look at https://theoryofsouls.wordpress.com/ for their comparisons.

Now according to Vedic theory (Gita), the universe itself repeats. This is natural, since all objects inside the universe are periodic. Now, when universe repeats, everything will start again in the exact same way. Thus the entire chain of reincarnation I have experienced in the previous universe will be exactly repeated. This is how Nietzsche’s eternal recurrence seems to become correct. Check out the above book.

However there appears to have some unanswered questions related to exactness and liberation (mokhsa). This author has also not found yet, any Vedic reference on eternal recurrence.

  • Welcome to Philosophy.SE! Can you make your point more clear, what is the argument against eternal return? Or are you saying that there is no effective argument? It seems that since "every life is controlled by different destiny" there is no periodic return? – James Kingsbery Jun 6 '16 at 20:14
  • His main point – life will be “exactly” repeated appears to be incorrect. Since our bodies are composed by finite combinations of particles then after some births the combinations will repeat. But both Nietzsche and Vivekananda ignored that every particle has three properties – Satta, Tamas, and Rajas. These three properties are analog and can be combined by any proportions. Thus by finite combination of particles life will never repeat exactly. So in this sense Nietzsche is wrong. – Subhendu Das Jun 7 '16 at 23:05
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The standard argument against willing the eternal return is how tragic the holocaust etc. is, that there is nothing good there, to joyfully rewill, as in Agamben, that all we can will is the lost potential of doing so.

Counter-arguments against it in fact happening may be unusual because of the paucity of evidence for it; despite excitable wikipedia articles it is oft asked if even Nietzsche believed it would, Buddhists seek to end or at least realise the end of the cycle of rebirths, etc..

And there's no physical evidence of anything before the big bang:

Since events before the Big Bang have no observational consequences, one may as well cut them out of the theory, and say that time began at the Big Bang. Events before the Big Bang, are simply not defined, because there's no way one could measure what happened at them.

though physicists think the universe did have a beginning

The answer to the question, “Did the universe have a beginning?” is, “It probably did.” We have no viable models of an eternal universe. The BGV theorem gives us reason to believe that such models simply cannot be constructed.

A cyclic universe (with no beginning), when the universe expands, collapses and starts over again, is dicsussed in physics, see e.g. here. But if the laws of nature hold between cycles then the universe would e.g. tend toward increased entropy (or size) across cycles.

I personally just find the idea of the eternal return as redundant and inflationary as deism etc.. Even if we have a clear philosophical notion of eternity, in the first place, I would assume that some things conclusively end, and any repetition is of diffference.

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Here are some thoughts:

Contra jobermark's answer, I think the physical and mathematical considerations cited here are not sufficient to disregard the doctrine of eternal recurrence (not that this doctrine is not to be (or to be) disregarded, but I need to think more about it). The problem is not that there are chaotic phenomena, (nor is it that there are periodic or pseudo-periodic phenomena, keeping in mind Subhendu Das' answer). It is that all such phenomena come "in one package", and it is nontrivial to sort the package out (see e.g. Hofstadter's butterfly).

As far as I can tell, the main line of attack to (Nietzsche's) doctrine of eternal recurrence is that it postulates the eternal recurrence of the same. Exactness is required for the idea to be the greatest weight (I believe much less than exactness is sufficient, but the details need to be worked out).

See the following papers (and the references thereof) for further details:

  • Neves' "Nietzsche for Physicists" at https://arxiv.org/abs/1611.08193
  • Krueger's "Nietzschean Recurrence as a Cosmological Hypothesis"
  • Nehamas' "The Eternal Recurrence"
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Eternal return is here presented as a necessary thing, given the assumptions, so we can disprove it by providing a plausible universe in which it is false.

I'm going with the Universe as physicists understand it. Specifically, Strauss's book "The Universe from Nothing". In this universe, space is expanding currently, and has the potential to expand eternally. There are other possibilities, including expansion followed by contraction, but it's likely that the Universe will expand forever. At some point, the amount of space expansions between two galaxies will be such that they are moving away from each other faster than light, and hence they will never be as close as they are today ever again. The Universe as we see it now is not, under those assumptions, repeatable.

This result is based on space being infinite, where the eternal return argument seems to envision finite space. Let's look at a finite space.

In this case, large enough black holes will be permanent, since if there is some very small density of stuff in the finite Universe it will offset Hawking radiation. Right now, most black holes are not evaporating, because the cosmic background radiation is enough to feed them faster than they decay. These black holes will evaporate and release their mass only because space is expanding and diluting the ambient energy.

Therefore, if the Universe is what it appears to be to physicists and astronomers, there are states that will never recur.

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Could naked monkeys be to eternal return as cats are to 401k's? Has the naked monkey progressed so far in his science that everything he sees with his scientific instruments can be instantly comprehended by him? How long would it take a cat to understand a 401k, even if you gave him internet access to learn all about it? It's hard to see yourself as just another dumb animal, but all knowledge isn't within human grasp. Our new god science isn't close to being omniscient because this god depends upon humans and humans are limited like every other animal. What about the notion that, just like the cat, there is knowledge that the mighty naked ape can never know?

  • I am trying to see how this is an argument against eternal return. If you have any reference to others who take a similar view this would help strengthen the answer. Welcome! – Frank Hubeny Sep 28 at 22:04

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