E
esse_est_percipi
Enlightened
- Jul 14, 2020
- 1,747
I just have to post this because the eternal recurrence (ER) idea bothers me so much.
It's a bit of a dry post so I apologize, and it will probably quickly be forgotten.
It's Nietzsche's idea that this exact universe might repeat an indefinite or infinite number of times. A nightmare scenario.
If Poincare recurrence is applicable to the universe, or if Boltzmann brains are possible, or if parallel universes are real, or if some big bounce model is true, then ER might be scientifically plausible.
But I don't think it's possible based on the following reductio argument and my limited knowledge of what infinity actually means and implies.
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(1) Assume ER is true and that 'eternal' is equivalent to 'infinite'
(2) Then we would already have necessarily lived this same life infinite times in the 'past' (or in identical parallel universes).
(3) Because if not, then there would have had to have been a 'first beginning' or 'first iteration' of our universe (e.g. it could be this universe, or 3, 7, 850 universes ago, or 20,000,000,000,987,564 universes ago, etc).
(4) But a first iteration would be arbitrary and beg the question why the iterations didn't stretch back one stage further, or to infinity.
(5) If this is all true, then we could never have reached this point in time in this universe
[ Because: this iteration would be iteration (infinity + 1).
But in the addition (infinity + 1), the left side of the sum is an actual infinity.
Actual infinities cannot be 'traversed' in reality
Because the real infinite cannot be summed in a set (as opposed to series which only tend to infinity) and 'overcome' to reach a 'present' **
So we can't have already lived an infinite amount of identical lives ]
(7) Which means that an infinite recurrence in the 'future' cannot happen either (this follows from (1), (2) and (5). And apart from the logic involved here, it just wouldn't be aesthetically pleasing or symmetrical for infinite recurrence not to apply to the 'past', yet to apply the 'future'. If ER is true at all, it has to be true that it applies across every inter-universe spacetime 'direction', or not at all.)
Conclusion: Assuming ER to be true leads to a contradiction (i.e. that this universe could never have been 'reached'. But it has been reached.)
So ER is false.
Q.E.D. (?)
__________________________________________________________________________________________________________________________________________________________
** this is correct as far as it is consistent with modern science, if potential infinity is distinguished from actual infinity (going back to Aristotle).
We could not have already lived an actually infinite number of identical lives, because as far as physics is concerned actual infinities cannot be instantiated in reality. Only potential infinities can, i.e. summing a series which tends to infinity as used in calculus.
So e.g. you can keep dividing the distance between two points forever, and this division is potentially infinite, but it is not an actual infinity. If distances between two points were actual infinities, then Zeno's paradoxes would hold and we would be living in alice in wonderland world.
The idea of already having lived an infinite amount of lives implies actual infinity, which mathematicians and set theorists can manipulate, but there is no empirical evidence that this is or can be part of physical reality.
e.g. "The conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics." (A. Fraenkel)
"Infinite totalities do not exist in any sense of the word (i.e., either really or ideally). More precisely, any mention, or purported mention, of infinite totalities is, literally, meaningless." (A. Robinson)
"Georg Cantor's grand meta-narrative, Set Theory, created by him almost singlehandedly in the span of about fifteen years, resembles a piece of high art more than a scientific theory." (Y. Manin)
"There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions." (Poincare)
"During the renaissance, particularly with G. Bruno, actual infinity transfers from God to the world. The finite world models of contemporary science clearly show how this power of the idea of actual infinity has ceased with classical (modern) physics. Under this aspect, the inclusion of actual infinity into mathematics, which explicitly started with G. Cantor only towards the end of the last century, seems displeasing. Within the intellectual overall picture of our century ... actual infinity brings about an impression of anachronism." (P. Lorenzen)
So the above deduction purporting to 'prove' the impossibility of eternal recurrence by equating 'eternal' with 'infinite' and precluding the possibility of traversing an actual infinite to reach the present has to be qualified with the clause: as far as modern science and maths knows.
It's a bit of a dry post so I apologize, and it will probably quickly be forgotten.
It's Nietzsche's idea that this exact universe might repeat an indefinite or infinite number of times. A nightmare scenario.
If Poincare recurrence is applicable to the universe, or if Boltzmann brains are possible, or if parallel universes are real, or if some big bounce model is true, then ER might be scientifically plausible.
But I don't think it's possible based on the following reductio argument and my limited knowledge of what infinity actually means and implies.
__________________________________________________________________________________________________________________________________________________________
(1) Assume ER is true and that 'eternal' is equivalent to 'infinite'
(2) Then we would already have necessarily lived this same life infinite times in the 'past' (or in identical parallel universes).
(3) Because if not, then there would have had to have been a 'first beginning' or 'first iteration' of our universe (e.g. it could be this universe, or 3, 7, 850 universes ago, or 20,000,000,000,987,564 universes ago, etc).
(4) But a first iteration would be arbitrary and beg the question why the iterations didn't stretch back one stage further, or to infinity.
(5) If this is all true, then we could never have reached this point in time in this universe
[ Because: this iteration would be iteration (infinity + 1).
But in the addition (infinity + 1), the left side of the sum is an actual infinity.
Actual infinities cannot be 'traversed' in reality
Because the real infinite cannot be summed in a set (as opposed to series which only tend to infinity) and 'overcome' to reach a 'present' **
So we can't have already lived an infinite amount of identical lives ]
(7) Which means that an infinite recurrence in the 'future' cannot happen either (this follows from (1), (2) and (5). And apart from the logic involved here, it just wouldn't be aesthetically pleasing or symmetrical for infinite recurrence not to apply to the 'past', yet to apply the 'future'. If ER is true at all, it has to be true that it applies across every inter-universe spacetime 'direction', or not at all.)
Conclusion: Assuming ER to be true leads to a contradiction (i.e. that this universe could never have been 'reached'. But it has been reached.)
So ER is false.
Q.E.D. (?)
__________________________________________________________________________________________________________________________________________________________
** this is correct as far as it is consistent with modern science, if potential infinity is distinguished from actual infinity (going back to Aristotle).
We could not have already lived an actually infinite number of identical lives, because as far as physics is concerned actual infinities cannot be instantiated in reality. Only potential infinities can, i.e. summing a series which tends to infinity as used in calculus.
So e.g. you can keep dividing the distance between two points forever, and this division is potentially infinite, but it is not an actual infinity. If distances between two points were actual infinities, then Zeno's paradoxes would hold and we would be living in alice in wonderland world.
The idea of already having lived an infinite amount of lives implies actual infinity, which mathematicians and set theorists can manipulate, but there is no empirical evidence that this is or can be part of physical reality.
e.g. "The conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics." (A. Fraenkel)
"Infinite totalities do not exist in any sense of the word (i.e., either really or ideally). More precisely, any mention, or purported mention, of infinite totalities is, literally, meaningless." (A. Robinson)
"Georg Cantor's grand meta-narrative, Set Theory, created by him almost singlehandedly in the span of about fifteen years, resembles a piece of high art more than a scientific theory." (Y. Manin)
"There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions." (Poincare)
"During the renaissance, particularly with G. Bruno, actual infinity transfers from God to the world. The finite world models of contemporary science clearly show how this power of the idea of actual infinity has ceased with classical (modern) physics. Under this aspect, the inclusion of actual infinity into mathematics, which explicitly started with G. Cantor only towards the end of the last century, seems displeasing. Within the intellectual overall picture of our century ... actual infinity brings about an impression of anachronism." (P. Lorenzen)
So the above deduction purporting to 'prove' the impossibility of eternal recurrence by equating 'eternal' with 'infinite' and precluding the possibility of traversing an actual infinite to reach the present has to be qualified with the clause: as far as modern science and maths knows.
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