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RECENT POSTS IN THIS TOPIC

Aleksandar Mikovic: on 4/20/15 at 18:34pm UTC, wrote Dear Lev, I am sorry to hear this, but I am pretty sure that I gave you 8,...

Alexey/Lev Burov: on 4/20/15 at 12:54pm UTC, wrote Dear Aleksandar, Thank you for your very interesting comments and the...

Aleksandar Mikovic: on 4/19/15 at 20:26pm UTC, wrote Dear Alexey, Thank you very much for warning me again about your essay,...

Alexey/Lev Burov: on 4/19/15 at 13:49pm UTC, wrote Dear Aleksandar, Apparently you somehow missed a comment of Lev above, so...

Luca Valeri: on 4/15/15 at 19:10pm UTC, wrote Hi Aleksandar I would not call von Weizsäcker a platonist. But he surely...

Aleksandar Mikovic: on 4/15/15 at 17:22pm UTC, wrote Dear Luca, Thank you for your remarks, it is very helpful for me when I...

Luca Valeri: on 4/13/15 at 23:00pm UTC, wrote Hi Aleksandar, According the rating it seems the community does not like...

Joe Fisher: on 4/9/15 at 15:45pm UTC, wrote Dear Aleksandar, I think Newton was wrong about abstract gravity; Einstein...


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FQXi FORUM
October 23, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Godel's Incompleteness Theorems and Platonic Metaphysics by Aleksandar Mikovic [refresh]
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Author Aleksandar Mikovic wrote on Mar. 10, 2015 @ 18:35 GMT
Essay Abstract

We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.

Author Bio

I am a professor of mathematics at Lusofona University in Lisbon and I do research in quantum gravity, string theory and related mathematics. I obtained my PhD in physics in 1990 from University of Maryland and I was a postdoc at Queen Mary College and at Imperial College in London. I published over 60 papers in quantum gravity, string theory and related mathematics.

Download Essay PDF File

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Colin Walker wrote on Mar. 11, 2015 @ 19:25 GMT
Dear Aleksandar,

Cosmology is where philosophy meets science, where metaphysics meets physics. I expect you will agree that a universe undergoing accelerating expansion is difficult to reconcile from the point of view of platonic metaphysics.

However, there does exist a plausible platonic cosmology. My essay discusses a new interpretation of supernova data in terms of photon energy loss. Walther Nernst around 1930 found that the energy lost from a photon due to the cosmological redshift would be Hh (Hubble times Planck) each cycle, independent of wavelength. Nernst-MacMillan cosmology proposes recycling between energy and matter so that the universe is eternal and isotropic in time, timeless in the platonic sense.

Would you agree that present-day cosmology clashes with platonic metaphysics?

Best wishes,

Colin

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Author Aleksandar Mikovic replied on Mar. 13, 2015 @ 06:54 GMT
Dear Colin,

Time evolution can be incorporated in a platonic metaphysics by considering space-time trajectories, i.e. histories. As far as the idea of passing of time (change in time) is concerned, one can also incorporate it into a platonic metaphysics, which I discussed in my paper "Temporal Platonic Metaphysics", arxiv:0903.1800.

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John C Hodge wrote on Mar. 11, 2015 @ 19:57 GMT
I think the idea of science is that mankind can understand natural law.

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Lev Burov wrote on Mar. 12, 2015 @ 02:54 GMT
Dear Aleksandar,

In your overview you mention of materialism, "Although a logical possibility, one can argue that this scenario is highly implausible." However in our paper we provide an exact proof that chaosogenesis by anthropic principle is a logical impossibility based on discoverability and precision of the laws of nature. Perhaps you would find it interesting, as it supports your hypothesis.

http://fqxi.org/community/forum/topic/2353

Lev

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Sylvain Poirier wrote on Mar. 12, 2015 @ 14:24 GMT
Dear Aleksandar,

I have similar ideas to yours, that is a metaphysics combining a mathematical Platonism with a non-mathematical reality made of consciousness with the flow of time. I presented this in my essay, showing how it provides what I see as the most natural and coherent interpretation of quantum physics.

However I have a different view about the role of the Incompleteness theorem. First, I consider that we should not forget the completeness theorem of first-order logic that provides a strong case for mathematical Platonism. Second, I see the Incompleteness theorem as one manifestation among others of an intrinsic time of mathematical reality, but that does not affect the laws of physics of our universe, and is unrelated to our time.

Why do you say that "any TOE has to include the arithmetic" ? Euclidean geometry doesn't, and, as I explained in my essay, I see the laws of physics as avoiding the dependence towards the actual infinity of natural numbers with its undecidabilities.

You describe the second incompleteness theorem as "a consistent theory T cannot have a statement referring to the consistency of T". This is not what it says. What it says, is that any consistent theory able to express arithmetic and thus describe itself (if its axioms are algorithmically defined), will also be able to express its own consistency as a formula, but will be unable to prove the truth of this formula. See my exposition of the incompleteness theorem for more details.

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Author Aleksandar Mikovic wrote on Mar. 13, 2015 @ 07:23 GMT
Dear Sylvain,

Thank you for your comments. My idea of time in a platonic metaphysics is that it serves to distinguish between an abstract mathematical universe and a real one, i.e. a real universe is a mathematical universe in time.

By definition, a TOE has to be able to explain arithmetics, as well as geometry, so it must contain the axioms for arithmetics.

I agree with your formulation of the 2nd theorem. I wanted to say basically the same, but I have chosen a too short sentence.

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Peter Martin Punin wrote on Mar. 13, 2015 @ 17:15 GMT
Dear Dr Micovic,

Being myself a convinced Platonist convaincu, I read your essay several times and really with great pleasure.

I totally agree with you that anti-Platonistic approaches – materialist approaches and other – are as metaphysical as Platonism. In my own essay, I insist further on this point, since this latter does not seem obvious to everyone. Many people continue to...

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Author Aleksandar Mikovic replied on Mar. 14, 2015 @ 09:32 GMT
Dear Dr Punin,

I share completely your convictions about the platonic metaphysics, and after looking at your essay, I see that the basic motivation is the same as in my essay, i.e. to show that the platonic metaphysics is the best metaphysics for science and mathematics. My further motivation was to convince my physics colleauges that materialism is a belief, and that it does not follow from science. Since we can not experimentally, nor mathematically, confirm or refute a given metaphysics, then the only thing left is to compare different metaphysics and see which one is more plausible. My main idea was to use the definition and a meaning of a natural law in a given metaphysics, and to compare. In this respect, a platonic metaphysics only makes sense for me and the Godel theorems reinforce this belief.

The opponents of platonism use the problem of learning to reject it. However, I believe that only within platonism one can obtain a sensible epistemology, and my previous essay was an attempt to demonstrate that this is possible if the idea of time flow is introduced. Also the time-flow idea helps to distinguish between an abstract and a real universe. I will read the technical part of your essay, and let you know my opinion. And the Dantas essay, as well.

Best regards,

Aleksandar Mikovic

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Sylvain Poirier replied on Mar. 18, 2015 @ 07:51 GMT
In reply to : " Now arises the following question: Can a system Sy(inf) possessing an “infinity of appropriate axioms” be sheltered from GIT-undecidabilities? This question is in turn undecidable."

No it's not, except in a trivial way, which is that the assumption is ambiguous (admits several possibilities). Because there is not only one possible "infinity of appropriate axioms" :)

2 main cases can be considered. Any algorithmically definable set of axioms will still be subject to GIT-undecidabilities. In particular, we can consider algorithmic systems obtained by going up the hierarchy of stronger and stronger systems, each claiming the consistency of previous ones, up to any algorithmically definable ordinal, but this runs into troubles at undefinable ordinals. In fact, set theory already implicitly contains this procedure at a very high level corresponding to the whole hierarchy of ordinals that its model contains. On the other hand, we can abstractly accept as an axiomatic system the countable set of "all arithmetical truths", to which GIT-undecidabilities no more apply, because this axiomatic system is not algorithmically definable.

Maybe you meant : "the infinity of all axioms which are appropriate". The problem is that there is no mathematical definition for "appropriate", any more than for "the smallest uninteresting number". So this makes an undefined claim, which I do not see very meaningful. It seems Godel hoped that mathematicians would find more and more appropriate axioms that would potentially solve all problems. I think he was dreaming.

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Peter Martin Punin wrote on Mar. 16, 2015 @ 19:47 GMT
Dear Aleksandar

It is really rare to find such a point of agreement with another approach, knowing that in philosophy of science, there are for n people at least n + 1 opinions.

On the one hand, materialism is a metaphysical belief just like Platonism. On the other hand, the notion of “best metaphysics”, against misleading appearances and false evidence can be approached...

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Sylvain Poirier wrote on Mar. 17, 2015 @ 21:49 GMT
I just wrote explanations about the conflict of philosophies in this contest, especially the Platonist vs Anti-Platonist opposition, and a list of best essays I could find, especially so as to better help the Platonists find each other. Any comment ?

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Author Aleksandar Mikovic wrote on Mar. 20, 2015 @ 09:32 GMT
Dear Sylvain,

I liked your analysis of the essays, and I have the following comments:

- I would classify myself as a dualist: mind (consciousness) and matter exist independently in the platonic realm of ideas.

- I agree with the division into platonist and anti-platonists, but the relation with the interpretation of Quantum Mechanics is less clear. For example, within the dualism (both mind and matter exist independently) one can have various interpretations of QM: de-Broglie-Bohm interpretation, the many-worlds, collapse due to Quantum Gravity, etc.

- I agree that many of the highest rated essays have this status because of the popularity of the authors and also due to the philosophical convictions of the readers. But the greatest value of this contest is the exchange of the ideas.

Best regards,

Aleksandar

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Sylvain Poirier replied on Mar. 22, 2015 @ 09:51 GMT
Dear Aleksandar,

Did you study the interpretations problem carefully or do you just report vague rumors about it ? As I wrote in my report, it appears to me that the de-Broglie-Bohm interpretation is a purely materialistic interpretation, only supported by materialists, and motivated as a desperate attempt to save materialism in the face of its implausibility shown by quantum mechanics. I...

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Author Aleksandar Mikovic replied on Mar. 26, 2015 @ 13:16 GMT
Dear Sylvain,

I have studied the problem of measurement in QM quite thoroughly, and the standard approaches try to solve the problem without introducing the concept of consciousness. The reason is that consciousness is a complex and poorly understood concept, so that one tries to explain the measurement problem by using first only simpler concepts. It may happen that consciousness plays a role, but by the principle of Occam's razor, one first considers simpler explanations. Also I do not see why a measurement interpretation of QM which is not based on consciousness implies that consciousness does not exist or that it implies a materialistic metaphysics.

Best regards,

Aleksandar

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Jonathan Khanlian wrote on Mar. 27, 2015 @ 17:42 GMT
Hi Aleksander,

I obviously realize that physics could be viewed in a materialistic way, but I didn't realize there was a view that metaphysics could be materialistic? Is that the view that any theory of the physical world is encoded in physical neurons in someone's mind? In other words, would that mean that from this point of view, the an object in the material system (i.e. a brain made of material) was organizing its material neuron firings in such a way as to represent some notion about the material in the universe, of which it was a part of? I feel like this isn't what you meant, but this is the only thing I could imagine materialistic metaphysics to be.

If the universe is finite do you think a TOE is possible in theory? Can you think of a way that Godel's work might still apply if the universe were known to be of finite size at any given time?

I'd love to talk about Godel some more. And let's not forget Turing either! Please check out my Digital Physics essay if you get a chance.

Thanks,

Jon

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Author Aleksandar Mikovic replied on Mar. 29, 2015 @ 08:17 GMT
Dear Jon,

Yes, you understood it correctly, a materialistic metaphysics is what you described in your example of a human brain. However, the whole point of my essay was to demonstrate that a materialistic metaphysics is a very untenable metaphysics, because it implies that there are no laws in nature at the fundamental level. I also tried to argue that the only tenable metaphysics is a Platonic metaphysics, which includes both mathematical and non-mathematical ideas and the idea of passage of time.

The Godel theorems imply that a TOE does not exist, where TOE means a mathematical theory containing a finite number of equations and symbols, i.e. a theory which can be written on a finite piece of paper. This result does not depend on the size of the universe, so that even if the universe is finite in size, a TOE still does not exist. However, we do not need a TOE. It is sufficient to have an approximate TOE, i.e. a theory which describes a sufficiently large number of physical phenomena, and this is something which is possible.

Regards,

Aleksandar

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Joe Fisher wrote on Apr. 9, 2015 @ 15:45 GMT
Dear Aleksandar,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Luca Valeri wrote on Apr. 13, 2015 @ 23:00 GMT
Hi Aleksandar,

According the rating it seems the community does not like your platonic metaphysics.

I like the idea of a temporal platonic metaphysics. According to von Weizsäcker Platos philosophy contains two movements. The ascending from the cave to the sun, from the shadow to the light, from the phenomena to the invariant structures, eidos. From the subjective view to a objective one. This is a step most physicist do.

The second movement is the descending from the sun to cave. From eidos, the invariant structures to the phenomena. From timelessness to temporality, from possibility to factuality. This philosophy was never finished by Plato. And not finished by most physicist. As I understand your essay it is this you try to do with your temporal platonic physics.

In my essay I argue, that even a phenomenological description needs the eidos to be understandable. And that the time is a precondition for the possibility of physics, mathematics and even logic. If this is true, the time structure itself cannot be completely be described in precise concepts.

In my essay mathematics can be constructed as imagination of possible future acts. Insofar only a constructive math can be developed in that framework. And no incompleteness in the sense of Gödel appears. However I like to stress, that if we view the history of physics as a succession of closed theories a la Heisenberg, where the newer theory contains the older one as limiting case, one could argue that from the view of a TOE, whether it could be the limit of another closed theory and which are its own limit in the phenomena that it explains.

Best regards,

Luca

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Author Aleksandar Mikovic wrote on Apr. 15, 2015 @ 17:22 GMT
Dear Luca,

Thank you for your remarks, it is very helpful for me when I hear other people's views on platonism. I agree with you that platonic metaphysics has not evolved much from the original Plato's ideas, but the developements in modern theoretical physics have given a new impetus. My main inspiration was the Mathematical Universe paper by Max Tegmark. The MU was generalized in my first FQxXi essay, where I introduced the concepts of temporal change and the concept of non-finitary ideas, so that one obtains a more realistic metaphysics in the Platonic realm of ideas. In my second FQXi essay I wanted to argue that a platonic metaphysics is much more plausible than a materialistic metaphysics, and Godel's theorems play a fundamental role in that. Given that many of my colleauges are materialists, then my views are not that popular.

There are not many scientists or philosophers who tried to develop a platonic metaphysics. I am familiar with the attempts made by R. Penrose and M. Tegmark, although I heard that Godel himself had some kind of platonic metaphysics. I did not know that Weizsacker also was a platonist, so I will look into his work and the related works, including yours.

Best regards,

Aleksandar

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Luca Valeri replied on Apr. 15, 2015 @ 19:10 GMT
Hi Aleksandar

I would not call von Weizsäcker a platonist. But he surely knows Plato very good and thinks, that the main philosophical questions have already been posed in Platos work. In his book 'Time and Knowledge' he referenced Plato in more then 100 pages. Kant only 70.

My view (and this became much clearer to me in the discussions in the forum) is more that objective knowledge must be mathematical. In my essay I try to avoid discussions about ontology and reality as much as possible.

I hope you'll read my essay and leave a comment on it, although I had too little time to write it and develop a clear path of reasoning.

Best regards

Luca

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Alexey/Lev Burov wrote on Apr. 19, 2015 @ 13:49 GMT
Dear Aleksandar,

Apparently you somehow missed a comment of Lev above, so I am sort of repeating that. It is a pleasure to see that rare agreement as between yours and our essays. For instance you write, “if the natural laws are finite-duration random regularities, then the Earth can stop orbiting the Sun tomorrow, which means that our reality can disintegrate at anytime in the future.” A similar idea is expressed in our essay as a necessity of immediate disintegration in that case. I do not see any point of our contradiction with your ideas; however, I think that we have something which could be new and interesting for you. I rate your essay high and invite you in my blog to express your opinion and give us your rating as well.

All the best,

Alexey Burov

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Author Aleksandar Mikovic replied on Apr. 19, 2015 @ 20:26 GMT
Dear Alexey,

Thank you very much for warning me again about your essay, which I like and which is nicely written. I will post my comments on your essay blog and vote for it.

Best regards,

Aleksandar

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Alexey/Lev Burov replied on Apr. 20, 2015 @ 12:54 GMT
Dear Aleksandar,

Thank you for your very interesting comments and the high grade for our essay. However, something has gone wrong with your vote, and instead of a high rating, we’ve received from you a very low one, a 1. We’ve documented our ratings and vote counts before and after your vote, so this discrepancy is definitely the case. Perhaps the easiest way to correct it would be for you to contact administration, or if you want I can do that for you. For that you can send me an email to levburov@gmail.com, which I can then forward on with the request.

Kind Regards,

Lev

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Author Aleksandar Mikovic replied on Apr. 20, 2015 @ 18:34 GMT
Dear Lev,

I am sorry to hear this, but I am pretty sure that I gave you 8, since your rating

jumped for 0,1 point yesterday, after I had voted. One explanation is that somebody gave you a low score without making any comment.

Best regards,

Aleksandar

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