Godel\'s Incompleteness Theorems and Platonic Metaphysics by Aleksandar Mikovic

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 ?

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.

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 do not see there any trace of a fundamental realm of consciousness, and even if Bohm himself seemed to mention such an idea, the logical connection between the idea of consciousness and the effective content of his interpretation is actually non-existent as far as I could see (his hidden variables may be called an "implicate order" but this does not mean any form of consciousness).

The Many-worlds interpretation does not recognize consciousness as fundamental either ; it only develops a relativity of viewpoints, in a development that claims to be equally applicable to any sophisticated physical system (with memory) in guise of observer. Or did you see anyone presenting it otherwise ? I admit that Mikhail Borisovich Menskij has a view combining the many-worlds with a fundamental role of consciousness, however I do not consider his view very philosophically coherent and I don't think many other scientists are ever likely to follow it.

I know that the "collapse due to Quantum Gravity" came famous as proposed by Penrose but I do not see it very clear either, since as far as I know it remains quite vague without any precise conception of this quantum gravity. If the collapse comes from quantum gravity then it has concretely nothing to do with consciousness, and while I did not look at his ideas in details, I would be surprised if he could effectively justify the claim of a connection between quantum gravity and consciousness. Could he ? Already as I mentioned there, even the magnitudes of quantities do not seem to fit (perceptions by consciousness involve too light physical processes for quantum gravity to be involved).

On the other hand, I think my specific presentation of the mind makes collapse interpretation makes things much more coherent, in themselves and with the proper meaning of the idea of consciousness as fundamental. So I look forward for your more detailed review of this issue.

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

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

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

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

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