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awarded  Necromancer
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comment What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?
You haven't answered the question, just provided more unfounded assertions ... On what basis are idealizations to be judged acceptable, or not? Exact theories tend to be the domain of metaphysics only, and physics meaning nature, rarely works that way .. nevertheless nothing in logic, at least, says an axiomatic system must be constrained like this. The argument a computing machine is 'unphysical' addresses nothing since most 'physical laws' are abstract metaphysical descriptions of how we believe nature to be, subject to correction given observation. The world differs from its description!
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revised Extremal black hole with no angular momentum and no electric charge
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revised Solid objects inside the event horizon - can they remain “solid”?
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revised Extremal black hole with no angular momentum and no electric charge
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revised Extremal black hole with no angular momentum and no electric charge
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awarded  Student
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comment What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?
All mathematical descriptions of physical systems are also idealisations so - unphysical. How are mathematical descriptions of physical systems so different from idealisations of computing machines? It seems arbitrary to accept one and reject the other .... With respect to axioms being inadequate, I've already addressed that with the apple illustration. Probable behaviour conforming to ideal behaviour is sufficient epistemological grounds for asserting axiomatic ontologies. Newton's gravity, it turns out, is inadequate given relativity, yet we didn't, and haven't discarded it have we?
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comment What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?
Peter Selinger's work 'Generators and relations for n-qubit Clifford operators' is classified as 'Quantum Physics', so is it really true Physics doesn't use generators and relations? Also, isn't Anton Zeilinger's claim that “quantum randomness is irreducible and a manifestation of mathematical undecidability” suggested by his experiment given appropriate coding, “whenever a mathematical proposition is undecidable within the axioms encoded in the state, the measurement associated with the proposition gives random outcomes.”? It's not clear your claims above are true if others disagree.
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revised Extremal black hole with no angular momentum and no electric charge
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revised Extremal black hole with no angular momentum and no electric charge
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answered Extremal black hole with no angular momentum and no electric charge
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answered Is the universe finite or infinite?
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revised How can something happen when time does not exist?
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revised How can something happen when time does not exist?
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answered How can something happen when time does not exist?
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revised Could there be more universes?
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comment Can we construct Axiomatic system of physical laws?
It's not clear what you mean by 'an axiom is not a function'. Also we're not talking specifically about QM but about the axiomatic system that underpins it. QM must presuppose certain things to be able to work, and it is 'those certain things' that show up in its axioms. Axioms can be derived (i.e. also conclusions) but axioms are not only the axioms of logic. They are specific to the formal system being used. Mathematics has axioms (i.e. 1+0=1 is always true, you can't divide by 0, etc). The axioms of physics are nearly always mathematical, nearly always equations (F=MA). What is 'PM'?
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comment Does Gödel preclude a workable ToE?
Ill add, that he was really only using Peano's proofs for their structure. From Peano's proof he constructed 'proposition axioms' by removing Peano's specific fundamental properties of natural numbers and inserting arbitrary formula which represented them (p,q, and r). [He even says this in his paper, though its in German] So this is showing how he moved from specific arithmetic example to general case, meaning first order logic. He could do this because everything expressible in arithmetic is expressible in logic (or geometry, set theory, lattices, etc)