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> finitely axiomatized formal system I said “description.” You’re adding additional constraints that may or may not be warranted.

by egdod 7y ago

lidHanteyk 7y ago
I'm merely helping you catch up on the past century of improvements in logic. What would your description consist of, if not a finite listing of axioms? I bet that you'll complain if my description includes a susbystem for arithmetic, in accordance with Gödel's Incompleteness.
- egdod 7y ago
  Why would a description of physics necessarily include a formal system or arithmetic?
  - lidHanteyk 7y ago
    It necessarily includes a formal system. That much has been hammered into the ground already, and you'll discover it for yourself as soon as you attempt to formalize your description. All existing attempts to describe physics have encountered some sort of incompleteness. Newtonian physics yields ordinary differential equations, which can encode Turing-complete problems. [0][1] Quantum mechanics yields Hamiltonian operators, which can encode Turing-complete problems too. [2][3] Both of these paradigms predate Turing's work; physics was Turing-complete a long time before you came along to look at the problem. I can empathize with your original point: Surely reality exists! It seems so real! But reality can be real without existing. Ultimately, our models are only hypotheses about reality, and what they have shown us here is that even our models are so complex as to admit problems that are not going to be solved by mere assertion of existence. [0] https://link.springer.com/chapter/10.1007%2F11494645_21 https://link.springer.com/chapter/10.1007%2F11494645_21 [1] https://sapientia.ualg.pt/bitstream/10400.1/1008/1/05-GCB-stable.pdf https://sapientia.ualg.pt/bitstream/10400.1/1008/1/05-GCB-st... [2] https://www.nature.com/articles/nature16059 https://www.nature.com/articles/nature16059 [3] https://eprints.ucm.es/38062/1/spectral-gap_supplementary.pdf https://eprints.ucm.es/38062/1/spectral-gap_supplementary.pd...
    - egdod 7y ago
      > It necessarily includes a formal system. That much has been hammered into the ground already, and you'll discover it for yourself as soon as you attempt to formalize your description. That’s a bald assertion, not an answer. And one can certainly imagine descriptions of physics that don’t require a formal system. Here’s one: “every particle remains at rest for all t.” Now, that doesn’t describe our universe very well. But it might be a perfectly good description of a single-electron universe. There’s no a priori reason to assume that a valid description of physics is axiomatizable in a formal system. Aruguments to the contrary are necessarily based on our own ignorance, not on anything fundamental.
      - lidHanteyk 7y ago
        Sorry, but what is a particle?

> finitely axiomatized formal system I said “description.” You’re adding additional constraints that may or may not be warranted.

by egdod 7y ago

> finitely axiomatized formal system I said “description.” You’re adding additional constraints that may or may not be warranted.

lidHanteyk 7y ago

I'm merely helping you catch up on the past century of improvements in logic. What would your description consist of, if not a finite listing of axioms? I bet that you'll complain if my description includes a susbystem for arithmetic, in accordance with Gödel's Incompleteness.

egdod 7y ago
Why would a description of physics necessarily include a formal system or arithmetic?
- lidHanteyk 7y ago
  It necessarily includes a formal system. That much has been hammered into the ground already, and you'll discover it for yourself as soon as you attempt to formalize your description. All existing attempts to describe physics have encountered some sort of incompleteness. Newtonian physics yields ordinary differential equations, which can encode Turing-complete problems. [0][1] Quantum mechanics yields Hamiltonian operators, which can encode Turing-complete problems too. [2][3] Both of these paradigms predate Turing's work; physics was Turing-complete a long time before you came along to look at the problem. I can empathize with your original point: Surely reality exists! It seems so real! But reality can be real without existing. Ultimately, our models are only hypotheses about reality, and what they have shown us here is that even our models are so complex as to admit problems that are not going to be solved by mere assertion of existence. [0] https://link.springer.com/chapter/10.1007%2F11494645_21 https://link.springer.com/chapter/10.1007%2F11494645_21 [1] https://sapientia.ualg.pt/bitstream/10400.1/1008/1/05-GCB-stable.pdf https://sapientia.ualg.pt/bitstream/10400.1/1008/1/05-GCB-st... [2] https://www.nature.com/articles/nature16059 https://www.nature.com/articles/nature16059 [3] https://eprints.ucm.es/38062/1/spectral-gap_supplementary.pdf https://eprints.ucm.es/38062/1/spectral-gap_supplementary.pd...
  - egdod 7y ago
    > It necessarily includes a formal system. That much has been hammered into the ground already, and you'll discover it for yourself as soon as you attempt to formalize your description. That’s a bald assertion, not an answer. And one can certainly imagine descriptions of physics that don’t require a formal system. Here’s one: “every particle remains at rest for all t.” Now, that doesn’t describe our universe very well. But it might be a perfectly good description of a single-electron universe. There’s no a priori reason to assume that a valid description of physics is axiomatizable in a formal system. Aruguments to the contrary are necessarily based on our own ignorance, not on anything fundamental.
    - lidHanteyk 7y ago
      Sorry, but what is a particle?