One can't say that physics is axiomatic without having an elementary set of laws or rules that serve as axioms. Makes me think that physics isn't axiomatic but parts of it like QFT or ED are. It's like a collection of separate axiomatic domains which may or may not be unifiable.
Is physics axiomatic? I say yes, but we don’t get to choose the axioms. Nature, through experiment, does that for us.
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That elementary set of laws or rules that we take at face value I would call "physical axioms", if I may coin such a term. They are inductive observations which we take as true in order to make deductions therefrom. Determining these "physical axioms" is done through observation.
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Nature reveals its axioms through experiment, but it can't choose them. The natural question remains: why these axioms and not other ones?
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I agree that’s a relevant and deep question.. I think that’s a question, while extremely important, we’re not currently in the position to answer in any meaningful sense
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Ooooooh. Hot take. Maybe I disagree. From what Nature shows us, we can only inductively conclude the axioms. Then again, any axiom is just a sort self-evidently true, unobjectionable statement. In that case, we don't really need Nature to tell us much. What a think piece
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I suppose I just meant that any theory we could possibly come up with must rest upon assumptions (axioms) which are physically motivated, and there is no way to determine these a priori. We can only use facilitate this choice.
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What about things like Haag's Theorem?
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I think that whether real axioms for the actual universe exist is an open question. A given theory has axioms. The world has behavior, which *seems* to exhibit strong consistencies. That's about as much as we can say.
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Humans are still the one choosing the axioms because we are the one interpreting the result of the experiment. Axioms are just propositions, unassailable by a truth assignment. Humans make propositions, not nature.
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