Friday, April 8, 2016

mathematics - What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?


I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly.


Hilbert's sixth problem consisted roughly about finding axioms for physics (and it was proposed in $1900$). I guess that at the time, such thing was impossible due to the nature of physics which is mainly based on observations and models. But it seems that after Gödel's work on $1931$, the axioms which were seen as self-evident truths started to be seen as unprovable statements and the job of a mathematician is grossly about deriving theorems from these axioms.


So if this shift of axiomatic conception really happened, couldn't we just accept anything (including the physical observations) as axioms and reason about their consequences? Thus somehow solving Hilbert's sixth problem?




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