So far I never mentioned how I understand
the famous Löwenheim-Skolem result (*):
"no matter how fancy your axiomatic system, which seems to talk about real numbers, complex numbers, geometries, fields etc.,
in the end, all it really does is talk about the countable natural numbers, nothing more and nothing less."
In my opinion it is the most shocking result of the Grundlagenstreit.
But does this tell us something about the true nature of physical reality?
(*) and let me be very clear that I am a layman who read exactly one book about number theory (and I understood perhaps half of it).