- #36
nikkkom
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friend said:If you assert that everything mathematical is physical, then you run up against Godel's Incompleteness theorem, and physics becomes incomplete or inconsistent.
What does it even mean for *physics* to be "incomplete", and why it's bad?
As to *math*, Godel's Incompleteness theorem basically says that no (consistent) system of axioms can be non-extendable: for any system of axioms, there will be true, but unprovable statements. Take one of such statements, add it to your axioms, and you have an extended system of axioms. And still, there will be true, but unprovable statements for it too. Rinse, repeat.
Yes, this is a bit of unexpected / counter-intuitive fact (it's more comforting to think that "ultimate full set of axioms of math", sufficient to prove all theorems, exists), but it's not illogical.