[FOM] extramathematical notions and the CH (corrected version)
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Mon Feb 4 04:47:00 EST 2013
Quoting joeshipman at aol.com:
> And it is not so implausible that a number defined in a physical
> theory and experimentally measurable could be non-computable. For
> example, some versions of quantum gravity involve summing amplitudes
> or probabilities over spacetime topologies represented as
> homeomorphism classes of 4-dimensional manifolds, which we know are
> not recursively classifiable so the theory does not come with an
> algorithm for predicting the result.
There's an interesting possibility, that there could be a physical
constant C such that we could prove (modulo physical theorising)
using, say, CH, that some algorithm provides an approximation of C,
but not without CH. It is a natural line of thought that physical
theories should be "robust" in the sense of not depending on whether
we do our (experimentally relevant) calculations in L or not, for
instance, but it seems difficult to articulate this idea with any
precision.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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