[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  

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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