FOM: Church's Thesis

Joe Shipman shipman at
Fri Sep 17 10:55:45 EDT 1999

>The same difficulty you're encountering with a single bit is a
>(in spades) with a sequence of bits.  The class of noncomputable
>sequences is stable under recursive (or must we all now say
>permutations.  Supposing that Church's thesis had failed, yielding a
>noncomputable sequence, nothing in this scenario prevents an adversary
>stepping in unbeknownst to you and recursively permuting its bits.
>Putting it another way, the sequence may be mathematically definable
>but it doesn't follow that you know the definition.

My point was that if we could KNOW that Church's Thesis is false, it
would be in the context of some mathematized physical theory within
which one could derive an experimental procedure for calculating a
noncomputable sequence; and the sequence would be definable within this
mathematized theory and presumably within ZFC.

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