FOM: Various Church-Turing theses

[Arnon Avron]

> As far as CT-psych (intuitive computability) is concerned, I think the 
> identification of total recursive functions with intuitively computable 
> functions is more secure than the identification of partial recursive 
> functions with intuitively enumerable sets (or one-sided computable 
> functions).  The prescription "simultaneously for all N search for proofs 
> that the Nth Turing machine computation does not halt, extending your 
> mathematical axioms beyond ZFC using appropriate mathematical methods, and 
> outputting those N where a proof is found", while vague, could provide a 
> counterexample.

Why are you sure that this counterexample (or "counterexample" - I dont
want to make a judgment) is PARTIAL?

Arnon Avron
School of Computer Science
Tel-Aviv University