[FOM] Counterfactuals in relative computability theory

[Richard Heck]

On 08/14/2016 05:37 PM, Timothy Y. Chow wrote:
>
> If you ask people to imagine how the Church-Turing thesis could be
> false, you'll typically elicit hypothetical scenarios in which some
> algorithm is presented to the mathematical community and the community
> agrees that it meets their tacit criteria for being an algorithm, yet
> the algorithm computes a non-recursive function.  A natural way to
> phrase this situation in terms of possible worlds is to postulate a
> possible world in which there are two distinct mathematically precise
> abstract objects, one of which the community calls an "algorithm" and
> the other of which the community calls a "recursive function."  

We don't need to imagine this. We already did it, as Colin pointed out.
Our forebearers decided to call one of these classes the "recursive"
functions, and another one the "primitive recursive" functions. And they
did this without disagreeing about which plausibly corresponds to the
computable functions.

Richard