[FOM] Is mathematical realism compatible with classical reasoning?

W.Taylor at math.canterbury.ac.nz W.Taylor at math.canterbury.ac.nz
Tue Aug 1 23:38:28 EDT 2017

Quoting Patrik Eklund <peklund at cs.umu.se>:

> Years after 1931,
> Church said something substantial,
> Post said something substantial, also in dialogue with Church,
> young Turing said something substantial, under the supervision of Church,
> older Kleene said something substantial, and took the role of
> formulating a thesis.

I take it you mean that each of them proved that another trial formulation
was equivalent to the previous ones.  Yes, that is substantial, and OC
philosophically satisfying.

> However, that thesis isn't substantially substantial.

I read this to mean that yes, the thesis is merely a definition of
computability, that is "justified" by the previous substantial theorems.

And OC there were other formulations after CT was declared, proved equivalent,
which also helped in this "justification".

Have I read you right?

If so, it would seem that any substance to the thesis, beyond mere definition,
is a mainly psychological/cultural substance.  It seems to say...

"Almost all mathematicians think this is a good definition,
and we expect that this will continue to hold in the foreseeable future".

If I have misunderstood your PoV please correct me.

If I have got you substantially accurately, then I am at a loss to  
comprehend -

>>> The Church-Post-Turing-Kleene thesis remains unsolved...

- from your earlier post.

Bill Taylor

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