[FOM] Is mathematical realism compatible with classical reasoning?

Patrik Eklund peklund at cs.umu.se
Sat Jul 29 00:54:56 EDT 2017

Hi Bill,

Recursion was driven into a form where the founder of that "final form", 
widely accepted today, first didn't believe it was the final form. What 
was his justification really to do that?

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 
older Kleene said something substantial, and took the role of 
formulating a thesis.

However, that thesis isn't substantially substantial.

How many of us have really deeply dissected papers from that time? Or do 
we actually mostly believe in papers and books written decades after to 
be the de facto truth and ultimate substantiality about that thesis and 
what caused it? Church's control over his journal is an important 
ingredient in that cooking.

Did anyone ever take just a few lines from those original papers, and 
question their justification, or would it be considered foundational 
heresy to do so?

If we would try out some of those paths, we may want to ignore words 
like "computation" and "computers" for a while, but we may not want to 
overlook "types".

A century ago, Hilbert brought Bernays to Göttingen, and the rest is 
history of foundations as it has been written, but it may not be the 
foundations as it actually is, substantially.

"Wir mussen wissen! Wir werden wissen!" To me, the formulation of that 
Thesis is nothing but Ignorabimus.



On 2017-07-28 07:17, W.Taylor at math.canterbury.ac.nz wrote:
> Quoting Patrik Eklund <peklund at cs.umu.se>:
>>  The Church-Post-Turing-Kleene thesis remains
>> unsolved basically because they don't share a common metalanguage.
> I'm not sure I follow this, but is it in any way related to the common
> disagreement as to whether -
> a:   Church-Post-Turing-Kleene says something substantive;
>   OR
> b:   it is merely a definition of what is meant by "computable".   ?
> - Bill Taylor
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