On Thursday, February 28, 2019 at 10:54:28 AM UTC-6, Bruno Marchal wrote:
>
>
> On 27 Feb 2019, at 19:18, Philip Thrift <cloud...@gmail.com <javascript:>> 
> wrote:
>
>
>
> On Wednesday, February 27, 2019 at 11:25:06 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 26 Feb 2019, at 19:41, Philip Thrift <cloud...@gmail.com> wrote:
>>
>>
>>
>> There is another approach vs. the JD Hamkins / set theory & mathematical 
>> logic (math dept.) approach. the one of Martin Escardo / type & programming 
>> language theory (computer science dept.).
>>
>> Martin Escardo
>> http://www.cs.bham.ac.uk/~mhe/
>>
>> *higher-type computation = *
>>
>> *sets that can be exhaustively searched by an algorithm, in the sense of 
>> Turing, in finite time, as those that are topologically compact*
>>
>>
>> ?
>>
>> If it is an algorithm in the sense of Turing, and if the search is 
>> required to be finite, then the set is finite.
>>
>
>
>
> In any case, there is programming he has written
>
> M.H. Escardo. *Infinite sets that admit fast exhaustive search*. 
>
>
> In that sense, there is no problem. The universal dovetailer exhaust all 
> computations with all oracles in that sense.
>
>
>
>
> In LICS'2007, IEEE, pages 443-452, Poland, Wroclaw, July.
>
> pdf <https://www.cs.bham.ac.uk/~mhe/papers/exhaustive.pdf> (paper), hs 
> <https://www.cs.bham.ac.uk/~mhe/papers/exhaustive.hs> (companion Haskell 
> program extracted from the paper
>
> from   https://www.cs.bham.ac.uk/~mhe/papers/
>
>
> One could say: *There is nothing outside the code.*
>
> (The program stands on its own.)
>
>
>
>
> Programs can’t do that when becoming inputs to universal programs. You 
> can’t escape truth so easily, even if you can’t define it. All Gödel-Löbian 
> machines know that. There is definitely something outside the code, if 
> there is a code. And that is the many universal codes which gives the 
> behaviour and the experience to the person attached to their infinitely 
> many codes in arithmetic. But the laws of physics must be derived from 
> this, and by using the self-reference logics of Gödel-Löb-Solovay (G*), we 
> get the qualia as supplementary gifts, in the form of immediate “volume” 
> type of truth that we cannot prove, nor define, yet indubitably known.
>
> Bruno
>


We have only scratched the surface of the subject of *Semantic*s (of code) 
in PLT.

*PLT: A path to enlightenment in Programming Language Theory*
https://steshaw.org/plt/

- pt 


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