> On 2 Jun 2019, at 20:45, 'Brent Meeker' via Everything List 
> <[email protected]> wrote:
> 
> 
> 
> On 6/2/2019 2:53 AM, Bruno Marchal wrote:
>> 
>> Assuming there is an ontological world, which is precisely what I have never 
>> found any evidence for.
> 
> You refer to ontological existence and phenomenological existence all the 
> time.

Oops sorry. I meant “assuming an ontological *physical* world".

With mechanism: the ontological existence is given by the use of the 
existential quantification rule in the first order logic applied to the base 
(and weak) Turing-complete used (very elementary arithmetic like RA, or the SK 
theory extended in a first order theory, etc.).

The phenomenological existences are given by the modal first-order “extension" 
of Solovay theorem. I put “extension” in quote, because the first order modal 
extension, unlike their proposition variant, are not axiomatisable. qG is 
PI_2-complete, qG* is PI_1 complete in the Oracle of the Arithmetical Truth. 
(Yes, the arithmetical Noùs is far more powerful than God itself!).

Bruno





> 
> Brent
> 
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