Bruno Marchal wrote:
> On 24 Jul 2011, at 22:08, benjayk wrote:
>>> Yes. A tiny part of arithmetic is already sufficiently rich to
>>> implement (in the original mathematical sense) very complex emulation
>>> bearing entities much powerfull than that tiny arithmetical entities,
>>> and those can become lucid on the web of arithmetical dream, which
>>> will be, as seen from inside (the points of view), terribly complex,
>>> so that paradoxically, the whole of mathematics can only scratch the
>>> arithmetical truth. Analytical truth and physical truth are
>>> simplification of the arithmetical truth by arithmetical creatures.
>> I think you confuse arithmetical truth with TRUTH.
> That is a consequence of comp. If "we" are machine at some level, then  
> it is absolutely undecidable if there is anything more than  
> arithmetical truth.
> The analytical truth and the physical truth and the theological truth  
> can be seen as internal "epistemological views". In arithmetic there  
> are defined by Bp, or variants, or by by scheme B_n x & x (x  
> arithmetical formula, B_n being some other Löbian machine, for example)
My point is that this truth has little to do with arithmetic in particular.
Arithmetic just happens to be powerful enough to point towards it. All other
universal systems accomplish the same. So to say just number relations exist
and all else is an "epistemological view" on that is a very narrow
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