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)




Arithmetics just is able
to point to what is beyond it,

You mean PA? OK. That is just a LUM, or Plotinus man.



so from this perspective you can call it
arithmetical truth.

The LUM itself cannot. The LUM will call it God (and get rather miserable for that blasphem).



But you could call it german truth as well, because
german can be used to do this as well (obviously, because it can state
everything arithmetic can).

Err.. Yes, but computationalism makes it reciprocal.

Bruno


http://iridia.ulb.ac.be/~marchal/



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