On 27 Jul 2011, at 15:36, benjayk wrote:

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Bruno Marchal wrote:On 24 Jul 2011, at 22:08, benjayk wrote:Yes. A tiny part of arithmetic is already sufficiently rich toimplement (in the original mathematical sense) very complexemulationbearing entities much powerfull than that tiny arithmeticalentities,and those can become lucid on the web of arithmetical dream, whichwill be, as seen from inside (the points of view), terriblycomplex,so that paradoxically, the whole of mathematics can only scratchthearithmetical 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,thenit 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 (xarithmetical formula, B_n being some other LĂ¶bian machine, forexample)My point is that this truth has little to do with arithmetic inparticular.

`Indeed, any first order specification of a universal system will do.`

`They are "ontologically" equivalent: with the combinators you have the`

`numbers, and with the numbers, you have the combinators. So`

`combinatoric truth and arithmetical truth, and Conway-game-of-life`

`truth are all the same truth, with different shape or implementations.`

Arithmetic just happens to be powerful enough to point towards it.All otheruniversal systems accomplish the same. So to say just numberrelations existand all else is an "epistemological view" on that is a very narrow interpretation.

`Arithmetical truth contains fortranic truth, lispic truth,`

`combinatoric truth, etc.`

`It does not contains theological truth, nor physical truth, except in`

`the 'epistemological' points of view of the creature they have all.`

`So, arithmetic is made into a theory of everything, and arithmetical`

`truth does play the role of the big unameable things. If you take`

`fortran programs as ontology, exactly the same can be said. Once you`

`search a theory of everything, comp does confuse truth and`

`arithmetical truth, or Truth and fortranic truth, etc. When number`

`relation exist, all other universal system exist in a similar`

`ontological sense. In arithmetical truth the fortranic truth is`

`automatically given, you don't need to introduce points of view,`

`unlike the analytical and the physical, for which you need the`

`epistemology (to interview the fortran program or the numbers).`

Bruno

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