On 01/02/11 20:07, Bruno Marchal wrote:
In step 8 you state that 'a “physical universe” really “exists” and is too little in the sense of not being able to generate the entire UD*, nor any reasonable portions of it,'. However, if we adopt Tipler's Omega point scenario, we get infinite computational power as the universe collapses into the big crunch. Tipler specifically states that all possible computations will be carried out in such a scenario, including all possible experiential realities.

Any UD does that, indeed. No need of physical omega point. arithmetic gives you alpha points for any alpha constructive ordinal, and even quasi names for above the constructive ordinals. Machine's theologies are rich. If the rational Mandelbrot is Turing universal (Sigma_1 complete) then it represents already an Omega points.

Yes, but your point in step 8 is that a physical universe is *too little*, but with omega point it is not too little, it is as rich as arithmetically possible.

Yes, 'If the rational Mandelbrot is Turing universal (Sigma_1 complete) then it represents already an Omega points.', but, also, Omega point represents already the Turing universal rational Mandelbrot. Neither is necessarily richer than or prior to the other.

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