0, + and * => Physical laws ?


Stephen’s question:

Could you give us a sketch of exactly how ‘physical rules’ or the appearance thereof are the “consequences of 0, + and *”? I think that there is more to the explanation than the fact that 0, + and * exist…. This is the part of your work that I still do not understand.

Bruno’s answer

Well, it is the second part. the one I call AUDA.

In a sketch.

1) define provable-by-machine-PA in the arithmetical language {0, s,  +, *, “E”, “A”, etc.}. Like in Gödel 1931. This gives Bp (for  beweisbar <some arithmetical proposition>. This will play the role of  the “scientific rational opinion of the machine”.

2) Solovay: the truth about the logic of Bp is given by G*. The  provable part of it is given by G.

3) define the knowledge of the machine by Bp & p. (Theatetus) The  logic of Bp & p is given by S4Grz (a logic of a form of intuitionist evolving antisymmetrical knowledge.

4) define observable by Bp & Dt  (logic Z and Z*-

5) define feel-able by Bp & Dt & p (logic X and X*)

Note that the splitting proof/truth (G/G*) extends to Bp & Dt, and to Bp & Dt & p; that is the observable and the feel-able.

Then (eneter the arithmetical UD): restrict the arithmetical realization of the sentence letters p to the sigma_1 sentence. You get the logic Z1* (quanta and qualia). the quanta appears in the non communicable part, and are particular case of qualia, and this assure our coherence: we share histories (this is what Everett confirms the most: we are collectively multiplied by huge factor, and symmetry and linearity appears at the arithmetical quantum bottom.

If comp is correct, and if the Theatetus’s idea is correct, Z1* gives the probability one, and you can deduce the other probabilities from there (von Neumann old criteria for a genuine quantum logic).

I hope I was not too sketchy. Use this to dig on the second part (the interview of the LUM, it is AUDA) of the sane04 paper.

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