On Sunday, September 1, 2019 at 8:57:19 AM UTC-5, Bruno Marchal wrote:
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> On 1 Sep 2019, at 13:57, Philip Thrift <[email protected] <javascript:>>
> wrote:
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> Even if mathematical physics only ranges over a subset of mathematics
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> https://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation
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> mathematics by itself can range over all mathematical-fictional worlds, it
> is still (so far, until AIs take their place) only human brains that have
> fabricated those worlds (in writing!).
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> Physics does not range on a subset of mathematics. It is not a
> mathematical structure among all the others. With mechanism, the physical
> reality emerges from the whole arithmetical reality, in way enforced from
> the mechanist hypothesis, making it testable (and verified up to now thanks
> to QM without collapse).
>
> Here is an image. You can imagine the entire mathematical reality by the
> volume of an infinite sphere. The physical reality is the border of that
> sphere, its surface, as seen from inside the sphere. That surface does not
> exist (as the shore is supposed to be infinite), but it is still apparent.
>
> That is only an image, but it can been made more precise once you
> understand well the first person indeterminacy. The mind is more like "all
> computations", and the physical reality is given by a *first person*
> statistic on the leaves of all (halting) computations.
>
> The goal is too explain as many things as possible, and thus assuming as
> less as possible. As I tend to believe in the existence of my
> laptop-computer, I am obliged to believe in at least one universal system.
> We cannot prove the existence of a universal system without assuming one. I
> use arithmetic because it is the simplest one. Then, with mechanism, I can
> explain why we cannot assume more than a universal system. It leads to a
> contradiction, (or redundancy).
>
> It is not just that elementary arithmetic explains where the beliefs in
> real number, analysis and physics come from, it is that with mechanism,
> there is no other explanation available, and it determines the entire
> physical realm, so we can test mechanism by comparing it to the physical
> data and current theories.
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> Bruno
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The dialectics of a language* and matter occurs only in these possibilities:
• natural objects (its internal natural language)
• human brains (creating fictions)
• human-made devices
* The *language of arithmetic* consists of
• A 0-ary function symbol (i.e. a constant) 0,
• A unary function symbol S,
• Two binary function symbols +, ·,
• Two binary relation symbols =, <,
• For each n, infinitely many n-ary predicate symbols {X^i}_n
- https://www.sas.upenn.edu/~htowsner/prooftheory/PeanoArithmetic.pdf
@philipthrift
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