Arithmetic potentialism and the universal algorithm

[Philip Thrift]

Via https://twitter.com/JDHamkins/status/1272615229403398144 :



Joel David Hamkins, “Arithmetic potentialism and the universal algorithm,” arxiv: 1801.04599, available at http://jdh.hamkins.org/arithmetic-potentialism-and-the-universal-algorithm

"Please feel free to skip over the more technical parts of this paper. In the seminar discussion, we shall concentrate on the basic idea of arithmetic potentialism, including a full account of the universal algorithm and the significance of it for potentialism, as well as remarks of the final section of the paper."

@philipthrift

[Bruno Marchal]

> On 15 Jun 2020, at 22:09, Philip Thrift <cloud...@gmail.com> wrote:
>
> Via https://twitter.com/JDHamkins/status/1272615229403398144 :
>
>
>
> Joel David Hamkins, “Arithmetic potentialism and the universal algorithm,” arxiv: 1801.04599, available at http://jdh.hamkins.org/arithmetic-potentialism-and-the-universal-algorithm
>

> "Please feel free to skip over the more technical parts of this paper. In the seminar discussion, we shall concentrate on the basic idea of arithmetic potentialism, including a full account of the universal algorithm and the significance of it for potentialism, as well as remarks of the final section of the paper.”

This is interesting, and some of this can be related to mechanism. To be sure, the “universal algorithm” is not related to the universal dovetailer and is not an algorithm in the CT sense. It is Woodin proof that all sequence (not just the computable) can be generated in some model of PA. The universal dovetailer, on the contrary, is the same in all models of PA.

What is weird, is that some of the modal logics found by Hamkins (S5 and S4.2) through his “arithmetical potentialism” are the one I was going for to extract the Minkowski space from the UD. It might be a coincidence, though, as his potentialism might require a strong non-mechanist axioms to make sense. If Nature violate the three modal logics S4Grz1, X1* and Z1*, I will have to look more closely to this, as it might suggest some non mechanist theory of mind.

Bruno



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