David Johnston

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Infra-Bayesian physicalism: a formal theory of naturalized induction

Γ=Σ^R, it's a function from programs to what result they output. It can be thought of as a computational universe, for it specifies what all the functions do.

Should this say "elements are function... They can be thought of as...?"

Can you make a similar theory/special case with probability theory, or do you really need infra-bayesianism? If the second, is there a simple explanation of where probability theory fails?

Counterexamples to some ELK proposals

Do you run into a distinction between benign and malign tampering at any point? For example, if humans can never tell the difference between the tampered and non-tampered result, and their own sanity has not been compromised, it is not obvious to me that the tampered result is worse than the non-tampered result.

It might be easier to avoid compromising human sanity + use hold-out sensors than to solve ELK in general (though maybe not? I haven't thought about it much).

Generalizing Koopman-Pitman-Darmois

I'm a bit curious about what job "dimension" is doing here. Given that I can map an arbitrary vector in  to some point in  via a bijective measurable map (https://en.wikipedia.org/wiki/Standard_Borel_space#Kuratowski's_theorem), it would seem that the KPD theorem is false. Is there some other notion of "sufficient statistic complexity" hiding behind the idea of dimensionality, or am I missing something?