I’d say that the only way to persuade someone using epistomology A of epistomology B is to show that A endorses B. Humans have a natural epistemology that can be idealized as a Bayesian prior of hypotheses being more or less plausible interacting with worldly observations. “The world runs on math.” starts out with some plausibility, and then quickly drowns out its alternatives given the right evidence. Getting to Solomonoff Induction is then just a matter of ruling out the alternatives, like a variant of Occam’s razor which counts postulated entities. (That one is ruled out because is forbids postulating galaxies made of billions of stars.)
In the end, our posterior is still human-specializing-to-math-specializing-to-Solomonoff. If we find some way to interact with uncomputable entities, we will modify Solomonoff to not need to run on Turing machines. If we find that Archangel Uriel ported the universe to a more stable substrate than divine essence in 500 BC, we will continue to function with only slight existential distress.
I’d say that the only way to persuade someone using epistomology A of epistomology B is to show that A endorses B. Humans have a natural epistemology that can be idealized as a Bayesian prior of hypotheses being more or less plausible interacting with worldly observations. “The world runs on math.” starts out with some plausibility, and then quickly drowns out its alternatives given the right evidence. Getting to Solomonoff Induction is then just a matter of ruling out the alternatives, like a variant of Occam’s razor which counts postulated entities. (That one is ruled out because is forbids postulating galaxies made of billions of stars.)
In the end, our posterior is still human-specializing-to-math-specializing-to-Solomonoff. If we find some way to interact with uncomputable entities, we will modify Solomonoff to not need to run on Turing machines. If we find that Archangel Uriel ported the universe to a more stable substrate than divine essence in 500 BC, we will continue to function with only slight existential distress.