I should note, I don’t know how to argue persuasively for faith in solomonoff induction (especially as a model of the shape of the multiverse). It’s sort of at the root of our epistemology. We believe it because we have to ground truth on something, and it seems to work better than anything else.
I can only hope someone will be able to take this argument and formalise it more thoroughly in the same way that hofstadter’s superrationality has been lifted up into FDT and stuff (does MIRI’s family of decision theories have a name? Is it “LDTs”? I’ve been wanting to call them “reflective decision theories” (because they reflect each other, and they reflect upon themselves) but that seemed to be already in use. (Though, maybe we shouldn’t let that stop us!))
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 should note, I don’t know how to argue persuasively for faith in solomonoff induction (especially as a model of the shape of the multiverse). It’s sort of at the root of our epistemology. We believe it because we have to ground truth on something, and it seems to work better than anything else.
I can only hope someone will be able to take this argument and formalise it more thoroughly in the same way that hofstadter’s superrationality has been lifted up into FDT and stuff (does MIRI’s family of decision theories have a name? Is it “LDTs”? I’ve been wanting to call them “reflective decision theories” (because they reflect each other, and they reflect upon themselves) but that seemed to be already in use. (Though, maybe we shouldn’t let that stop us!))
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.