Slightly more spelled-out thoughts about bounded minds:
We can’t actually run the hypotheses of Solomonoff induction. We can only make arguments about what they will output.
In fact, almost all of the relevant uncertainty is logical uncertainty. The “hypotheses” (programs) of Solomonoff induction are not the same as the “hypotheses” entertained by bounded Bayesian minds. I don’t know of any published formal account of what these bounded hypotheses even are and how they relate to Solomonoff induction. But informally, all I’m talking about are ordinary hypotheses like “the Ponzi guy only gets money from new investors”.
In addition to “bounded hypotheses” (of unknown type), we also have “arguments”. An argument is a thing whose existence provides fallible evidence for a claim.
Arguments are made of pieces which can be combined “conjuctively” or “disjunctively”. The conjunction of two subarguments is weaker evidence for its claim than each subargument was for its subclaim. This is the sense in which “big arguments” are worse.
Slightly more spelled-out thoughts about bounded minds:
We can’t actually run the hypotheses of Solomonoff induction. We can only make arguments about what they will output.
In fact, almost all of the relevant uncertainty is logical uncertainty. The “hypotheses” (programs) of Solomonoff induction are not the same as the “hypotheses” entertained by bounded Bayesian minds. I don’t know of any published formal account of what these bounded hypotheses even are and how they relate to Solomonoff induction. But informally, all I’m talking about are ordinary hypotheses like “the Ponzi guy only gets money from new investors”.
In addition to “bounded hypotheses” (of unknown type), we also have “arguments”. An argument is a thing whose existence provides fallible evidence for a claim.
Arguments are made of pieces which can be combined “conjuctively” or “disjunctively”. The conjunction of two subarguments is weaker evidence for its claim than each subargument was for its subclaim. This is the sense in which “big arguments” are worse.