The inferential method that solves the problems with frequentism — and, more importantly, follows deductively from the axioms of probability theory — is Bayesian inference.
You seem to be conflating Bayesian inference with Bayes Theorem. Bayesian inference is a method, not a proposition, so cannot be the conclusion of a deductive argument. Perhaps the conclusion you have in mind is something like "We should use Bayesian inference for..." or "Bayesian inference is the best method for...". But such propositions cannot follow from mathematical axioms alone.
Moreover, the fact that Bayes Theorem follows from certain axioms of probability doesn't automatically show that it's true. Axiomatic systems have no relevance to the real world unless we have established (whether explicitly or implicitly) some mapping of the language of that system onto the real world. Unless we've done that, the word "probability" as used in Bayes Theorem is just a symbol without relevance to the world, and to say that Bayes Theorem is "true" is merely to say that it is a valid statement in the language of that axiomatic system.
In practice, we are liable to take the word "probability" (as used in the mathematical axioms of probability) as having the same meaning as "probability" (as we previously used that word). That meaning has some relevance to the real world. But if we do that, we cannot simply take the axioms (and consequently Bayes Theorem) as automatically true. We must consider whether they are true given our meaning of the word "probability". But "probability" is a notoriously tricky word, with multiple "interpretations" (i.e. meanings). We may have good reason to think that the axioms of probability (and hence Bayes Theorem) are true for one meaning of "probability" (e.g. frequentist). But it doesn't automatically follow that they are also true for other meanings of "probability" (e.g. Bayesian).
I'm not denying that Bayesian inference is a valuable method, or that it has some sort of justification. But justifying it is not nearly so straightforward as your comment suggests, Luke.
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Don't programmers do this all the time? At least with current architectures, most computer systems have safeguards against unauthorized access to the system kernel as opposed to the user documents folders...
Isn't that basically saying "this line of code is harder to modify than that one"?
In fact, couldn't we use exactly this idea---user access protocols---to (partially) secure an AI? We could include certain kernel processes on the AI that would require a passcode to access. (I guess you have to stop the AI from hacking its own passcodes... but this isn't a problem on current computers, so it seems like we could prevent it from being a problem on AIs as well.)
[Responding to an old comment, I know, but I've only just found this discussion.]
Never mind special access protocols, you could make code unmodifiable (in a direct sense) by putting it in ROM. Of course, it could still be modified indirectly, by the AI persuading a human to change the ROM. Even setting aside that possibility, there's a more fundamental problem. You cannot guarantee that the code will have the expected effect when executed in the unpredictable context of an AGI. You cannot even guarantee that the code in question will be executed. Making the code unmodifiable won't achieve the desired effect if the AI bypasses it.
In any case, I think the whole discussion of an AI modifying its own code is rendered moot by the fuzziness of the distinction between code and data. Does the human brain have any code? Or are the contents just data? I think that question is too fuzzy to have a correct answer. An AGI's behaviour is likely to be greatly influenced by structures that develop over time, whether we call these code or data. And old structures need not necessarily be used.
AGIs are likely to be unpredictable in ways that are very difficult to control. Holden Karnofsky's attempted solution seems naive to me. There's no guarantee that programming an AGI his way will prevent agent-like behaviour. Human beings don't need an explicit utility function to be agents, and neither does an AGI. That said, if AGI designers do their best to avoid agent-like behaviour, it may reduce the risks.