I acknowledge the snark. I get annoyed when people repeatedly make the mistake of not defining their terms, running rampant with them, being shocked when they get mismatched intuitions, and conclude the undefinitions wrong. It’s no more logical than, “you’re wrong because I feel that way.”
I explain why this isn’t right. Only one algorithm is dependent on yours. The other is just correlated.
Correlated is doing a lot of equivocating in your intuitions. It’s merely correlated not causal, he says! What’s the difference? everyone asks. Oh, there is none, they are extensionally identical, but using the word correlated will trick the functional decision theorist into taking a different action.
One man’s modus tollens is another man’s modus ponens.
You say, “since my intuitions imply the functional decision theorist will take different actions in these extensionally equivalent scenarios, clearly the functional decision theorist can be Dutch booked.”
I say, “since the functional decision theorist is rational and cannot be Dutch booked, clearly your intuitions are wrong about what the functional decision theorist will do. Go back and straighten out your definitions.”
Second, as I explain, measuring similarity is even more difficult.
I literally told you how to measure similarity: KL(p||q).
Re calculator, whether they output the same thing depends on how you interpret their outputs, as explained in the post.
I didn’t think this was your main objection because you told us the isomorphism. However, if the isomoprhism is unknown, or there isn’t an isomorphism but some other transformation, you can use the mutual information to recover it. Re: mutual information neural estimation.
99.9% accurate in the sense that 99.9% of the time, the predictor guesses right.
And it’s a stipulation of the thought experiment that the predictor is reliable—doesn’t matter if this could exist in the real world.
Ah yes, the principle of explosion proves every proposition true and false. Just sneak in contradictory axioms (by not defining your terms) and you can prove anything you want!
I acknowledge the snark. I get annoyed when people repeatedly make the mistake of not defining their terms, running rampant with them, being shocked when they get mismatched intuitions, and conclude the undefinitions wrong. It’s no more logical than, “you’re wrong because I feel that way.”
Correlated is doing a lot of equivocating in your intuitions. It’s merely correlated not causal, he says! What’s the difference? everyone asks. Oh, there is none, they are extensionally identical, but using the word correlated will trick the functional decision theorist into taking a different action.
One man’s modus tollens is another man’s modus ponens.
You say, “since my intuitions imply the functional decision theorist will take different actions in these extensionally equivalent scenarios, clearly the functional decision theorist can be Dutch booked.”
I say, “since the functional decision theorist is rational and cannot be Dutch booked, clearly your intuitions are wrong about what the functional decision theorist will do. Go back and straighten out your definitions.”
I literally told you how to measure similarity: KL(p||q).
I didn’t think this was your main objection because you told us the isomorphism. However, if the isomoprhism is unknown, or there isn’t an isomorphism but some other transformation, you can use the mutual information to recover it. Re: mutual information neural estimation.
Ah yes, the principle of explosion proves every proposition true and false. Just sneak in contradictory axioms (by not defining your terms) and you can prove anything you want!