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!
My experience taking philosophy classes at MIT was academic philosophers are trained very poorly at scrutinizing philosophical arguments. People adjacent to philosophy—logicians, mathematicians, linguists, (not physicists)—are generally better able to work through philosophical arguments. The first two because learning the language forces them to learn how to think argumentatively, the third because it deals with similar structure without the baggage introduced by academic philosophers.
For example, if I present the Grandfather Paradox to a professor in these four fields, I expect:
The logician would ask me for the axioms, and keep pushing until I admit one of them is, “your grandfather cannot die.”
The mathematician would say, “obviously you cannot kill your grandfather, otherwise you have a contradiction.”
The linguist would ask me what exactly I mean by grandfather—biological? has he frozen sperm? does he have children yet? a twin brother?—and conclude, “you can kill your grandfather, at least the person that word refers to in the mind of the time traveler.”
The philosopher would say, “oh that’s such an interesting thought experiment. I don’t know, can you? It doesn’t seem like you can’t, and yet that seems like it would create a contradiction.” Then they would try putting the paradox in premise-conclusion form, and two hours later conclude, “well many of these axioms and implications seem a little fishy, but I would have to say you can/cannot [equally likely] kill your grandfather”.