Then I claim that a non-psychic predictor, no matter how good, is very different from a psychic.
The powers of a non-psychic predictor are entirely natural and causal. Once he has written down his hidden choice, then he becomes irrelevant. If this isn’t clear, then we can make an analogy with the urn example. After the ball is drawn but before its colour is revealed, the contents of the urn are irrelevant. As I pointed out, the urn could even be destroyed before the colour of the ball is revealed, so that the ball’s colour truly is the only state. Similarly, after the predictor writes his choice but before it is revealed, he might accidentally behead himself while shaving.
Now of course your beliefs about the talents of the late predictor might inform your beliefs about his hidden choice. But that’s the only way they can possibly be releveant. The coin and the predictor’s hidden choice on the paper really are the only states of the world now, and your own choice is free and has no effect on the state. So, if you display a strict preference for the coin, then your uncertainty is still not captured by subjective probability. You still violate P2.
To get around this, it seems you would have to posit some residual entanglement between your choice and the external state. To me this sounds like a strange thing to argue. But I suppose you could say your cognition is flawed in a way that is invisible to you, yet was visible to the clever but departed predictor. So, you might argue that, even though there is no actual psychic effect, your choice is not really free, and you have to take into account your internalities in addition to the external states.
My question then would be, does this entanglement prevent you from having a total ordering over all maps from states (internal and external) to outcomes? If yes, then P1 is violated. If no, then can I not just ask you about the ordering of the maps which only depend on the external states, and don’t we just wind up where we were?
Then I claim that a non-psychic predictor, no matter how good, is very different from a psychic.
The powers of a non-psychic predictor are entirely natural and causal. Once he has written down his hidden choice, then he becomes irrelevant. If this isn’t clear, then we can make an analogy with the urn example. After the ball is drawn but before its colour is revealed, the contents of the urn are irrelevant. As I pointed out, the urn could even be destroyed before the colour of the ball is revealed, so that the ball’s colour truly is the only state. Similarly, after the predictor writes his choice but before it is revealed, he might accidentally behead himself while shaving.
Now of course your beliefs about the talents of the late predictor might inform your beliefs about his hidden choice. But that’s the only way they can possibly be releveant. The coin and the predictor’s hidden choice on the paper really are the only states of the world now, and your own choice is free and has no effect on the state. So, if you display a strict preference for the coin, then your uncertainty is still not captured by subjective probability. You still violate P2.
To get around this, it seems you would have to posit some residual entanglement between your choice and the external state. To me this sounds like a strange thing to argue. But I suppose you could say your cognition is flawed in a way that is invisible to you, yet was visible to the clever but departed predictor. So, you might argue that, even though there is no actual psychic effect, your choice is not really free, and you have to take into account your internalities in addition to the external states.
My question then would be, does this entanglement prevent you from having a total ordering over all maps from states (internal and external) to outcomes? If yes, then P1 is violated. If no, then can I not just ask you about the ordering of the maps which only depend on the external states, and don’t we just wind up where we were?