I do disagree with 3, though I disagree (mostly connotatively) with 1 and 2 as well.
The arguments you refer to were not written at the time I wrote my previous response, so I’m not sure what your point in the “Edit” is.
Nevertheless, I’ll write my response to your argument now.
In theoretical Newcomb, CDT doesn’t care about the rule of Omega being right, so CDT does not play Newcomb.
You are correct when you say that CDT “doesn’t care” about Omega being right. But that doesn’t mean that CDT agents don’t know that Omega is going to be right. If you ask a CDT agent to predict how they will do in the game, they will predict that they will earn far less money than someone who one-boxes. There is no observable fact that a one-boxer and a two-boxer will disagree on (at least in this sense). The only disagreement the two will have is about the counterfactual statement “if you had made a different choice, that box would/would not have contained money”.
That counterfactual statement is something that different decision theories implicitly give different views on. Its truth or falsity is not in the problem; it’s part of the answer. CDT agents don’t rule out the theoretical possibility of a predictor who can accurately predict their actions. CDT just says that the counterfactual which one-boxers use is incorrect. This is wrong, but CDT is just giving a wrong answer to the same question.
I do disagree with 3, though I disagree (mostly connotatively) with 1 and 2 as well.
The arguments you refer to were not written at the time I wrote my previous response, so I’m not sure what your point in the “Edit” is.
Nevertheless, I’ll write my response to your argument now.
You are correct when you say that CDT “doesn’t care” about Omega being right. But that doesn’t mean that CDT agents don’t know that Omega is going to be right. If you ask a CDT agent to predict how they will do in the game, they will predict that they will earn far less money than someone who one-boxes. There is no observable fact that a one-boxer and a two-boxer will disagree on (at least in this sense). The only disagreement the two will have is about the counterfactual statement “if you had made a different choice, that box would/would not have contained money”.
That counterfactual statement is something that different decision theories implicitly give different views on. Its truth or falsity is not in the problem; it’s part of the answer. CDT agents don’t rule out the theoretical possibility of a predictor who can accurately predict their actions. CDT just says that the counterfactual which one-boxers use is incorrect. This is wrong, but CDT is just giving a wrong answer to the same question.