It’s not clear what the “Omega offers the decision in a correct-calculator world” event is, since we already know that Omega offers the decision in “even” worlds, in some of which “even” is correct, and in some of which it’s not (as far as you know), and 99% of “even” worlds are the ones where calculator is correct, while you clearly assign 50% as probability of your event.
I “weakly” argue for the 50% probability as well. My argument follows the Pearl-type of counterfactual (Drescher calls it “choice-friendly”) -- when you counterfactually set a variable, you cut directed arrows that lead to it, but not directed arrows that lead out or undirected arrows (which in another comment I mistakenly called bi-directed). My intuition is that the “causing” node might possibly be logically established before the “caused” node thus possibly leading to contradiction in the counterfactual, while the opposite direction is not possible (the “caused” node cannot be logically established earlier than the “causing” node). Directly logically establishing the counterfactual node is harmless in that it invalidates the counterfactual straight away, the argument “fears” of the “gap” where we possibly operate by using a contradictory counterfactual.
Pearl’s counterfactuals (or even causal diagrams) are unhelpful, as they ignore the finer points of logical control that are possibly relevant here. For example, that definitions (facts) are independent should refer to the absence of logical correlation between them, that is inability to infer (facts about) one from the other. But this, too, is shaky in the context of this puzzle, where the nature of logical knowledge is called into question.
Is it a trivial remark regarding the probability theory behind Pearl’s “causality”, or an intuition with regard to future theories that resemble Pearl’s approach?
It is a statement following from my investigation of logical/ambient control and reality-as-normative-anticipation thesis which I haven’t written much about, but this all is regardless called in question as adequate foundation in light of the thought experiment.
I “weakly” argue for the 50% probability as well. My argument follows the Pearl-type of counterfactual (Drescher calls it “choice-friendly”) -- when you counterfactually set a variable, you cut directed arrows that lead to it, but not directed arrows that lead out or undirected arrows (which in another comment I mistakenly called bi-directed). My intuition is that the “causing” node might possibly be logically established before the “caused” node thus possibly leading to contradiction in the counterfactual, while the opposite direction is not possible (the “caused” node cannot be logically established earlier than the “causing” node). Directly logically establishing the counterfactual node is harmless in that it invalidates the counterfactual straight away, the argument “fears” of the “gap” where we possibly operate by using a contradictory counterfactual.
Pearl’s counterfactuals (or even causal diagrams) are unhelpful, as they ignore the finer points of logical control that are possibly relevant here. For example, that definitions (facts) are independent should refer to the absence of logical correlation between them, that is inability to infer (facts about) one from the other. But this, too, is shaky in the context of this puzzle, where the nature of logical knowledge is called into question.
Is it a trivial remark regarding the probability theory behind Pearl’s “causality”, or an intuition with regard to future theories that resemble Pearl’s approach?
It is a statement following from my investigation of logical/ambient control and reality-as-normative-anticipation thesis which I haven’t written much about, but this all is regardless called in question as adequate foundation in light of the thought experiment.