My understanding is that the question is about how to do counterfactual math. There is no essential distinction between the two types (observational vs. logical) of knowledge, they are “limiting cases” of each other (you always only observe your mental reasoning, or calculator outputs, or publications on one end; Laplace’s demon on the other end).
ETA: my thinking went an U-turn from setting the calculator value without severing the Q->calculator correlation (i.e. treating calculator as an observed variable with a fictional observation), to setting the calculator value only after severing the Q->calculator correlation. (It would be clearer to me if I visualized the Q->calc arrow.) Judea Pearl definitely bubbles up my reading list. (My mistake again, sorry for the noise with too many comments!)
ETA2: my current answer (reasoning above) is fifty-fifty (Q as likely odd as even) in the counterfactual world without update (Q most likely even) in the real world.
OK, my final understanding is that the question is whether to build the two world models with a shared Q node or with separate Q nodes. We have separate calculator nodes so by analogy I see no strong reason for there to be a shared Q node, but also no strong reason for separate Q nodes since the counterfactual calculator is severed from the Q node. My inclination is that sharing nodes (as opposed to structure+parameters) between counterfactual worlds is the wrong thing to do, but sharing nodes is a limiting case of sharing structure+parameters… so the “logical” nodes should be shared and I’ve been the most wrong (by entertaining all other solutions). (But then the “logical” here is defined exactly as what is shared between all legitimate counterfactuals, so it is weaker than the “classically logical”; not all formulas are logical in this sense, but the ones that a mere calculator can compute probably are.)
My understanding is that the question is about how to do counterfactual math. There is no essential distinction between the two types (observational vs. logical) of knowledge, they are “limiting cases” of each other (you always only observe your mental reasoning, or calculator outputs, or publications on one end; Laplace’s demon on the other end).
ETA: my thinking went an U-turn from setting the calculator value without severing the Q->calculator correlation (i.e. treating calculator as an observed variable with a fictional observation), to setting the calculator value only after severing the Q->calculator correlation. (It would be clearer to me if I visualized the Q->calc arrow.) Judea Pearl definitely bubbles up my reading list. (My mistake again, sorry for the noise with too many comments!)
ETA2: my current answer (reasoning above) is fifty-fifty (Q as likely odd as even) in the counterfactual world without update (Q most likely even) in the real world.
OK, my final understanding is that the question is whether to build the two world models with a shared Q node or with separate Q nodes. We have separate calculator nodes so by analogy I see no strong reason for there to be a shared Q node, but also no strong reason for separate Q nodes since the counterfactual calculator is severed from the Q node. My inclination is that sharing nodes (as opposed to structure+parameters) between counterfactual worlds is the wrong thing to do, but sharing nodes is a limiting case of sharing structure+parameters… so the “logical” nodes should be shared and I’ve been the most wrong (by entertaining all other solutions). (But then the “logical” here is defined exactly as what is shared between all legitimate counterfactuals, so it is weaker than the “classically logical”; not all formulas are logical in this sense, but the ones that a mere calculator can compute probably are.)