The probability that a counterfactual is true should be handled with the same probabilistic machinery we always use. Once the set of prior information is defined, it can be computed as usual with Bayes. The confusing point seems to be that the prior information is contrary to what actually occurred, but there’s no reason this should be different than any other case with limited prior information.
For example, suppose I drop a glass above a marble floor. Define:
sh = “my glass shattered”
f = “the glass fell to the floor under the influence of gravity”
and define sh_0 and f_0 as the negations of these statements. We wish to compute
P(sh_0|f_0,Q) = P(sh_0|Q)P(f_0|sh_0,Q)/P(f_0|Q),
where Q is all other prior information, including my understanding of physics. As long as these terms exist, we have no problem. The confusion seems to stem from the assumption that P(f_0|sh_0,Q) = P(f_0|Q) = 0, since f_0 is contrary to our observations, and in this case seemingly mutually exclusive with Q.
But probability is in the mind. From the perspective of an observer at the moment the glass is dropped, P(f_0|Q) at least includes cases in which she is living in the Matrix, or aliens have harnessed the glass in a tractor beam. Both of these cases hold finite probability consistent with Q. From the perspective of someone remembering the observed event, P(f_0|Q) might include cases in which her memory is not trustworthy.
In the usual colloquial case, we’re taking the perspective of someone running a thought experiment on a histroical event with limited information about history and physics. The glass-dropping case limits the possible cases covered by P(f_0|Q) considerably, but the Kennedy-assassination case leaves a good many of them open. All terms are well defined in Bayes’ rule above, and I see no problem with computing in principle the probability of the counterfactual being true.
As usual, I’m late to the discussion.
The probability that a counterfactual is true should be handled with the same probabilistic machinery we always use. Once the set of prior information is defined, it can be computed as usual with Bayes. The confusing point seems to be that the prior information is contrary to what actually occurred, but there’s no reason this should be different than any other case with limited prior information.
For example, suppose I drop a glass above a marble floor. Define:
sh = “my glass shattered”
f = “the glass fell to the floor under the influence of gravity”
and define sh_0 and f_0 as the negations of these statements. We wish to compute
P(sh_0|f_0,Q) = P(sh_0|Q)P(f_0|sh_0,Q)/P(f_0|Q),
where Q is all other prior information, including my understanding of physics. As long as these terms exist, we have no problem. The confusion seems to stem from the assumption that P(f_0|sh_0,Q) = P(f_0|Q) = 0, since f_0 is contrary to our observations, and in this case seemingly mutually exclusive with Q.
But probability is in the mind. From the perspective of an observer at the moment the glass is dropped, P(f_0|Q) at least includes cases in which she is living in the Matrix, or aliens have harnessed the glass in a tractor beam. Both of these cases hold finite probability consistent with Q. From the perspective of someone remembering the observed event, P(f_0|Q) might include cases in which her memory is not trustworthy.
In the usual colloquial case, we’re taking the perspective of someone running a thought experiment on a histroical event with limited information about history and physics. The glass-dropping case limits the possible cases covered by P(f_0|Q) considerably, but the Kennedy-assassination case leaves a good many of them open. All terms are well defined in Bayes’ rule above, and I see no problem with computing in principle the probability of the counterfactual being true.