Back when the FDT paper came out, I considered counterpossibles an inherently interesting question.
For example, I wondered, is there a Bayesian formulation of probabilistic primality testing? Well, there is, as Gaifman explains, but can we compute P(x is prime|witnesses) for a particular x and particular witnesses? That seems to require counterpossibles: even if the number is prime, we have to consider the probability that these would have been witnesses if it were not.
Maybe back then, it didn’t seem so strange to me to say, oh by the way when we figure out counterpossibles we can plug that solution into a decision theory.
Now though, I’m more interested in decision theory than in counterpossibles. And I don’t think counterpossibles are essential to decision theory, so saying you’ll solve counterpossibles as a subproblem seems like a distraction.
It would be one thing if counterpossibles were easy, so whatever you think of counterpossibles, it’s just the best way to solve decision theory. But… well, October 2027 will be the ten-year anniversary of the FDT paper.
Who knows what I would have thought of this post if you had made it when FDT first came out. I mean, a lot of your post is just repeating the unsolved subproblems in the FDT paper itself. But many years later, my response to hearing that is not “yes, we know, that’s right in the paper” but “yes, that’s why FDT was a disappointment and I’m thinking about the next thing”.
Back when the FDT paper came out, I considered counterpossibles an inherently interesting question.
For example, I wondered, is there a Bayesian formulation of probabilistic primality testing? Well, there is, as Gaifman explains, but can we compute P(x is prime|witnesses) for a particular x and particular witnesses? That seems to require counterpossibles: even if the number is prime, we have to consider the probability that these would have been witnesses if it were not.
Maybe back then, it didn’t seem so strange to me to say, oh by the way when we figure out counterpossibles we can plug that solution into a decision theory.
Now though, I’m more interested in decision theory than in counterpossibles. And I don’t think counterpossibles are essential to decision theory, so saying you’ll solve counterpossibles as a subproblem seems like a distraction.
It would be one thing if counterpossibles were easy, so whatever you think of counterpossibles, it’s just the best way to solve decision theory. But… well, October 2027 will be the ten-year anniversary of the FDT paper.
Who knows what I would have thought of this post if you had made it when FDT first came out. I mean, a lot of your post is just repeating the unsolved subproblems in the FDT paper itself. But many years later, my response to hearing that is not “yes, we know, that’s right in the paper” but “yes, that’s why FDT was a disappointment and I’m thinking about the next thing”.