I still don’t understand the whole deal about counterfactuals, exemplified as “I<strong>f Oswald had not shot Kennedy, then someone else would have<a>”. Maybe MIRI means something else by the counterfactuals?
If it’s the counterfactual conditionals, then the approach is pretty simple, as discussed with jessicata elsewhere: there is the macrostate of the world (i.e. a state known to a specific observer, which consists of many possible substates, or microstates) of the world, one of these microstates led to the observed macroscopic event, some other possible microstates would have led to the same or different possible macrostates, e.g. Oswald shoots Kennedy, Oswald’s gun jams, someone else shooting Kennedy, and so on. The problem is constructing a set of microstates and their probability distribution that together lead to the pre-shooting macrostate. Once you know those, you can predict the odds of each post-shooting-time macrostate. When you think about the problem this way, there are no counterfactuals, only state evolution. It can be applied to the past, to the present or to the future.
I posted about it before, but just to reiterate my question. If you can “simply” count possible (micro-)states and their probabilities, then what is there except this simple counting?
Just to give an example, of, say, the Newcomb’s problem, the pre-decision microstates of the brain of the “agent”, while known to the Predictor, are not known to the agent. Some of these microstates lead to the macrostate corresponding to two-boxing, and some lead to the macrostate corresponding to one-boxing. Knowing what microstates these might be, and assigning our best-guess probabilities to them lets us predict what action an agent would take, if not as perfectly as the Predictor would, then as well as we ever can. What do UDT or FDT say beyond that, or contrary to that?
When you think about the problem this way, there are no counterfactuals, only state evolution. It can be applied to the past, to the present or to the future.
This doesn’t give very useful answers when the state evolution is nearly deterministic, such as an agent made of computer code.
For example, consider an agent trying to decide whether to turn left or turn right. Suppose for the sake of argument that it actually turns left, if you run physics forward. Also suppose that the logical uncertainty has figured that out, so that the best-estimate macrostate probabilities are mostly on that. Now, the agent considers whether to turn left or right.
Since the computation (as pure math) is deterministic, counterfactuals which result from supposing the state evolution went right instead of left mostly consist of computer glitches in which the hardware failed. This doesn’t seem like what the agent should be thinking about when it considers the alternative of going right instead of left. For example, the grocery store it is trying to get to could be on the right-hand path. The potential bad results of a hardware failure might outweigh the desire to turn toward the grocery store, so that the agent prefers to turn left.
For this story to make sense, the (logical) certainty that the abstract algorithm decides to turn left in this case has to be higher than the confidence that hardware will not fail, so that turning right seems likely to imply hardware failure. This can happen due to Löb’s theorem: the whole above argument, as a hypothetical argument, suggests that the agent would turn left on a particular occasion if it happened to prove ahead of time that its abstract algorithm would turn left (since it would then be certain that turning right implied a hardware failure). But this means a proof of left-turning results in left-turning. Löb’s theorem, left-turning is indeed provable.
The Newcomb’s-problem example you give also seems problematic. Again, if the agent’s algorithm is deterministic, it does basically one thing as long as the initial conditions are such that it is in Newcomb’s problem. So, essentially all of the uncertainty about the agent’s action is logical uncertainty. I’m not sure exactly what your intended notion of counterfactual is, but, I don’t see how reasoning about microstates helps the agent here.
I am going to use term “real counterfactual” to mean the metaphysical claim that events could have turned out otherwise in reality, and the term “logical counterfactual” to mean the purely hypothetical consideration of something that hasn’t happened.
Decision theory is about choosing possible courses of action according to their utility, which implies choosing them for, among other things, their probability. A future action is an event that has not happened yet. A past counterfactual is an event that didn’t happen. Calculating the probability of either is a similar process. Using counterfactuals in this sense does not imply or require a commitment to their real existence. Counterfactuals are even useful when considering systems known to be deterministic, such as deterministic algorithms. For the determinist, counterfactuals are useful but not true.
An Omega or Laplace’s daemon like agent in a deterministic universe could calculate from exact microstates to exact microstates [*], and so would not need counterfactual macrostates, even of a logical kind. But that does not tell us cognitively limited agents that counterfactuals are not useful to us. We cannot “just” calculate microstates.
And even if the relationship between macrostates and microsates works the way you say, deterministic evolution is a further assumption. Determinism trivially excludes real counterfactuals, whilst having no impact on logical ones (cf compatibilist free will). Determinism is neither a given, nor sufficiently impactive.
[*] although it might hav to exclude itself to avoid Loeian obstacles.
I still don’t understand the whole deal about counterfactuals, exemplified as “I<strong>f Oswald had not shot Kennedy, then someone else would have<a>”. Maybe MIRI means something else by the counterfactuals?
If it’s the counterfactual conditionals, then the approach is pretty simple, as discussed with jessicata elsewhere: there is the macrostate of the world (i.e. a state known to a specific observer, which consists of many possible substates, or microstates) of the world, one of these microstates led to the observed macroscopic event, some other possible microstates would have led to the same or different possible macrostates, e.g. Oswald shoots Kennedy, Oswald’s gun jams, someone else shooting Kennedy, and so on. The problem is constructing a set of microstates and their probability distribution that together lead to the pre-shooting macrostate. Once you know those, you can predict the odds of each post-shooting-time macrostate. When you think about the problem this way, there are no counterfactuals, only state evolution. It can be applied to the past, to the present or to the future.
I posted about it before, but just to reiterate my question. If you can “simply” count possible (micro-)states and their probabilities, then what is there except this simple counting?
Just to give an example, of, say, the Newcomb’s problem, the pre-decision microstates of the brain of the “agent”, while known to the Predictor, are not known to the agent. Some of these microstates lead to the macrostate corresponding to two-boxing, and some lead to the macrostate corresponding to one-boxing. Knowing what microstates these might be, and assigning our best-guess probabilities to them lets us predict what action an agent would take, if not as perfectly as the Predictor would, then as well as we ever can. What do UDT or FDT say beyond that, or contrary to that?
This doesn’t give very useful answers when the state evolution is nearly deterministic, such as an agent made of computer code.
For example, consider an agent trying to decide whether to turn left or turn right. Suppose for the sake of argument that it actually turns left, if you run physics forward. Also suppose that the logical uncertainty has figured that out, so that the best-estimate macrostate probabilities are mostly on that. Now, the agent considers whether to turn left or right.
Since the computation (as pure math) is deterministic, counterfactuals which result from supposing the state evolution went right instead of left mostly consist of computer glitches in which the hardware failed. This doesn’t seem like what the agent should be thinking about when it considers the alternative of going right instead of left. For example, the grocery store it is trying to get to could be on the right-hand path. The potential bad results of a hardware failure might outweigh the desire to turn toward the grocery store, so that the agent prefers to turn left.
For this story to make sense, the (logical) certainty that the abstract algorithm decides to turn left in this case has to be higher than the confidence that hardware will not fail, so that turning right seems likely to imply hardware failure. This can happen due to Löb’s theorem: the whole above argument, as a hypothetical argument, suggests that the agent would turn left on a particular occasion if it happened to prove ahead of time that its abstract algorithm would turn left (since it would then be certain that turning right implied a hardware failure). But this means a proof of left-turning results in left-turning. Löb’s theorem, left-turning is indeed provable.
The Newcomb’s-problem example you give also seems problematic. Again, if the agent’s algorithm is deterministic, it does basically one thing as long as the initial conditions are such that it is in Newcomb’s problem. So, essentially all of the uncertainty about the agent’s action is logical uncertainty. I’m not sure exactly what your intended notion of counterfactual is, but, I don’t see how reasoning about microstates helps the agent here.
I am going to use term “real counterfactual” to mean the metaphysical claim that events could have turned out otherwise in reality, and the term “logical counterfactual” to mean the purely hypothetical consideration of something that hasn’t happened.
Decision theory is about choosing possible courses of action according to their utility, which implies choosing them for, among other things, their probability. A future action is an event that has not happened yet. A past counterfactual is an event that didn’t happen. Calculating the probability of either is a similar process. Using counterfactuals in this sense does not imply or require a commitment to their real existence. Counterfactuals are even useful when considering systems known to be deterministic, such as deterministic algorithms. For the determinist, counterfactuals are useful but not true.
An Omega or Laplace’s daemon like agent in a deterministic universe could calculate from exact microstates to exact microstates [*], and so would not need counterfactual macrostates, even of a logical kind. But that does not tell us cognitively limited agents that counterfactuals are not useful to us. We cannot “just” calculate microstates.
And even if the relationship between macrostates and microsates works the way you say, deterministic evolution is a further assumption. Determinism trivially excludes real counterfactuals, whilst having no impact on logical ones (cf compatibilist free will). Determinism is neither a given, nor sufficiently impactive.
[*] although it might hav to exclude itself to avoid Loeian obstacles.