Conditioning on ‘A(obs) = act’ is still a conditional, not a counterfactual. The difference between conditionals and counterfactuals is the difference between “If Oswald didn’t kill Kennedy, then someone else did” and “If Oswald didn’t kill Kennedy, then someone else would have”.
I still disagree. We need a counterfactual structure in order to consider the agent as a function A(obs). EG, if the agent is a computer program, the function A() would contain all the counterfactual information about what the agent would do if it observed different things. Hence, considering the agent’s computer program as such a function leverages an ontological commitment to those counterfactuals.
To illustrate this, consider counterfactual mugging where we already see that the coin is heads—so, there is nothing we can do, we are at the mercy of our counterfactual partner. But suppose we haven’t yet observed whether Omega gives us the money.
A “real counterfactual” is one which can be true or false independently of whether its condition is met. In this case, if we believe in real counterfactuals, we believe that there is a fact of the matter about what we do in the coin=tails case, even though the coin came up heads. If we don’t believe in real counterfactuals, we instead think only that there is a fact of how Omega is computing “what I would have done if the coin had been tails”—but we do not believe there is any “correct” way for Omega to compute that.
The obs→act representation and the P(act|obs) representation both appear to satisfy this test of non-realism. The first is always true if the observation is false, so, lacks the ability to vary independently of the observation. The second is undefined when the observation is false, which is perhaps even more appealing for the non-realist.
Now consider the A(obs)=act representation.A(tails)=pay can still vary even when we know coin=heads. So, it fails this test—it is a realist representation!
Putting something into functional form imputes a causal/counterfactual structure.
This indeed makes sense when “obs” is itself a logical fact. If obs is a sensory input, though, ‘A(obs) = act’ is a logical fact, not a logical counterfactual. (I’m not trying to avoid causal interpretations of source code interpreters here, just logical counterfactuals)
I still disagree. We need a counterfactual structure in order to consider the agent as a function A(obs). EG, if the agent is a computer program, the function A() would contain all the counterfactual information about what the agent would do if it observed different things. Hence, considering the agent’s computer program as such a function leverages an ontological commitment to those counterfactuals.
To illustrate this, consider counterfactual mugging where we already see that the coin is heads—so, there is nothing we can do, we are at the mercy of our counterfactual partner. But suppose we haven’t yet observed whether Omega gives us the money.
A “real counterfactual” is one which can be true or false independently of whether its condition is met. In this case, if we believe in real counterfactuals, we believe that there is a fact of the matter about what we do in the coin=tails case, even though the coin came up heads. If we don’t believe in real counterfactuals, we instead think only that there is a fact of how Omega is computing “what I would have done if the coin had been tails”—but we do not believe there is any “correct” way for Omega to compute that.
The obs→act representation and the P(act|obs) representation both appear to satisfy this test of non-realism. The first is always true if the observation is false, so, lacks the ability to vary independently of the observation. The second is undefined when the observation is false, which is perhaps even more appealing for the non-realist.
Now consider the A(obs)=act representation.A(tails)=pay can still vary even when we know coin=heads. So, it fails this test—it is a realist representation!
Putting something into functional form imputes a causal/counterfactual structure.
This indeed makes sense when “obs” is itself a logical fact. If obs is a sensory input, though, ‘A(obs) = act’ is a logical fact, not a logical counterfactual. (I’m not trying to avoid causal interpretations of source code interpreters here, just logical counterfactuals)
Ahhh ok.