Embedded agency and beliefs also lead to some kind of embedded truth values, with all the strangeness of depending on possible values of deterministic things. Consider some complicated computation F that would compute a particular value F() such as 2 or 5, but we don’t yet know which one. And consider a different computation G=F+10. Does the value G() of G depend on F()? Well, F() is some particular number, what does it mean to depend on it? And also we don’t know the number. But there is still some sense in which G() depends on F(). Even though G() is also just some particular number. It doesn’t make much sense to claim that 15 depends on 5, outside the context of the computations we are talking about.
Now, we can also consider truth value of a claim that G()>14. Does the truth value of that claim depend on F()? It seems that it does in some sense, in the same way that G() depends on F(), that is the claim G()>14 is true iff the claim F()>4 is true, and the truth value of F()>4 depends on the value of F(). Even though F() evaluates to some particular number such as 5, bringing about a different sense in which G() (which is just 15) or G()>14 (which is just true) don’t depend on F().
The complicated computation F could be some person making a decision F(), and the complicated computation G could be defining an outcome of that decision we are considering, so that G()>14 is a claim about that outcome with some truth value. If everything is deterministic, it might still make sense to say that G() depends on F(), and even that the truth of G()>14 depends on F(). And also that it’s F that determines F(), and therefore that it’s F that determines the truth value of G()>14.
(I think there is some equivocation about beliefs vs. decisions in the post, but it doesn’t seem essential to the core puzzle it’s bringing up. A decision is distinct from a belief about that decision, and if you are making decisions because of beliefs about those decisions, you run into Löbian traps, so it’s not a good way of thinking about the role of beliefs about decisions.)
Hmm… well, I certainly agree that a decision is distinct from a belief about that decision (indeed, I explicitly argue against the opposing view), and that making decisions because of beliefs about those decisions is nonsensical.
I’m not sure about the rest of it. If you are making the assumption that everything is deterministic, it seems like that just gets you to @Shmi-style “decisions are not about changing the world, they are about learning what world you live in”, and (as I say in the post) that fully dissolves the “puzzle”.
Embedded agency and beliefs also lead to some kind of embedded truth values, with all the strangeness of depending on possible values of deterministic things. Consider some complicated computation F that would compute a particular value F() such as 2 or 5, but we don’t yet know which one. And consider a different computation G=F+10. Does the value G() of G depend on F()? Well, F() is some particular number, what does it mean to depend on it? And also we don’t know the number. But there is still some sense in which G() depends on F(). Even though G() is also just some particular number. It doesn’t make much sense to claim that 15 depends on 5, outside the context of the computations we are talking about.
Now, we can also consider truth value of a claim that G()>14. Does the truth value of that claim depend on F()? It seems that it does in some sense, in the same way that G() depends on F(), that is the claim G()>14 is true iff the claim F()>4 is true, and the truth value of F()>4 depends on the value of F(). Even though F() evaluates to some particular number such as 5, bringing about a different sense in which G() (which is just 15) or G()>14 (which is just true) don’t depend on F().
Uh… this is interesting, but I’m not sure what it has to do with the post? Could you please spell out the connection a bit? What am I missing?
The complicated computation F could be some person making a decision F(), and the complicated computation G could be defining an outcome of that decision we are considering, so that G()>14 is a claim about that outcome with some truth value. If everything is deterministic, it might still make sense to say that G() depends on F(), and even that the truth of G()>14 depends on F(). And also that it’s F that determines F(), and therefore that it’s F that determines the truth value of G()>14.
(I think there is some equivocation about beliefs vs. decisions in the post, but it doesn’t seem essential to the core puzzle it’s bringing up. A decision is distinct from a belief about that decision, and if you are making decisions because of beliefs about those decisions, you run into Löbian traps, so it’s not a good way of thinking about the role of beliefs about decisions.)
Hmm… well, I certainly agree that a decision is distinct from a belief about that decision (indeed, I explicitly argue against the opposing view), and that making decisions because of beliefs about those decisions is nonsensical.
I’m not sure about the rest of it. If you are making the assumption that everything is deterministic, it seems like that just gets you to @Shmi-style “decisions are not about changing the world, they are about learning what world you live in”, and (as I say in the post) that fully dissolves the “puzzle”.