“but a fundamental assumption behind TDT and UDT is the existence of a causal structure behind logical statements, which sounds implausible to me.”
None of the theories mentioned make any assumption like that; see the FDT paper above.
Page 14 of the FDT paper:
Instead of a do operator, FDT needs a true operator, which takes a logical sentence φ and updates P to represent the scenario where φ is true...
...Equation (4) works given a graph that accurately describes how changing the value of a logical variable affects other variables, but it is not yet clear how to construct such a thing—nor even whether it can be done in a satisfactory manner within Pearl’s framework.
This seems wrong, if you’re saying that we can’t formally establish the behavior of different decision theories, or that applying theories to different cases requires ad-hoc emendations; see section 5 of “Functional Decision Theory” (and subsequent sections) for a comparison and step-by-step walkthrough of procedures for FDT, CDT, and EDT. One of the advantages we claim for FDT over CDT and EDT is that it doesn’t require ad-hoc tailoring for different dilemmas (e.g., ad-hoc precommitment methods or ratification procedures, or modifications to the agent’s prior).
The main thing that distinguishes FDT from CDT is how the true operator mentioned above functions. As far as I’m aware this is always inserted by hand. This is easy to for situations where entities make perfect simulations of one another, but there aren’t even rough guidelines for what to do when the computations that are done cannot be delineated in such a clean manner. In addition, if this was a rich research field I would expect more “math that bites back”, i.e., substantive results that reduce to clearly-defined mathematical problems whose result wasn’t expected during the formalization.
This point about “load-bearing elements” is at its root an intuitive judgement that might be difficult for me to convey properly.
Page 14 of the FDT paper:
The main thing that distinguishes FDT from CDT is how the true operator mentioned above functions. As far as I’m aware this is always inserted by hand. This is easy to for situations where entities make perfect simulations of one another, but there aren’t even rough guidelines for what to do when the computations that are done cannot be delineated in such a clean manner. In addition, if this was a rich research field I would expect more “math that bites back”, i.e., substantive results that reduce to clearly-defined mathematical problems whose result wasn’t expected during the formalization.
This point about “load-bearing elements” is at its root an intuitive judgement that might be difficult for me to convey properly.