Perhaps referring directly to Goedel was not apt. What Goedel showed was that Hilbert/Russell’s efforts were futile. And what Hilbert and Russell were trying to do was create a formal system where actual self-reference was impossible. And the reason he was trying to do that, finally, was that self-reference creates paradoxes which reduce to either incompleteness or inconsistency. And the same is true of these more advanced decision theories. Because they are self-referencing, they create an infinite regress that precludes the existence of a “best” decision theory at all.
So, finding a best decision theory is impossible once self-reference is allowed, because of the nature of self-reference, but not quite because of Goedel’s theorems, which are the stronger declaration that any formal system by necessity contains self-referential aspects that make it incomplete or inconsistent.
Perhaps referring directly to Goedel was not apt. What Goedel showed was that Hilbert/Russell’s efforts were futile. And what Hilbert and Russell were trying to do was create a formal system where actual self-reference was impossible. And the reason he was trying to do that, finally, was that self-reference creates paradoxes which reduce to either incompleteness or inconsistency. And the same is true of these more advanced decision theories. Because they are self-referencing, they create an infinite regress that precludes the existence of a “best” decision theory at all.
So, finding a best decision theory is impossible once self-reference is allowed, because of the nature of self-reference, but not quite because of Goedel’s theorems, which are the stronger declaration that any formal system by necessity contains self-referential aspects that make it incomplete or inconsistent.