“If you don’t take the time to check your logical equivalencies, you will take Dutch Books”
You’re very wrong here.
By Goedel’s Incompleteness Theorem, there is no way to “take the time to check your logical equivalencies”. There are always things that are logically equivalent that your particular method of proving, no matter how sophisticated, will not find, in any amount of time.
This is somewhat specific to Bayesianism, as Bayesianism insists that you always give a definite numerical answer.
Not being able to refuse answering (by Bayesianism) + no guarantee of self-consistency (by Incompleteness) ⇒ Dutch booking
I admit defeat. When I am presented with enough unrefusable bets that incompleteness prevents me from realising are actually Dutch Books such that my utility falls consistently below some other method, I will swap to that method.
You’re very wrong here.
By Goedel’s Incompleteness Theorem, there is no way to “take the time to check your logical equivalencies”. There are always things that are logically equivalent that your particular method of proving, no matter how sophisticated, will not find, in any amount of time.
This is somewhat specific to Bayesianism, as Bayesianism insists that you always give a definite numerical answer.
Not being able to refuse answering (by Bayesianism) + no guarantee of self-consistency (by Incompleteness) ⇒ Dutch booking
I admit defeat. When I am presented with enough unrefusable bets that incompleteness prevents me from realising are actually Dutch Books such that my utility falls consistently below some other method, I will swap to that method.