I don’t think this proves probability and utility are inextricable. I prefer Jaynes’ approach of motivating probabilities by coherence conditions on beliefs—later, he notes that utility and probability are on equal footing in decision theory as explained in this post, but (as far as I remember) ultimately decides that he can’t carry this through to a meaningful philosophy that stands on its own. By choosing to introduce probabilities as conceptually prior, he “extricates” the two in a way that seems perfectly sensible to me.
I don’t think this proves probability and utility are inextricable. I prefer Jaynes’ approach of motivating probabilities by coherence conditions on beliefs—later, he notes that utility and probability are on equal footing in decision theory as explained in this post, but (as far as I remember) ultimately decides that he can’t carry this through to a meaningful philosophy that stands on its own. By choosing to introduce probabilities as conceptually prior, he “extricates” the two in a way that seems perfectly sensible to me.