Thanks for the reply. I re-read your post and your post on Savage’s proof and you’re right on all counts. For some reason, it didn’t actually click for me that P7 was introduced to address unbounded utility functions and boundedness was a consequence of taking the axioms to their logical conclusion.
Well, it’s worth noting that P7 is introduced to address gambles with infinitely many possible outcomes, regardless of whether those outcomes are bounded or not (which is the reason I argue above you can’t just get rid of it). But yeah. Glad that’s cleared up now! :)
Thanks for the reply. I re-read your post and your post on Savage’s proof and you’re right on all counts. For some reason, it didn’t actually click for me that P7 was introduced to address unbounded utility functions and boundedness was a consequence of taking the axioms to their logical conclusion.
Well, it’s worth noting that P7 is introduced to address gambles with infinitely many possible outcomes, regardless of whether those outcomes are bounded or not (which is the reason I argue above you can’t just get rid of it). But yeah. Glad that’s cleared up now! :)