I’m not completely sure what your comment means. The result hasn’t “changed”, it has appeared. Without the extra axiom there’s not enough axioms to nail down a single result (and even with it I had to resort to lexicographic chance at one point). That’s what incompleteness means here.
If you think that’s wrong, try to prove the “correct” result, e.g. that any agent who precommits to not paying won’t get the $1000, using only the original axioms and nothing else. Once you write out the proof, we will know for certain that one of us is wrong or the original axioms are inconsistent, which would be even better :-)
I was also previously suspicious to the word “change”, but lately made my peace with it. Saying that there’s change is just a way of comparing objects of the same category. So if you look at an apple and a grape, what changes from apple to grape is, for example, color. A change is simultaneously what’s different, and a method of producing one from the other. Application of change to time, or to the process of decision-making, are mere special cases. Particular ways of parsing change in descriptions of decision problems can be incorrect because of explicit dependence bias: those changes as methods of determining one from the other are not ambient dependencies. But other usages of “change” still apply. For example, your decision to take one box in Newcomb’s instead of two changes the content of the box.
I’m not completely sure what your comment means. The result hasn’t “changed”, it has appeared. Without the extra axiom there’s not enough axioms to nail down a single result (and even with it I had to resort to lexicographic chance at one point). That’s what incompleteness means here.
If you think that’s wrong, try to prove the “correct” result, e.g. that any agent who precommits to not paying won’t get the $1000, using only the original axioms and nothing else. Once you write out the proof, we will know for certain that one of us is wrong or the original axioms are inconsistent, which would be even better :-)
I was also previously suspicious to the word “change”, but lately made my peace with it. Saying that there’s change is just a way of comparing objects of the same category. So if you look at an apple and a grape, what changes from apple to grape is, for example, color. A change is simultaneously what’s different, and a method of producing one from the other. Application of change to time, or to the process of decision-making, are mere special cases. Particular ways of parsing change in descriptions of decision problems can be incorrect because of explicit dependence bias: those changes as methods of determining one from the other are not ambient dependencies. But other usages of “change” still apply. For example, your decision to take one box in Newcomb’s instead of two changes the content of the box.