This actually sounds about right. What’s paradoxical here?
Not that it’s necessarily inconsistent, but in my view it does seem to be pointing out an important problem with the assumptions (hence indeed a paradox if you accept those false assumptions):
(ignore this part, it is just a rehash of the path dependence paradigm. It is here to show that I am not complaining about the math, but about its relation to reality):
Imagine you are going to be split (once). It is factually the case that there are going to be two people with memories, etc. consistent with having been you. Without any important differences to distinguish them, and if you insist on coming up with some probability number for “waking up” as one particular one of them obviously it has to be ½.
And then, if one of those copies subsequently splits, if you insist on assigning a probability number for those further copies, then from the perspective of that parent copy, the further copies also have to be ½ each.
And then if you take these probability numbers seriously and insist on them all being consistent then obviously from the perspective of the original the probability numbers for the final numbers have to be ½ and ¼ and ¼. As you say “this actually sounds about right”.
What’s paradoxical here is that in the scenario provided we have the following facts:
you have 3 identical copies all formed from the original
all 3 copies have an equal footing going forward
and yet, the path-based identity paradigm is trying to assign different weights to these copies, based on some technical details of what happened to create them. The intuition that this is absurd is pointing at the fact that these technical details aren’t what most people probably would care about, except if they insist on treating these probability numbers as real things and trying to make them follow consistent rules.
Ultimately “these three copies will each experience being a continuation of me” is an actual fact about the world, but statements like “‘I’ will experience being copy A (as opposed to B or C)” are not pointing to an actual fact about the world. Thus assigning a probability number to such a statement is a mental convenience that should not be taken seriously. The moment such numbers stop being convenient, like assigning different weights to copies you are actually indifferent between, they should be discarded. (and optionally you could make up new numbers that match what you actually care about instrumentally. Or just not think of it in those terms).
Did I understand you right that you argue against path-dependent identity here?
“‘I’ will experience being copy A (as opposed to B or C)” are not pointing to an actual fact about the world. Thus assigning a probability number to such a statement is a mental convenience that should not be taken seriously
Copies might be the same after copying but the room numbers in which they appear are different, and thus they can make bets on room numbers
The issue, to me, is not whether they are distinguishable.
The issues are:
is there any relevant-to-my-values difference that would cause me to weight them differently? (answer: no)
and:
does this statement make any sense as pointing to an actual fact about the world: “‘I’ will experience being copy A (as opposed to B or C)” (answer: no)
Imagine the statement: in world 1, “I” will wake up as copy A. in world 2 “I” will wake up as copy B. How are world 1 and world 2 actually different?
Answer: they aren’t different. It’s just that in world 1, I drew a box around the future copy A and said that this is what will count as “me”, and in world 2, I drew a box around copy B and said that this is what will count as “me”. This is a distinction that exists only in the map, not in the territory.
Not that it’s necessarily inconsistent, but in my view it does seem to be pointing out an important problem with the assumptions (hence indeed a paradox if you accept those false assumptions):
(ignore this part, it is just a rehash of the path dependence paradigm. It is here to show that I am not complaining about the math, but about its relation to reality):
Imagine you are going to be split (once). It is factually the case that there are going to be two people with memories, etc. consistent with having been you. Without any important differences to distinguish them, and if you insist on coming up with some probability number for “waking up” as one particular one of them obviously it has to be ½.
And then, if one of those copies subsequently splits, if you insist on assigning a probability number for those further copies, then from the perspective of that parent copy, the further copies also have to be ½ each.
And then if you take these probability numbers seriously and insist on them all being consistent then obviously from the perspective of the original the probability numbers for the final numbers have to be ½ and ¼ and ¼. As you say “this actually sounds about right”.
What’s paradoxical here is that in the scenario provided we have the following facts:
you have 3 identical copies all formed from the original
all 3 copies have an equal footing going forward
and yet, the path-based identity paradigm is trying to assign different weights to these copies, based on some technical details of what happened to create them. The intuition that this is absurd is pointing at the fact that these technical details aren’t what most people probably would care about, except if they insist on treating these probability numbers as real things and trying to make them follow consistent rules.
Ultimately “these three copies will each experience being a continuation of me” is an actual fact about the world, but statements like “‘I’ will experience being copy A (as opposed to B or C)” are not pointing to an actual fact about the world. Thus assigning a probability number to such a statement is a mental convenience that should not be taken seriously. The moment such numbers stop being convenient, like assigning different weights to copies you are actually indifferent between, they should be discarded. (and optionally you could make up new numbers that match what you actually care about instrumentally. Or just not think of it in those terms).
Copies might be the same after copying but the room numbers in which they appear are different, and thus they can make bets on room numbers
The issue, to me, is not whether they are distinguishable.
The issues are:
is there any relevant-to-my-values difference that would cause me to weight them differently? (answer: no)
and:
does this statement make any sense as pointing to an actual fact about the world: “‘I’ will experience being copy A (as opposed to B or C)” (answer: no)
Imagine the statement: in world 1, “I” will wake up as copy A. in world 2 “I” will wake up as copy B. How are world 1 and world 2 actually different?
Answer: they aren’t different. It’s just that in world 1, I drew a box around the future copy A and said that this is what will count as “me”, and in world 2, I drew a box around copy B and said that this is what will count as “me”. This is a distinction that exists only in the map, not in the territory.