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).
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.
Except, this is exactly how people reason about the identities of everything.
Suppose you own a ball. And then a copy of this ball is created. Is there 50% chance that you now own the newly created ball? Do you half-own both balls? Of course not! Your ball is the same phisical object, no matter how many copies of it are created, you know which of the balls is yours.
Now, suppose that two balls are shuffled so that you don’t know where is yours. Naturally, you assume that for every ball there is 50% probability that it’s “your ball”. Not because the two balls are copies of each other - they were so even before the shuffling. This probability represents your knowledge state and the shuffling made you less certain about which ball is yours.
And then suppose that one of these two balls is randomly selected and placed in a bag, with another identical ball. Now, to the best of your knowledge there is 50% probability that your ball is in the bag. And if a random ball is selected from the bag, there is 25% chance that it’s yours.
So as a result of such manipulations there are three identical balls and one has 50% chance to be yours, while the other two have 25% chance to be yours. Is it a paradox? Oh course not. So why does it suddenly become a paradox when we are talking about copies of humans?
The moment such numbers stop being convenient, like assigning different weights to copies you are actually indifferent between
But we are not indifferent between them! That’s the whole point. The idea that we should be indifferent between them is an extra assumption, which we are not making while reasoning about ownership of the balls. So why should we make it here?
It is a fact about the balls that one ball is physically continuous with the ball previously labeled as mine, while the other is not. It is a fact about our views on the balls that we therefore label that ball, which is physically continuous, as mine and the other not.
And then suppose that one of these two balls is randomly selected and placed in a bag, with another identical ball. Now, to the best of your knowledge there is 50% probability that your ball is in the bag. And if a random ball is selected from the bag, there is 25% chance that it’s yours.
So as a result of such manipulations there are three identical balls and one has 50% chance to be yours, while the other two have 25% chance to be yours. Is it a paradox? Oh course not. So why does it suddenly become a paradox when we are talking about copies of humans?
It is objectively the case here that 25% of the time this procedure would select the ball that is physically continuous with the ball originally labeled as “mine”, and that we therefore label as “mine”.
Ownership as discussed above has a relevant correlate in reality—physical continuity in this case. But a statement like “I will experience being copy B (as opposed to copy A or C)” does not. That statement corresponds to the exact same reality as the corresponding statements about experiencing being copy A or C. Unlike in the balls case, here the only difference between those statements is where we put the label of what is “me”.
In the identity thought experiment, it is still objectively the case that copies B and C are formed by splitting an intermediate copy, which was formed along with copy A by splitting the original.
You can choose to disvalue copies B and C based on that fact or not. This choice is a matter of values, and is inherently arbitrary.
By choosing not to disvalue copies B and C, I am not making an additional assumption—at least not one that you are already making by valuing B and C the same as each other. I am simply not counting the technical details of the splitting order as relevant to my values.
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).
Except, this is exactly how people reason about the identities of everything.
Suppose you own a ball. And then a copy of this ball is created. Is there 50% chance that you now own the newly created ball? Do you half-own both balls? Of course not! Your ball is the same phisical object, no matter how many copies of it are created, you know which of the balls is yours.
Now, suppose that two balls are shuffled so that you don’t know where is yours. Naturally, you assume that for every ball there is 50% probability that it’s “your ball”. Not because the two balls are copies of each other - they were so even before the shuffling. This probability represents your knowledge state and the shuffling made you less certain about which ball is yours.
And then suppose that one of these two balls is randomly selected and placed in a bag, with another identical ball. Now, to the best of your knowledge there is 50% probability that your ball is in the bag. And if a random ball is selected from the bag, there is 25% chance that it’s yours.
So as a result of such manipulations there are three identical balls and one has 50% chance to be yours, while the other two have 25% chance to be yours. Is it a paradox? Oh course not. So why does it suddenly become a paradox when we are talking about copies of humans?
But we are not indifferent between them! That’s the whole point. The idea that we should be indifferent between them is an extra assumption, which we are not making while reasoning about ownership of the balls. So why should we make it here?
It is a fact about the balls that one ball is physically continuous with the ball previously labeled as mine, while the other is not. It is a fact about our views on the balls that we therefore label that ball, which is physically continuous, as mine and the other not.
It is objectively the case here that 25% of the time this procedure would select the ball that is physically continuous with the ball originally labeled as “mine”, and that we therefore label as “mine”.
Ownership as discussed above has a relevant correlate in reality—physical continuity in this case. But a statement like “I will experience being copy B (as opposed to copy A or C)” does not. That statement corresponds to the exact same reality as the corresponding statements about experiencing being copy A or C. Unlike in the balls case, here the only difference between those statements is where we put the label of what is “me”.
In the identity thought experiment, it is still objectively the case that copies B and C are formed by splitting an intermediate copy, which was formed along with copy A by splitting the original.
You can choose to disvalue copies B and C based on that fact or not. This choice is a matter of values, and is inherently arbitrary.
By choosing not to disvalue copies B and C, I am not making an additional assumption—at least not one that you are already making by valuing B and C the same as each other. I am simply not counting the technical details of the splitting order as relevant to my values.
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.