Any conditional duplication is (for the purposes of the scenario’s credence of heads when asked) identical to unconditionally duplicating and then killing the duplicate in room 2 on heads before awakening.
What’s more, it’s the same as just not asking the duplicate in room 2 on heads, without any killing involved.
What’s more, it doesn’t matter when that duplication happens prior to being asked, before the coin flip or after, so longer as neither knows which one is going to be asked on heads.
I’m not sure whether you’re agreeing with my first point or not, regarding the equivalence of conditional duplication with unconditional duplication + conditional killing.
Since you said that the martingale condition is fully satisfied for both unconditional duplication and for conditional killing, do you believe that it is necessarily (regardless of SIA belief) satisfied for the sequence of both?
It’s the equivalence between (conditional duplication) and (unconditional duplication + conditional killing) that I’m disputing (or at least saying that you can’t just assume for free).
The difference is clear for the formal martingale: let’s count the full agent histories from beginning to end. Conditional duplication has three histories - (Sunday, awake, room 1, T), (Sunday, awake, room 2, T) and (Sunday, awake, room 1, H). While (unconditional duplication + conditional killing) has four—those three plus extra one heads: the “death” history of just (Sunday).
Thus the martingale in the (ud + ck) case has an extra possible future observation to consider: specifically, the non-observation. That’s why “awake” gives information in the (ud+ck) case (not all your duplicates would be guaranteed to see it) but not in the (cd) case (where all your duplicates are guaranteed to see it).
(It doesn’t help if one says that “non-observations don’t count”, because then the theory breaks breaks the martingale in the case of just “conditional killing” on its own.)
Now, philosophically, I’m partial to the idea that “instant duplication followed by deletion” should be the same as “not creating duplicates at all”; that’s a strong pro-SIA argument. But that doesn’t fix the martingale; it instead shows that if we assumed that there were instantly-deleted duplicates, then that assumption would fix the martingale.
I consider the cd = ud+ck equivalence to be much more fundamental than any martingale property, so I guess that’s the difference.
If we have an epistemic model in which we need to consider whether or not a duplicate was created and destroyed without ever making any observations, then as I see it that model should be discarded as it contains internal flaws. It shouldn’t even make any difference if we bring in an inert lump of random matter instead of a non-conscious duplicate, either. From an epistemic point of view, all non-observers are equivalently irrelevant.
Any conditional duplication is (for the purposes of the scenario’s credence of heads when asked) identical to unconditionally duplicating and then killing the duplicate in room 2 on heads before awakening.
What’s more, it’s the same as just not asking the duplicate in room 2 on heads, without any killing involved.
What’s more, it doesn’t matter when that duplication happens prior to being asked, before the coin flip or after, so longer as neither knows which one is going to be asked on heads.
So the duplication isn’t the problem.
SIA (which I tend to agree with) treats unconditional and conditional duplication as the same; but that’s an assumption we don’t get to take for free.
On heads, being killed or not being asked have clear effects in terms of expectation of alternative observations to see or not see.
That’s why unconditional duplication is fully martingale, while conditional duplication isn’t.
I’m not sure whether you’re agreeing with my first point or not, regarding the equivalence of conditional duplication with unconditional duplication + conditional killing.
Since you said that the martingale condition is fully satisfied for both unconditional duplication and for conditional killing, do you believe that it is necessarily (regardless of SIA belief) satisfied for the sequence of both?
If not, how does the first equivalence break?
Yep, the martingale is satisfied for both.
It’s the equivalence between (conditional duplication) and (unconditional duplication + conditional killing) that I’m disputing (or at least saying that you can’t just assume for free).
The difference is clear for the formal martingale: let’s count the full agent histories from beginning to end. Conditional duplication has three histories - (Sunday, awake, room 1, T), (Sunday, awake, room 2, T) and (Sunday, awake, room 1, H). While (unconditional duplication + conditional killing) has four—those three plus extra one heads: the “death” history of just (Sunday).
Thus the martingale in the (ud + ck) case has an extra possible future observation to consider: specifically, the non-observation. That’s why “awake” gives information in the (ud+ck) case (not all your duplicates would be guaranteed to see it) but not in the (cd) case (where all your duplicates are guaranteed to see it).
(It doesn’t help if one says that “non-observations don’t count”, because then the theory breaks breaks the martingale in the case of just “conditional killing” on its own.)
Now, philosophically, I’m partial to the idea that “instant duplication followed by deletion” should be the same as “not creating duplicates at all”; that’s a strong pro-SIA argument. But that doesn’t fix the martingale; it instead shows that if we assumed that there were instantly-deleted duplicates, then that assumption would fix the martingale.
I consider the cd = ud+ck equivalence to be much more fundamental than any martingale property, so I guess that’s the difference.
If we have an epistemic model in which we need to consider whether or not a duplicate was created and destroyed without ever making any observations, then as I see it that model should be discarded as it contains internal flaws. It shouldn’t even make any difference if we bring in an inert lump of random matter instead of a non-conscious duplicate, either. From an epistemic point of view, all non-observers are equivalently irrelevant.
I agree about 75% with this perspective.