On 12/08/2017 3:22 am, Bruno Marchal wrote:
On 11 Aug 2017, at 13:40, Bruce Kellett wrote:


Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you* expect when pushing the button in Helsinki?

I expect to die, to be 'cut', according to the protocol. The guys in W and M are two new persons, and neither was around in H to make any prediction whatsoever.

Fair enough.

You think the digital mechanism thesis is wrong.

Correct.

There is a fundamental problem with your person-duplication thought experiments. This is that the way in which you interpret the scenario inherently involves an irreducible 1p-3p confusion. The first person (1p) concerns only things that the person can experience directly for himself. It cannot, therefore, involve things that he is told by other people, because such things are necessarily third person (3p) knowledge -- knowledge which he does not have by direct personal experience. So our subject does not know the protocol of the thought experiment from direct experience (he has only been told about it, 3p). When he presses the button in the machine, he can have no 1p expectations about what will happen (because he has not yet experienced it). He presses the button in the spirit of pure experimental enquiry -- "what will happen if I do this?" His prior probability for any particular outcome is zero. So when he presses the button in Helsinki, and opens the door to find himself in Moscow, he will say, "WTF!". In particular, he will not have gained any 1p knowledge of duplication. In fact, he is for ever barred from any such knowledge.

If he repeats the experiment many times, he will simply see his experiences as irreducibly random between M and W, with some probability that he can estimate by keeping records over a period of time. If you take the strict 1p view of the thought experiment, the parallel with the early development of QM is more evident. In QM, no-one has the 3p knowledge that all possible outcomes are realized (in different worlds).

So, before pressing the button in H, his prior probabilities are p(M) = p(W) = 0, with probably, p(H) = 1. On the other hand, if you allow 3p knowledge of the protocol to influence his estimation of probabilities before the experiment, you can't rule out 3p knowledge that he can gain at any time after pressing the button. In which case, the 1p-3p confusion is complete, p(M) = p(W) = 1, and he can expect to see both cities. In that case, the pure 1p view becomes irrelevant.

Bruce

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