Vladimir_Nesov comments on Counterfactual Calculation and Observational Knowledge - Less Wrong

11 Post author: Vladimir_Nesov 31 January 2011 04:28PM

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Tags: decision_theory udt counterfactual_calculation

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Comment author: Vladimir_Nesov 01 February 2011 05:41:23PM 0 points [-]

My point is that Omega, before the world split, knows what I will do should the calculator return "even". And he knows how I will answer various logical puzzles in that case. But unless he actually knows (in advance) what the calculator will do, there is no way that he can transfer information dependent on the "even" from me in the "even" world to the paper in the "odd" world.

Unpack "transfer information". If Omega in "odd" world knows what you'd answer should the calculator return "even", it can use this fact to control things in its own "odd" world, all of this without it being able to predict whether the calculator displays "even" or "odd". Considering the question in advance of observing the calculator display is not necessary.

Comment author: Perplexed 01 February 2011 06:20:05PM 0 points [-]

If Omega in "odd" world knows what you'd answer should the calculator return "even", it can use this fact to control things in its own "odd" world.

Yes, and Omega in "even" world knows all about what would have happened in "odd" world.

But neither Omega knows what "really" happened; that was the whole point of my question; the one in which I apparently used the word 'counterfactual' an excessive number of times.

Let me try again by asking this question: What knowledge does the 'odd' Omega need to have so as to write 'odd' on the exam paper? Does he need to know (subject says to write 'odd' & subject sees 'even' on calculator)? Or does he instead need to know (subject says to write 'odd' | subject sees 'even' on calculator)? Because I am claiming that the two are different and that the second is all that Omega has. Even if Omega knows whether Q is really odd or even.

Comment author: Vladimir_Nesov 01 February 2011 06:39:13PM 0 points [-]

Does he need to know (subject says to write 'odd' & subject sees 'even' on calculator)? Or does he instead need to know (subject says to write 'odd' | subject sees 'even' on calculator)? Because I am claiming that the two are different and that the second is all that Omega has.

I don't know what the first option you listed means, and agree that Omega follows the second.

Comment author: Vladimir_Nesov 01 February 2011 06:32:14PM *  0 points [-]

Yes, and Omega in "even" world knows all about what would have happened in "odd" world.

But neither Omega knows what "really" happened

I agree, "actuality" is not a property of possible worlds (if we forget about impossible possible worlds for a moment), but it does make sense to talk about "current observational event" (what we usually call actual reality), and counterfactuals located outside it (where one of the observations went differently). These notions would then be referred to from the context of a particular agent.

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