FAWS comments on Counterfactual Calculation and Observational Knowledge - Less Wrong

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

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Comment author: FAWS 01 February 2011 04:44:00PM -1 points [-]

This would be correct if Q could be different, but Q is the same both in the counterfactual and the actual word. There is no possibility for the actual world being Even World and the counterfactual Odd World.

The possibilities are:

  1. Actual: Even World, Right Calculator (99% of Even Words); Counterfactual: Even World, Wrong Calculator (1% of Even Worlds).

  2. Actual: Odd World, Wrong Calculator (1% of Odd Words); Counterfactual: Odd World, Right Calculator (99% of Odd Words).

The prior probability of either is 50%. If we assume That Omega randomly picks one you out of 100% of possible words(either 100% of all Even Worlds or 100% of all Odd Words) to decide for all possible words where the calculator result is different (but the correct answer is the same), then there is a 99% chance all worlds are Even and your choice affects 1% of all worlds and a 1% chance all words are Odd and your choice affects 99% of all worlds. The result of the calculator in the counterfactual world doesn't provide any evidence on whether all words are Even or all worlds are Odd since in either case there would be such a world to talk about.

If we assume that Omega randomly visits one world and randomly mentions the calculator result of one other possible world and it just happened to be the case that in that other world the result was different; or if Omega randomly picks a world, then randomly picks a world with the opposite calculator result and tosses a coin as to which world to visit and which to mention then the calculator result in the counterfactual word is equally relevant and hearing Omega talk about it just as good as running the calculator twice. In this case you are equally likely to be in a Odd world and might just as well toss a coin as to which result you fill in yourself.

Comment author: FAWS 01 February 2011 05:14:01PM *  0 points [-]

If someone is sure enough that I'm wrong to downvote all my post on this they should be able to tell me where I'm wrong. I would be extremely interested in finding out.

Comment author: Perplexed 02 February 2011 02:23:48AM 0 points [-]

I don't know why you were downvoted. But I do notice that somewhere on this thread, the meaning of "Even World" has changed from what it was when Shokwave introduced the term. Originally it meant a world whose calculator showed 'Even'.