Morendil comments on My Fundamental Question About Omega - Less Wrong

6 Post author: MrHen 10 February 2010 05:26PM

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Comment author: Morendil 10 February 2010 05:49:19PM *  14 points [-]

Any puzzlement we feel when reading such thought experiments would, I suspect, evaporate if we paid more attention to pragmatics.

The set-up of the scenario ("Suppose that Omega, etc.") presupposes some things. The question "What do you do?" presupposes other things. Not too surprisingly, these two sets of presuppositions are in conflict.

Specifically, the question "What do you do" presupposes, as parts of its conditions of felicity, that it follows a set-up in which all of the relevant facts have been presented. There is no room left to spring further facts on you later, and we would regard that as cheating. ("You will in fact give $5 to Omega because he has slipped a drug into your drink which causes you to do whatever he suggests you will do!")

The presuppositions of "What do you do" lead us to assume that we are going about our normal lives, when suddenly some guy appears before us, introduces himself as Omega, says "You will now give me $5", and looks at us expectantly. Whereupon we nod politely (or maybe say something less polite), and go on our way. From which all we can deduce is that this wasn't in fact the Omega about which the Tales of Newcomb were written, since he's just been shown up as an imperfect predictor.

The presuppositions carried by "Omega is a perfect predictor" are of an entirely different order. Logically, whatever predictions Omega makes will in fact turn out to have been correct. But these presuppositions simply don't match up with those of the "What do you do?" question, in which what determines your behaviour is only the ordinary facts of the world as you know it, plus whatever facts are contained in the scenario that constitutes the set-up of the question.

If Omega is a perfect predictor, all we have is a possible world history, where Omega at some time t appears, makes a prediction, and at some time t' that prediction has been fulfilled. There is no call to ask a "What do you do" question. The answers are laid out in the specification of the world history.

One-boxing is the correct choice in the original problem, because we are asked to say in which of two world-histories we walk away with $1M, and given the stipulation that there exist no world-histories to choose from in wich we walk away with $1M and two boxes. We're just led astray by the pragmatics of "What do you do?".

[EDIT: in case it isn't clear, and because you said you were curious what people thought the obvious answer was, I think the obvious answer is "get lost"; similarly the obvious answer to the original problem is "I take the two boxes". The obvious answer just happens to be the incorrect choice. I have changed the paragraph just previous to say "the correct choice" instead of "the correct answer".

Also, in the previous paragraph I assume I want the $1M, and it is that which makes one-boxing the correct choice. Of course it's presented as a free-will question, that is, one in which more than one possible world-history is available, and so I can't rule out unlikely worlds in which I want the $1M but mistakenly pick the wrong world-history.]

Comment author: Morendil 19 March 2010 11:00:30PM *  2 points [-]

Recording an oops: when I wrote the above I didn't really understand Newcomb's Problem. I retract pretty much all of the above comment.

I'm now partway through Gary Drescher's Good and Real and glad that it's given me a better handle on Newcomb, and that I can now classify my mistake (in my above description of the "original problem") as "evidentialist".