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Lumifer comments on 0 And 1 Are Not Probabilities - Less Wrong

34 Post author: Eliezer_Yudkowsky 10 January 2008 06:58AM

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Comment author: Lumifer 20 August 2015 05:18:06PM *  0 points [-]

It seems that EY position boils down to

Pragmatically speaking, the real question for people who are not AI programmers is whether it makes sense for human beings to go around declaring that they are infinitely certain of things. I think the answer is that it is far mentally healthier to go around thinking of things as having 'tiny probabilities much larger than one over googolplex' than to think of them being 'impossible'.

And that's a weak claim. EY's ideas of what is "mentally healthier" are, basically, his personal preferences. I, for example, don't find any mental health benefits in thinking about one over googolplex probabilities.

Comment author: Wes_W 20 August 2015 05:27:16PM *  0 points [-]

Cromwell's Rule is not EY's invention, and relatively uncontroversial for empirical propositions (as opposed to tautologies or the like).

If you don't accept treating probabilities as beliefs and vice versa, then this whole conversation is just a really long and unnecessarily circuitous way to say "remember that you can be wrong about stuff".

Comment author: EHeller 20 August 2015 05:44:34PM 2 points [-]

The part that is new compared to Cromwell's rule is that Yudkowsky doesn't want to give probability 1 to logical statements (53 is a prime number).

Because he doesn't want to treat 1 as a probability, you can't expect complete sets of events to have total probability 1, despite them being tautologies. Because he doesn't want probability 0, how do you handle the empty set? How do you assign probabilities to statements like "A and B" where A and B are logical exclusive? (the coin lands heads AND the coin lands tails).

Removing 0 and 1 from the math of probability breaks most of the standard manipulations. Again, it's best to just say "be careful with 0 and 1 when working with odds ratios."

Comment author: Lumifer 20 August 2015 05:48:30PM 1 point [-]

Nobody is saying EY invented Cromwell's Rule, that's not the issue.

The issue is that "0 and 1 are not useful subjective certainties for a Bayesian agent" is a very different statement than "0 and 1 are not probabilities at all".

Comment author: Wes_W 20 August 2015 06:05:37PM *  0 points [-]

You're right, I misread your sentence about "his personal preferences" as referring to the whole claim, rather than specifically the part about what's "mentally healthy". I don't think we disagree on the object level here.