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Sarokrae 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: Sarokrae 18 October 2011 11:50:36AM 2 points [-]

Digging up an old thread here, but an interesting point I want to bring up: a friend of mine claims that he internally assigns probability 1 (i.e. an undisprovable belief) only to one statement: that the universe is coherent. Because if not, then mnergarblewtf. Is it reasonable to say that even though no statement can actually have probability 1 if you're a true Bayesian, it's reasonable to internally establish an axiom which, if negated, would just make the universe completely stupid and not worth living in any more?

Comment author: grouchymusicologist 18 October 2011 01:35:36PM 0 points [-]

No, it's not. It's the same fundamental mistake that a lot of religious rhetoric about "faith" and "meaning" is founded on: that wanting something to be true counts as evidence that it is true. There's no reason to think that the universe depends for any of its properties on whether someone finds it stupid or not, or worth living in.

I'd also suggest you try to draw your friend out a bit on what it means exactly for the universe to be "coherent." Can that notion be expressed formally? What would we expect to see if we lived in an incoherent universe?

Obviously, I'm dubious that the "coherence" of the universe is in any proper sense a philosophical or scientific idea -- it sounds a lot more like an aesthetic one.

Comment author: Sarokrae 18 October 2011 03:30:34PM *  0 points [-]

I think he just means "coherent" as "one which we can actually model based on our observations", i.e. one in which this whole exercise (rationality) makes any sense.

He expects that the universe be incoherent with probability zero, and doesn't think there would be any sensible observations if this were the case (or any observation being possible if this were the case).

ETA: Merriam-Webster Definition of COHERENT

1 a : logically or aesthetically ordered or integrated : consistent <coherent style> <a coherent argument> b : having clarity or intelligibility : understandable <a coherent person> <a coherent passage>

So, understandable and consistent: a universe which philosophy, mathematics and science can apply to in any meaningful way.

Comment author: Alejandro1 18 October 2011 03:41:19PM 0 points [-]

A charitable paraphrase of "The universe is coherent" could be a statement of the universal validity of non-contradiction: For every p, not (p and not p). However, given the existence of paraconsistent logic and philosophers who take dialethism seriously, I cannot assign probability 1 to the claim that no aspect of the universe requires a contradiction in its description.

I would go even further to say that I am quite more certain of many other claims (such as "1+1=2" and "2+2=4") than of such general and abstract propositions as "the universe is coherent" or even "there are no true contradictions".

Comment author: Sarokrae 18 October 2011 03:51:08PM *  0 points [-]

I don't think he goes quite that far - he assigns no statements probability 0 or 1 within our own logic system, even (P and ¬P), because he believes it to be possible (though not very likely) that some other logic system might supersede our own.

His belief is that it is not possible for ALL systems of logic to be incorrect, i.e. that (it is impossible to reason correctly about the universe) is necessarily false.

Comment author: nshepperd 18 October 2011 04:52:06PM 1 point [-]

There's a lot of logic to that. For extremely unlikely possibilities you can often get away with setting their probability to 0 to make the calculations a lot simpler. For possibilities where predicted utility is independent of your actions (like "reality is just completely random") it can also be worthwhile setting their probability to 0 (ie. ignoring them), since they're approximately a constant term in expected utility. These are good ways of approximating actual expected utility so you can still mostly make the right decisions, which bounded rationality requires.

Comment author: RichardKennaway 18 October 2011 06:19:54PM 0 points [-]

What is P(A|A)?

Comment author: Sarokrae 18 October 2011 10:02:23PM 0 points [-]

What do you mean by "|A"? It's well-defined in mathematics, sure, but in real life, surely the furthest you can go is "|experience/perception of evidence for A".

Also, there's also the probability that the particular version of logic you're using is wrong.

Comment author: [deleted] 18 October 2011 10:40:59PM 0 points [-]

What do you mean by "|A"? It's well-defined in mathematics, sure, but in real life, surely the furthest you can go is "|experience/perception of evidence for A".

How far you can go depends on what you mean by "go".

It's perfectly possible to calculate, say, P(I see the coin come up heads | the coin is flipped once, it is fair, and I see the outcome), and actually much more difficult to calculate P(I see the coin come up heads | I have experience/perception of evidence for the facts that the coin is flipped once, it is fair, and I see the outcome).

Comment author: Sarokrae 19 October 2011 07:36:30AM *  0 points [-]

"I see" is what I meant by perception/experience of evidence. Whenever I "see" something, there's always a non-zero chance of my brain deceiving me. The only thing you can really have to base your decisions on is P(I see the coin come up heads | I see/know the coin is flipped once, I know it is fair, and I see the outcome). P(the coin comes up heads|the coin is flipped once, it is fair and I know the outcome) is possible and easy to calculate, but not completely accurate to the world we live in.