Monday, October 25, 2021

A quick argument against subjective Bayesianism

  1. You should assign a prior probability less than 1/2 to the hypothesis that over the lifetime of the universe there were exactly 100 tosses of a fair coin and they were all heads.

  2. The hypothesis in (1) is contingent.

  3. If there is a contingent hypothesis to which you should assign a prior probability less than 1/2, then subjective Bayesianism is false.

  4. So, subjective Bayesianism is false.


Avi said...

I think fair coin in context assumes some kind of objective probability. Can you define it in a way consistent with subjective Bayesianism that still makes the whole argument work?

Alexander R Pruss said...

Think of it as physical chances. If subjective Bayesianism cannot make sense of physical chances, and cannot evaluate the probabilities of various hypotheses about physical chances (e.g., the probability of the Born rule being true in QM), then subjective Bayesianism is dead in the water.

Avi said...

Not so sure about that. My own flavor of subjective Bayesianism + verificationism would say "the probability of the Born rule being true in QM" does not, strictly speaking, exist; and in fact "the Born rule being true" is meaningless. What is meaningful is the probability distribution implied by the Born rule for what it predicts for our future experiences. You can simplify that into a hypothesis that says "all our future experiences will be roughly consistent with the Born rule" and assign that some probability, but it's meaningless to say that that hypothesis being true means the Born rule is somehow true in some physical sense.

You can give probabilities over any set of future experiences, and you can use physics as a simplification over such probabilities.

In this context you can define fair coin as something that you have a subjective expectation would have the relevant distribution of heads and tails. But that is not enough to make your argument go through.

I don't think this general worldview is dead in the water, and I probably haven't given enough details here to explain how I'd handle all edge cases, but so far I haven't found any strong objections.

Alexander R Pruss said...

So, on this view, QM, considered as a conjunction of its propositions, is either meaningless or enables no predictions. For either the Born rule is a conjunct of QM, in which case QM is meaningless, or else QM is understood not to include the Born rule, and hence enables no predictions.

This isn't a refutation, though it does suggest a reason to be suspicious of the story.

Avi said...

"QM is true" is meaningless, "Our observations will follow the Born rule as per QM" is meaningful. In regular conversation we might use the former to mean the latter, though.

My issue with statements like the former that are not merely taken as the latter is precisely that they don't enable any predictions. There is no meaning to saying it is true, above and beyond the predictions made by it.

By the same token "this is a fair coin but it was already flipped 100 times and will never be flipped again" is not meaningful (aside from predicting that it won't be flipped, or perhaps an implied prediction that an examination won't find it to be weighted more on one side).

Part of the motivation for this worldview is multiverse theories. If you accept that for basically any claim like this it's going to be "true" in some portions of the Level IV multiverse and "false" in other portions (and assume some other claims about personal identity) then it becomes meaningless to talk about truth and falsity in absolute terms. There is only probability over observations.

Alexander R Pruss said...

I agree that abundant multiverse theories fit poorly with objective chances. I conclude that it's so much the worse for abundant multiverse theories.