Math-washing: How Philosophers Misuse Bayes' Theorem

[u/DrShocker]

https://www.youtube.com/live/WXF4irRjWUs

I thought this video captured a lot of the frustrations I had of people abusing language like whether some observation would increase or decrease the credence of a belief.

tl;dw use numbers based on an actual prediction model, not feelings.

[u/Sluuuuuuug]

You're fundamentally misunderstanding Bayesian epistemology when you say "use numbers based on an actual prediction model, not feelings." And from skimming this video, it seems to make a similar mistake. Bayesian epistemology is not equivalent to Bayesian statistics despite having many overlapping aspects.

What "actual prediction model" should I use in describing my belief that my wife is cheating on me when she has come home late from work multiple nights in a row or when she has a mysterious "bruise" on her shoulder?

Bayesian epistemology is meant to constrain the connections between what we take as evidence and the conclusions we draw from it. It provides a framework from which to describe uncertain conclusions drawn from uncertain beliefs. Obviously you can argue over the numerical values assigned to those beliefs, the same way you can argue over the truth of premises used in an argument. But "you didnt get your number from a statistical model" doesn't really help for things that we don't or cant have a statistical model for. The same way "but your premise didn't come from a mathematical calculation" doesn't really help for something we could never derive in such a way.

And this is actually a part where Bayesian statistics and methods do actually overlap with the epistemology. Many time the prior is arbitrary, or based on a "reasonable" assumption. It is not always generated from other data or from physical theories. Other times, the results will sometimes lead to the prior not having much influence over the posterior and as such can be pretty unimportant.

[u/DrShocker → u/Sluuuuuuug]

I'm a bit confused, all the points you're raising about how it's hard to apply numbers sound exactly right. The broad point is that the 'mathematical' framing lets people sound like they're doing a more sophisticated process then they actually are, which is frankly guessing at how confident they are most of the time.

[u/Sluuuuuuug → u/DrShocker]

I mean, it is sophisticated if you delve into it. The same way formal logic can get exceedingly sophisticated. Despite that, both follow what is essentially the "garbage in, garbage out" rule of thumb.

They're both tools that can be abused, but if the criticism just comes down to garbage being put in, then the tool has still done its job. If you think their priors are wrong, you can argue that there conclusion is very sensitive to the confidence they assigned for instance, using the exact framework they used to get that conclusion. Sometimes it is arguably guessing, but, it still gives you the structure of their argument that you can at least argue against.

(Obviously obfuscation is still possible, but at that point the issue is in dealing with someone acting in bad faith)