> The word ‘Bayesianism’ is used for a variety of things, a whole spectrum of things at one end of which I have no quarrel with whatsoever and at the other end of which I think is just plain inductivism. So at the good end, Bayesianism is just a word for using conditional probabilities correctly. So if you find that your milkman was born in the same small village as you, and you are wondering what kind of a coincidence that is, and so on, you've got to look at the conditional probabilities, rather than the absolute probabilities. So there isn't just one chance in so many million, but there's a smaller chance.
His problem seems to be the extension of it to epistemology:
> At the other end of the spectrum, a thing which is called Bayesianism is what I prefer to call ‘Bayesian epistemology’, because it's the epistemology that's wrong, not Bayes’ theorem. Bayes’ theorem is true enough. But Bayesian epistemology is just the name of a mistake. It's a species of inductivism and currently the most popular species. But the idea of Bayesian epistemology is that, first of all, it completely swallows the justified true belief theory of knowledge.
His problem with inductivism is that when you follow it you don't try to make theories more believable by getting rid of ones that don't fit, but by confirming instances in which your theory does fit:
> It's inductivism with a particular measure of how strongly you believe a theory and with a particular kind of framework for how you justify theories: you justify theories by finding confirming instances. So that is a mistake because if theories had probabilities – which they don’t – then the probability of a theory (‘probability’ or ‘credence’, in this philosophy they’re identical, they’re synonymous)... if you find a confirming instance, the reason your credence goes up is because some of the theories that you that were previously consistent with the evidence are now ruled out.
> And so there's a deductive part of the theory whose credence goes up. But the instances never imply the theory. So you want to ask: “The part of the theory that's not implied logically by the evidence – why does our credence for that go up?” Well, unfortunately it goes down. And that's the thing that Popper and Miller proved in the 1980s. A colleague and I have been trying to write a paper about this for several years to explain why this is so in more understandable terms.
He cites this paper as an example of a proof, but claims it isn't very approachable (which is why he is working on one with more understandable terms).