This post focuses on philosophical objections to Bayesianism as an epistemology. I first explain Bayesianism and some standard objections to it, then lay out my two main objections (inspired by ideas in philosophy of science). A follow-up post will speculate about how to formalize an alternative.

Degrees of belief

The core idea of Bayesian epistemology: we should ideally reason by assigning credences to propositions which represent our degrees of belief that those propositions are true. (Note that this is different from Bayesianism as a set of statistical techniques, or Bayesianism as an approach to machine learning, which I don’t discuss here.)

If that seems like a sufficient characterization to you, you can go ahead and skip to the next section, where I explain my objections to it. But for those who want a more precise description of Bayesianism, and some existing objections to it, I’ll more specifically characterize it in terms of five subclaims. Bayesianism says that we should ideally reason in terms of:

Propositions which are either true or false (classical logic)
Each of which is assigned a credence (probabilism)
Representing subjective degrees of belief in their truth (subjectivism)
Which at each point in time obey the axioms of probability (static rationality)
And are updated over time by applying Bayes’ rule to new evidence (rigid empiricism)

I won’t go into the case for Bayesianism here except to say that it does elegantly formalize many common-sense intuitions. Bayes’ rule follows directly from a straightforward Venn diagram. The axioms of probability are powerful and mathematically satisfying. Subjective credences seem like the obvious way to represent our uncertainty about the world. Nevertheless, there are a wide range of alternatives to Bayesianism, each branching off from the claims listed above at different points:

Traditional epistemology only accepts #1, and rejects #2. Traditional epistemologists often defend a binary conception of knowledge—e.g. one defined in terms of justified true belief (or a similar criterion, like reliable belief).
Frequentism accepts #1 and #2, but rejects #3: it doesn’t think that credences should be subjective. Instead, frequentism holds that credences should correspond to the relative frequency of an event in the long term, which is an objective fact about the world. For example, you should assign 50%

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