Arguments Against Bayesian Epistemology
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With an account, you can revise, criticize, and comment on ideas.The Conjunction Problem
Deutsch also offers an argument against Bayesian epistemology: take quantum mechanics and general relativity, our two best physics theories. They contradict each other.
- T₁ = quantum mechanics
- T₂ = general relativity
Both are spectacularly successful. A Bayesian should assign high credence to each. But T₁ and T₂ contradict each other, and probability theory is absolute about contradictions:
p(T₁ ∧ T₂) = 0
Zero. The combined understanding that lets us build GPS satellites, which need both relativity for orbital corrections and quantum mechanics for atomic clocks is worth literally nothing under the probability calculus.
Meanwhile, the negation ¬T₁ ("quantum mechanics is false") tells you nothing about the world. It's the infinite set of every possible alternative, mostly nonsensical. Yet the probability calculus ranks it higher than the theory that lets us build lasers and transistors.
A framework that assigns zero value to our best knowledge is, Deutsch argues, not capturing what knowledge actually is. Instead: "What science really seeks to ‘maximise’ (or rather, create) is explanatory power." (Deutsch, "Simple refutation of the 'Bayesian' philosophy of science," 2014)
Bayesian epistemology never said contradictory theories are useful together. It says they can't both be true simultaneously, and they can't. That's why physicists are looking for a unified theory. p(T₁ ∧ T₂) = 0 is the correct answer. It would be a bug if it were anything else."