The Conjunction Problem
Deutsch also offers a separate, more intuitive argument: 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)
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)