315 | Branden Fitelson on the Logic and Use of Probability

What It Covers

Philosopher Branden Fitelson explains how probability theory applies to scientific reasoning, distinguishing between objective physical probabilities and epistemic probabilities used to evaluate evidence strength, confirmation, and argument quality across different scientific contexts.

Key Questions Answered

• •Two-Dimensional Argument Strength: Strong arguments require both high probability (conclusion likely given premises) and high relevance (evidence actually changes probability). Diagnostic tests demonstrate this: a pregnancy test for a biologically male person shows high reliability but zero relevance, illustrating why both dimensions matter for rational belief updating.
• •Bayes Factors Over Posteriors: Scientific papers report likelihood ratios (true positive rate divided by false positive rate) rather than posterior probabilities because researchers cannot know readers' prior beliefs. This base factor represents objective, invariant information discoverable in laboratories, while posterior probabilities depend on individual background knowledge and assumptions.
• •Confirmation Versus Probability: Evidence can strongly confirm a hypothesis while leaving it improbable, or weakly confirm while making it highly probable. The base rate fallacy occurs when people confuse these dimensions: rare disease with reliable test yields low probability despite high confirmation, causing systematic reasoning errors in medical and scientific contexts.
• •Falsification Power: Popper's insight about falsification has quantitative validity: seeking counterexamples provides more confirmational power than seeking positive instances. In the Wason selection task, checking the seven card (potential falsifier) is more informative than checking the three card (potential confirmer), though people systematically reverse this ordering due to confirmation bias.
• •Pluralist Bayesian Framework: No single probability function works for all arguments across contexts. Each scientific domain requires constructing appropriate probability models with context-specific assumptions and idealizations. Particle physics generates such powerful likelihood ratios that prior probabilities barely matter, while other sciences remain highly sensitive to priors, requiring explicit model construction for each case.