Truthlikeness and Verisimilitude: Measuring Distance from Truth
Why Popper's elegant definition of verisimilitude collapsed and how possible worlds rescued the concept of approximate truth
Defeasible Reasoning: Non-Monotonic Logic for Uncertain Inference
Why rational inference requires conclusions that can be withdrawn
Carnap's Inductive Logic: The Dream of Algorithmic Rationality
Why Carnap's quest to make inductive reasoning purely logical revealed the irreducible role of judgment in rational inference.
The Ramsey Test: Conditionals Through Belief Revision
How Ramsey's elegant test for conditionals encountered impossibility theorems and forced formal epistemologists to choose which intuitions to preserve
Higher-Order Probability: Can You Have Beliefs About Your Own Uncertainty?
The formal epistemology of uncertainty about uncertainty—when and why rational agents doubt their own beliefs.
The Lottery Paradox: Why Knowledge Isn't Just High Probability
Kyburg's paradox proves that no probability threshold can ground rational belief without violating basic logical closure—formal epistemology must choose its casualties.
Dempster-Shafer Theory: When Probability Isn't Enough for Uncertainty
Beyond probability distributions lies a formal framework for genuine ignorance—when your evidence supports possibilities without choosing between them.
AGM Theory: The Logic of Belief Revision
How rationality postulates constrain the logic of changing your mind—and why probability alone cannot capture belief revision.
Imprecise Probabilities: Embracing Indeterminacy in Rational Belief
When evidence fails to determine exact probabilities, credal sets formalize rational humility about belief—with surprising consequences for learning and decision.
Why Probability Can't Escape Philosophy: The Hidden Assumptions Behind Every Bayesian Model
Every Bayesian calculation inherits philosophical commitments about probability's meaning, prior selection, and rationality that mathematics presupposes but cannot prove.
Conditionalization and Its Rivals: When Should You Update Your Beliefs?
Master the formal criteria for choosing between Bayesian conditionalization, Jeffrey updating, and imaging based on your evidential context.
The Conjunction Fallacy Revisited: What Formal Epistemology Says About Human Reasoning
The famous proof of human irrationality may reveal more about experimental interpretation than cognitive limitation.
Scoring Rules and Epistemic Utility: A Mathematical Theory of Accuracy
How mathematical scoring rules reveal that probabilistic coherence is the only path to guaranteed accuracy—no betting required.