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Learn how to apply mathematical methods to philosophical problems and questions.
Week Two: Truth (Tarski's theory of truth, recursive definitions, complete induction over sentences, Liar Paradox).
Week Three: Rational Belief (propositions as sets of possible worlds, rational all-or-nothing belief, rational degrees of belief, bets, Lottery Paradox).
Week Four: If-then (indicative vs subjunctive conditionals, conditionals in mathematics, conditional rational degrees of belief, beliefs in conditionals vs conditional beliefs).
Week Five: Confirmation (the underdetermination thesis, the Monty Hall Problem, Bayesian confirmation theory).
Week Six: Decision (decision making under risk, maximizing xpected utility, von Neumann Morgenstern axioms and representation theorem, Allais Paradox, Ellsberg Paradox).
Week Seven: Voting (Condorcet Paradox, Arrows Theorem, Condorcet Jury Theorem, Judgment Aggregation).
Week Eight: Quantum Logic and Probability (statistical correlations, the CHSH inequality, Boolean and non-Boolean algebras, violation of distributivity)
- Hannes Leitgeb - Munich Center for Mathematical Philosophy
- Stephan Hartmann - Munich Center for Mathematical Philosophy
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