Coursera: Introduction to Mathematical Philosophy

This week I started my second Coursera course: Introduction to Mathematical Philosophy.

It actually started a couple of weeks ago so I need to catch up. I’ve only done the first week but am already finding it both mentally stimulating and sort of funny.

Here’s what I’ll learn:

  1. Infinity (Zeno’s Paradox, Galileo’s Paradox, very basic set theory, infinite sets)
  2. Truth (Tarski’s theory of truth, recursive definitions, complete induction over sentences, Liar Paradox)
  3. Rational Belief (propositions as sets of possible worlds, rational all-or-nothing belief, rational degrees of belief, bets, Lottery Paradox)
  4. If-then (indicative vs subjunctive conditionals, conditionals in mathematics, conditional rational degrees of belief, beliefs in conditionals vs conditional beliefs)
  5. Confirmation (the underdetermination thesis, the Monty Hall Problem, Bayesian confirmation theory)
  6. Decision (decision making under risk, maximizing expected utility, von Neumann Morgenstern axioms and representation theorem, Allais Paradox, Ellsberg Paradox)
  7. Voting (Condorcet Paradox, Arrows Theorem, Condorcet Jury Theorem, Judgment Aggregation)
  8. Quantum Logic (orthocomplemented lattices, projections, Gleason’s Theorem, probability and logic)