Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Online Course

Introduction to Mathematical Philosophy

Ludwig-Maximilians-Universität München via Coursera


Since antiquity, philosophers have questioned the foundations--the foundations of the physical world, of our everyday experience, of our scientific knowledge, and of culture and society. In recent years, more and more young philosophers have become convinced that, in order to understand these foundations, and thus to make progress in philosophy, the use of mathematical methods is of crucial importance. This is what our course will be concerned with: mathematical philosophy, that is, philosophy done with the help of mathematical methods.

As we will try to show, one can analyze philosophical concepts much more clearly in mathematical terms, one can derive philosophical conclusions from philosophical assumptions by mathematical proof, and one can build mathematical models in which we can study philosophical problems.

So, as Leibniz would have said: even in philosophy, calculemus. Let's calculate.


Week One: Infinity (Zeno's Paradox, Galileo's Paradox, very basic set theory, infinite sets).

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)

Taught by

Hannes Leitgeb and Stephan Hartmann

Related Courses


4.1 rating, based on 7 reviews

Start your review of Introduction to Mathematical Philosophy

  • Anonymous

    Anonymous is taking this course right now.

    The course is no longer available online, is there an opportunity to see it again or release the archived course??
  • Kristina Šekrst completed this course and found the course difficulty to be very hard.

    This is a great course, and the amount of trouble can clearly be seen. I love the fact that the new lectures are being added for the second iteration, and I simply cannot praise enough the booklets that accompanied each lecture. One could just read these...
  • Stephane Mysona completed this course.

  • Stephane Mysona completed this course.

  • Alan Salsac completed this course.

  • Martin Dunn completed this course.

  • Mark Oloughlin

    Mark Oloughlin completed this course.

Never stop learning Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free