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Online Course

Introduction to Mathematical Philosophy

Ludwig-Maximilians-Universität München via Coursera

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Overview

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.

Syllabus

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

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Reviews for Coursera's Introduction to Mathematical Philosophy Based on 7 reviews

  • 5 stars 57%
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  • 3 stars 43%
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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??
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Kristina Š
by Kristina 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 tutorials and feel like it's a lecture on its own. The only critique I have of this course is the lack of quizzes, since it's easy to fall behind, but the instructors preferred to stay within the traditional approach, as they have explained in the last video entry. Even though there are no quizzes, there are lots of problems to solve, and there are active discussion forums, so that fixes things a bit. This course gives a great blend of mathematics and philosophy, but it relies more heavily on the mathematical part and proofs, so this is a simple caveat.

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Stephane M
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