### Top 50 MOOCs

Get started with custom lists to organize and share courses.

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

# Introduction to Mathematical Philosophy

6 Reviews 287 students interested

Taken this course? Share your experience with other students. Write review

## 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

## Reviews for Coursera's Introduction to Mathematical Philosophy 4.0 Based on 6 reviews

• 5 stars 50%
• 4 star 0%
• 3 stars 50%
• 2 star 0%
• 1 star 0%

Did you take this course? Share your experience with other students.

• 1
Alan S
3.0 4 years ago
by completed this course.
Anonymous
5.0 2 years ago
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??
Stephane M
5.0 3 years ago
by completed this course.
Mark O
3.0 2 years ago
completed this course.
Martin D
3.0 3 years ago
by completed this course.
Stephane M
5.0 3 years ago
by completed this course.