Introduction to Mathematical Philosophy
Offered By: Ludwig-Maximilians-Universität München via Coursera
Course Description
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 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
Introduction to Mathematical ThinkingStanford University via Coursera 機率 (Probability)
National Taiwan University via Coursera 悖论:思维的魔方
Peking University via Coursera 离散数学概论 Discrete Mathematics Generality
Peking University via Coursera Discrete Mathematics
Indian Institute of Technology, Ropar via Swayam