# Introduction to Mathematical Philosophy

## Hannes Leitgeb and Stephan Hartmann, Ludwig-Maximilians-Universität München (LMU)

Learn how to apply mathematical methods to philosophical problems and questions.

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)

### Recommended Background

We will not presuppose more than bits of high school mathematics.

We will give you lists of additional references later in the course.

### Course Format

The class will consist of lecture videos, which are between 8 and 15 minutes in length. These contain 1-2 integrated quiz questions per video.

### FAQ

Will I get a Statement of Accomplishment after completing this class?

Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructors.

Dates:
• 27 April 2015, 8 weeks
• 14 April 2014, 8 weeks
• 29 July 2013, 10 weeks
Course properties:
• Free:
• Paid:
• Certificate:
• MOOC:
• Video:
• Audio:
• Email-course:
• Language: English

### Reviews

No reviews yet. Want to be the first?

Register to leave a review

Included in selections:
Mathematics
Calculus, Linear algebra, Functional and Complex Analysis and more

More on this topic:
History and Philosophy of Mechanics: Newton's Principia Mathematica
This course focuses on an in-depth reading of Principia Mathematica Philosophiae...
Classics in Western Philosophy
This course will introduce you to the Western philosophical tradition, through...
Problems in Philosophy
The course has two goals. First, to give you a sense of what philosophers think...
Honors Differential Equations (Spring 2009)
This course covers the same material as Differential Equations (18.03) with...
Proseminar in Philosophy I
An intensive seminar on the foundations of analytic philosophy for first-year...
More from 'Mathematics, Statistics and Data Analysis':
Predictive Analytics Final Project
Apply your predictive modelling acumen in a business case setting. The final...
LAFF – On Programming for Correctness
Learn to apply formal methods to systematically develop correct, loop-based...
Advanced Linear Algebra: Foundations to Frontiers
Learn advanced linear algebra for computing. Linear algebra is one of the fundamental...
Data Analysis in Social Science—Assessing Your Knowledge
Learn the methods for harnessing and analyzing data to answer questions of cultural...
FA20: Introduction to Analytics Modeling
Learn essential analytics models and methods and how to appropriately apply...
More from 'Coursera':
First Year Teaching (Secondary Grades) - Success from the Start
Success with your students starts on Day 1. Learn from NTC's 25 years developing...
Understanding 9/11: Why Did al Qai’da Attack America?
This course will explore the forces that led to the 9/11 attacks and the policies...
Aboriginal Worldviews and Education
This course will explore indigenous ways of knowing and how this knowledge can...
Analytic Combinatorics
Analytic Combinatorics teaches a calculus that enables precise quantitative...
Accountable Talk®: Conversation that Works
Designed for teachers and learners in every setting - in school and out, in...