There is a long tradition of fruitful interaction between philosophy and the sciences. Logic and statistics emerged, historically, from combined philosophical and scientific inquiry into the nature of mathematical and scientific inference; and the modern conceptions of psychology, linguistics, and computer science are the results of sustained reflection on the nature of mind, language, and computation. In today's climate of disciplinary specialization, however, foundational reflection is becoming increasingly rare. As a result, developments in the sciences are often conceptually ill-founded, and philosophical debates often lack scientific substance.


baker hall


In 2015, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, economics, and other sciences. The goals are to

  • introduce promising students to cross-disciplinary fields of research at an early stage in their career; and

  • forge lasting links between the various disciplines.

The summer school will be held from Monday, June 1 to Friday, June 19, 2015. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events.

The summer school is free. That is, we will provide:

  • full tuition

  • dormitory accommodations on the Carnegie Mellon campus

So students need only pay for round trip travel to Pittsburgh and living expenses while here. We expect to be able to accept about 25 students in 2015. There are no grades, and the courses do not provide formal course credit.

The summer school is open to undergraduates, as well as to students who will have just completed their first year of graduate school. Applicants need not be US citizens. There is a $30 nonrefundable application fee.

Applications are due by Friday, March 13, 2015. Please help us spread the word.


Week #1a
(June 1-3)

The Topology of Inquiry
Instructor: Kevin Kelly

The standard mathematical frameworks for understanding reasoning are logic and computability for mathematical reasoning and probability theory for empirical reasoning. In this summer school session, we examine an alternative, topological viewpoint according to which computational and empirical undecidability can both be viewed as reflections of topological complexity. That may sound a bit odd, since topology is usually understood to be "rubber geometry", or the study geometrical relationships preserved under stretching operations that neither cut nor paste pieces together. In fact, topology is better understood as studying the mathematical structure of epistemic verifiability. Topological concepts and results will be applied to provide a unified, explanatory perspective on empirical underdetermination, formal undecidability, and the elusive connection between simplicity and empirical truth.

Week #1b
(June 4-6)
Fifteenth conference on Theoretical Aspects of Rationality and Knowledge

TARK 2015 will take place at the Carnegie Mellon University, Pittsburgh, USA during June 4-6, 2015. The mission of the TARK conferences is to bring together researchers from a wide variety of fields, including Artificial Intelligence, Cryptography, Distributed Computing, Economics and Game Theory, Linguistics, Philosophy, and Psychology, in order to further our understanding of interdisciplinary issues involving reasoning about rationality and knowledge. 

Participants in the CMU Summer School will be invited to attend TARK 2015.


Week #2
(June 8-12)
Reasoning About Information
Instructor: Adam Bjorndahl

Three friends sit down to play the following game: They will each receive either a red hat or a blue hat, and the winner is the first person to guess the colour of their own hat (each player can see their opponents’ heads, but not their own). There is only one rule: each player must raise their hand if (and only if) they see a red hat.

The game begins and each player gets a red hat; of course, they all raise their hands. After a long moment of silence, one player shouts, “Red!” and wins the game. How did she figure it out?

Solving this little puzzle is fun, but there’s a deeper mystery lurking behind it: Was it really important that the players raise their hands? After all, since each player can see two red hats, each knew in advance that their friends would raise their hands.

In this summer school session, we’ll develop logics of knowledge and belief and use them to give a precise account of exactly what new information is gained when the players raise their hands. We’ll then turn to investigate a variety of other puzzles and “paradoxes”—including the muddy children puzzle, the two generals’ problem, Aumann’s agreement theorem, the three prisoners problem, and the infamous Monty Hall problem—developing the logics as we go.


Week #3
(June 15 - 19)
An Introduction to Decisions with Imprecise Probabilities [IP]
Instructor: Teddy Seidenfeld

  • How to understand a decision maker’s uncertainty?

One variety of choice problem is with a single decision maker, YOU. Consider what follows from the simple, prudential consideration that YOU should not expose YOURSELF to sure-losses. A second variety of choice is in decision problems involving multiple decision makers (who may have competing goals with YOUR own), and to consider what follows from the equally simple prudential consideration that YOU should not play the game in a way that allows the opponents to make YOU worse off than you might be by playing differently, particularly when they benefit at YOUR expense by doing so. A third variety of decision problem involves a group of cooperative decision makers who have the ability to coordinate their individual choices and agree they should not act in such a fashion that, under an alternative plan available to them, each would do strictly better.

The central topic for this week’s summer school is to explore how probability may be used to model a decision maker’s uncertainty from within each of these three perspectives, subject to the criterion that the decision maker avoids sure loss in each of the three forms identified above. The emphasis throughout is to understand what aspects of a decision maker’s uncertainty are better represented using a set of probabilities – IP Theory – in contrast with the canonical Bayesian framework of Subjective Expected Utility theory, where only one probability distribution is used to model a decision maker's uncertainty.

  • How does IP theory improve decision making?


How to apply

The deadline for 2015 applications has passed. Please check back next year.

Additional information

The Information page provides information about travel, accommodations, schedule, etc.


Summer School History

The summer school was launched in 2006. The National Science Foundation provided substantial funding in 2006 and 2007, and partial funding for 2009, 2010 and 2011.


Contact Information

The summer school is directed by Teddy Seidenfeld.

Inquiries may be directed to teddy[at]stat[dot]cmu[dot]edu.