In 2011, 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 6 to Thursday, June 23, 2011. 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:

Rational Choice
Monday, June 6 through Friday, June 10
Instructor: T. Seidenfeld
Assisting: Hailin Liu

How to choose rationally? One perspective on a choice problem is to frame it with a single decision maker, You, and to consider what follows from the simple, prudential consideration that You should not pass up sure-gains. That is, You should not choose option 1 if You are sure to do better under option 2 regardless which state of nature obtains. Another perspective on choice is to frame a problem as 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 permit the opponents to take advantage of You. That is, 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. These two perspectives on how to choose are not exclusive. A decision problem where You are uncertain about which state of nature obtains can be converted into a 2-person (zero-sum) game where You play against Nature. In this component of the summer school, we will examine decision theory and game theory in order to understand what each has to teach us about choosing rationally.

Lecture Slides:
Agenda: An Introduction to Rational Choice Theory
Sessions 1 - 3
Sessions 4 - 6
Sessions 7 - 9
Bibliography

 

 

 

 

 

 

 

 

 

 

 

An Introduction to Ramsey Theory

Thursday, June 16; 6:00 - 7:30 PM

Instructor: T. Seidenfeld

 

While working on the decision problem for first order logic, Frank Ramsey [1930] developed a combinatorial approach that now bears his name. For one example of his idea, imagine that we construct an undirected graph on K-many nodes, connecting each pair of nodes with edges of one of two colors, red or blue. How many nodes K3,2 does it take to insure that, no matter how we color the graph, there will be a trio of points each connected by the same color? How large do we need to make K to guarantee a homogeneous subgraph of 3 nodes in 2 colors? K = 5 will not do, as this picture reveals. In this introduction we will consider some fundamental theorems of Ramsey Theory.

A 2-coloring of 5 nodes with no homogeneous subgraph of 3 nodes.

Mathematical modeling of social behavior

Monday, June 13 to Friday, June 17

Instructor: K. Zollman

 

Philosophers and social scientists have long been interested in understanding the dynamics of social behavior. How could conventional language emerge when there is no preexisting language? How could cooperative institutions form out of the "state of nature"? How is it that groups of scientists can come to know so much about nature? In the last sixty years, many scholars have turned to utilizing mathematical and computer models to answer these and related questions. This summer school session will look at several applications of these methods to understanding problems in philosophy, economics, sociology, anthropology, and evolutionary biology.

 

 

 

 

 

The Topology of Inquiry

Monday, June 20 to Thursday, June 23

Instructor: K.T. 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 undecidability, on empirical underdetermination, on bounded rationality, and on the elusive connection between simplicity and empirical truth.