Overview

 

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.

 

In 2010, 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, 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 7 to Friday, June 25, 2010. 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 about 30 students in 2010. There are no grades, and the courses do not provide formal course credit.

 

 

Topics

 

The topics in 2010 will be:

 

Logic and Scientific Inquiry

Monday, June 7 to Friday, June 11

Instructor: Clark Glymour

 

Scientific method is about discovering and assessing explanations, and logic has important roles. We will go over some of the classical literature on model theory, finite axiomatizability and quantifier elimination and show how it bears on problems (some of them open formal problems) such as: finding the simplest explanation (by one criterion of simplicity), finding causal explanations, the possibilities and limits of reliable discovery by computer, and adaptations of logic programming to learning. Some probabilistic ideas will be introduced and real examples from neuroscience and elsewhere will be discussed.

 

 

 

 

 

Computability and Foundations

Monday, June 14 to Friday, June 18

Instructor: Wilfried Sieg

 

Computability is perhaps the most significant and distinctive notion modern logic has introduced. In the guise of decidability and effective calculability, it has a venerable history in mathematics and philosophy, but in contemporary discussions it is also the basic theoretical concept for computer science, artificial intelligence and cognitive science. The methodological issues surrounding Church's Thesis prompt a detailed discussion of the evolution of these notions, i.e., decidability, effective calculability and computability. All of them are relative to the capacities of a human agent, who proceeds "mechanically." That insight, basic for Turing's approach to calculability, leads to an axiomatic characterization of computability. This is important for two deeply related issues, namely, the incompleteness of formal theories (that internalize syntax) and the completeness of algorithms (that find proofs efficiently). We will discuss Gödel's incompleteness theorems, Church and Turing's undecidability theorem for predicate logic, and logically and heuristically guided proof search procedures.

 

 

 

 

 

Philosophical Logic and Formal Epistemology

Monday, June 21 to Friday, June 25

Instructor: Horacio Arlo-Costa

 

One of the central problems in formal epistemology is to develop exact formalisms capable of representing knowledge, belief, conditional belief, and belief change. We will consider the modal approach to represent knowledge and belief, which derives from the early work of Hintikka, Kripke and Aumann. We will then consider a semantic alternative to Kripke models deriving from the work of D. Scott and R. Montague in the 60's: neighborhood models. Next, we will review some of the basic building blocks of contemporary Bayesian epistemology. Finally, we will conclude by considering a family of open problems and philosophical puzzles inspired by recent work in formal epistemology. (A more detailed description can be found here.)

 

 

 

 

 

 

How to apply

 

A link to an online application, and instructions as to how to apply, will be posted on this page by the end of December, 2009. The application materials will consist of an online application form, an academic transcript, and a brief letter of reference.

 

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 $20 nonrefundable application fee.

  • All application materials will be due at the Philosophy Department by March 15, 2010.

  • By March 31, 2010, applicants will be informed of the admissions decisions and of other details relating to the Summer School.

  • Applicants who are admitted will be asked to confirm their planned attendance by April 15, 2010.

 

Additional information

 

The summer school was launched in 2006. The National Science Foundation provided substantial funding in 2006 and 2007, and partial funding for 2009 and 2010. You may also view:

Inquiries may be directed to Jeremy Avigad (avigad@cmu.edu).