Note: this is the web page for the 2010 program. For the current web page, click here.
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
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
So students need only pay for round trip travel to Pittsburgh and
living expenses while here. We expect to be able to accept about 30
students in 2010. There are no grades, and the courses do not
provide formal course credit.
Applications are due by March 15, 2010. Please help us
spread the word. There is a flyer that
is suitable for distributing, framing, or hanging on an office door,
and a plain-text announcement.
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 Arló-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
How to apply
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.
The application materials include an online application form,
an academic transcript, and a brief letter of reference.
All the materials are due 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.
Go to https://www.applyweb.com/apply/cmugphil/
and create an account.
Then, from the main menu, choose "Online application for graduate
admission." (We realize that this is confusing.)
From the next screen, choose "Summer School in Logic and Formal
Follow the instructions after that. (The "Personal Research
Statement" can be short and informal. Just tell us about your
academic interests, and some of the things you have done and
hope to do.)
If you enter information about the person writing you a
letter of recommendation, then, when you submit the
application, the system will automatically e-mail that person a
request for a letter and instructions as to how to upload it.
Note that you can begin the application at any time, and return to
it later on.
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:
The summer school is directed by Jeremy Avigad and David
Danks. Inquiries may be directed to Jeremy Avigad