Note: this is the web page for the 2012 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 2012, 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
The summer school will be held from Monday, June 4 to
Thursday, June 21, 2012. 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 25
students in 2012. 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 16, 2012. 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.
Graphical Causal Models
Monday, June 4 to Friday, June 8
Instructor: Richard Scheines
TA: Lizzie Silver
In the late 1980s and early 1990s, philosophers, computer scientists, and statisticians developed a graph theoretic representation of causal systems, which, when connected to probability through a few simple axioms, broke down a century of statistical dogma characterized by the slogan: "correlation isn't causation." This representation, called
"graphical causal models," or "causal Bayes nets," has produced an explosion of rigorous work on topics such as:
a) when are causal structures empirically (in)distinguishable,
b) are there tractable algorithms for searching an astronomically large space of causal structures,
c) can these algorithms be proved reliable, and in what sense?,
d) is it possible to tell if a "causal" parameter can be estimated from data, even if the model is unknown,
e) can we compute the shortest sequence of experiments required to identify causal structure, even in the presence of unmeasured, or hidden variables, and
f) can we characterize when ordinary regression analysis can be used to get at causal hypotheses.
In this week, I will gently introduce graphical causal models, show how they provide a unified representation for causal modeling in disciplines as diverse as economics, biology, sociology, psychology, and educational research, and touch on each of the topics above. By extensive use of Tetrad (state-of-the-art causal modeling software) and the Causality Lab
(educational software to simulate empirical research on causal questions), we will learn "hands-on" exactly how much more there is to the topic of causation than "correlation is not causation."
1) A long and interactive introduction to the pre-cursor concepts for
graphical causal models is available at:
Choose "Peek-In" - and browse through the course material.
2) Several overview papers are available on my web-site:
http://www.hss.cmu.edu/philosophy/scheines/cv.htm under the section:
"Causation and Statistics-Reviews/Handbook/Encyclopedia Articles."
A particularly gentle, but dated, introduction is the paper "An
Introduction to Causal Inference."
Logic and Philosophy of Science
Monday, June 11 to Friday, June 15
Instructor: Clark Glymour
In the 1950s, William Craig proved a theorem ("On Reaxiomatization within a System") that suggested to some philosophers that scientific theories are unnecessary. Although famous for his account of scientific explanation, Carl Hempel responded that we need theories to provide "inductive power." Other philosophers had a different response. One of the standard themes in philosophy of science is "inference to the best explanation" (but what that means has never been clear). 20th century philosophers proposed a number of criteria: deducibiity of phenomena, testability (Popper), finite axiomatizability (Davidson and others), informativeness, and so on.
This philosophical literature motivates a logical problem which we will answer in this week. Along the way, students will learn about (or review): some elementary model theory; first order number theory; recursive and recursively enumerable sets and their first order representations; independence; Craig's theorem; Kleene's finite axiomatizability theorem and Craig and Vaught's generalization of it.
The Topology of Inquiry
Monday, June 18 to Thursday, June 21
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.
1) "The Logic of Success"
British Journal for the Philosophy of Science, special millennium issue, 51, 2001, 639-666.
2) Several overview papers are available on my web-site:
(with O. Schulte) "Church's Thesis and Hume's Problem," in Logic and Scientific Methods, M. L. Dalla Chiara, et al., eds. Dordrecht: Kluwer, 1997, pp. 383-398.
3) "Justification as Truth-finding Efficiency: How Ockham's Razor Works", Minds and Machines 14: 2004, pp. 485-505.
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 $30 nonrefundable application fee.
Application materials include an online application form,
an academic transcript, and a brief letter of reference.
All materials are due by Friday March 16, 2012.
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, when you submit the
application, the system will automatically e-mail that person a
requesting a letter and providing instructions for uploading it.
Note that you can begin the application at any time, and return to
Please remember that all materials are due by Friday March 16, 2012.
By Friday March 30, 2012, 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 Friday April 13, 2012.
Please see the Information page to find out about travel, accommodations, schedule, etc.
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. You may also view:
The summer school is directed by Teddy Seidenfeld.
Inquiries may be directed to teddy[at]stat[dot]cmu[dot]edu.