In 2013, 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 3 to Friday, June 21, 2013. 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:

The Topology of Inquiry

Monday, June 3 to Friday, June 7

Instructor: K.T. Kelly
Email: kk3n[at]andrew[dot]cmu[dot]edu

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.

Background Reading:
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.

 

 

 

 

 

An Introduction to the theory of Rational Choice: Games and Decisions

Monday, June 10 to Friday, June 14

Instructor: Teddy Seidenfeld
Email: teddy[at]stat[dot]cmu[dot]edu
Office: Baker Hall 135-J

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.

 

 

 

Graphical Causal Models

Monday, June 17 to Friday, June 21

Instructor: Richard Scheines
Email: scheines[at]cmu[dot]edu

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." 

Background Reading:
1) A long and interactive introduction to the pre-cursor concepts for graphical causal models is available at:
https://oli.web.cmu.edu/openlearning/forstudents/freecourses/59
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."