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

• 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 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 provide:

Graphical Causal Models

Monday, June 4 to Friday, June 8

Instructor: Richard Scheines

 

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."

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.