Summer School in Logic and

Formal Epistemology, 2006

Information

This was a three-week summer program for undergrads and beginning graduate students, primarily from philosophy but also from related fields such as math and CS. David Danks led a course on causal inference in the first week, Wilfried Sieg covered computability in the second week, and Horacio Arlo-Costa covered formal epistemology in the third. Below are some teaching materials I produced for the program.

Week 2: Foundations of Computability

During the second week, students broke into two camps; I led a series of sessions on Goedel's incompleteness theorems for those who considered themselves more comfortable with formal methods. I produced slides for the first lecture only, doing much boardwork in the other sessions. These slides give a conceptual overview of Goedel's theorems, and hint at some of the technicalities involved. The concrete instantiation of the theorems to which we point in our exposition is that from the Princeton lectures of 1934.

• Incompleteness and Undecidability (link currently broken)

Week 3: Philosophical Logic

During the third week, I acted as a TA to Professor Arlo-Costa, guiding students through some discussion and exercise sessions. Professor Arlo-Costa had produced a long set of lecture notes (not all of whose material could be covered in the span of a week) which were in large part cobbled together from papers of his. Because of the students' varying backgrounds (especially as regards logico-mathematical matters), I saw fit to produce a few handouts to supplement his lectures. There are some explanatory notes and also solution write-ups to some of the exercises posed to the students.

• These notes try to boil many of the details given in Professor Arlo-Costa's lectures down to the most basic features of relational (Kripke) semantics and neighborhood semantics. Furthermore, I trace the broad outline of the use of canonical models to prove completeness results.
• This note complements the foregoing by illustrating the utility of relational semantics for demonstrating provability in various modal logics, taking an exercise from the course as a case study.
• Here is a brief introduction to belief revision, which goes into some of the nitty gritty about AGM contractions and the related notion of severe withdrawals.
• Finally, these are solutions to some of the assigned exercises.