Advanced Logic (350-0-21)

Topic

Completeness & Consequences: Philosophy & Model Th

Instructors

Sean Christopher Ebels Duggan
847/491-2553
Kresge 3-443

Meeting Info

Kresge Centennial Hall 2-415: Tues, Thurs 11:00AM - 12:20PM

Overview of class

This course will explore foundational results in metalogic: the mathematical theory of logics. In particular, we will look at (and prove, in detail) the foundational results relating the languages of first-order logic and interpretations of those languages. These results are: Gödel's completeness theorem, the compactness theorem, and the Löwenheim-Skolem theorems. We will also explore some philosophical questions concerning corollaries of these theorems, including Putnam's model-theoretic arguments against realism, Benacerraf's arguments that numbers cannot be objects, the existence of non-standard models of arithmetic, and the consistency of infinitesimal quantities.

Prerequisites: PHIL 150 or MATH 300 or PHIL 250

Registration Requirements

Prerequisites: PHIL 150 or MATH 300 or PHIL 250

Learning Objectives

Acquire facility with formal methods sufficient to explore the model-theoretic approach to logic, and be able to make clear and informed philosophical judgments about those results and their implications.

Evaluation Method

Most of the assessment will be by problem sets to explore formal methods, and short response papers to address philosophical questions. The final assessments will be a short philosophical paper, and a final exam concerning formal methods.

Class Materials (Required)

Class materials must be purchased.

Tim Button and Sean Walsh, Philosophy and Model Theory

Class Notes

Enrollment Requirements

Enrollment Requirements: Registration is reserved for Philosophy PhD Graduate Students Prerequisite: Students must have completed either PHIL 250 or MATH 300 in order to enroll in this course.