# Phil 140B

## Intermediate Logic

**Fall 2016**

**Professor Paolo Mancosu**

**Office:** 230 Moses Hall. Tel. 296-4325.

**Office hours: TBA **

**Email:** mancosu@socrates.berkeley.edu

**Lecture:** T, Th 11.00-12.30,

**GSI:** James Walsh, jameswalsh@berkeley.edu

**Office hours: TBA **

**Sections:**

TBA

## Description

This course covers the most important metalogical results that are of interest to philosophers. It is divided into three parts. The first two parts are mathematical in style whereas the last part is philosophical. In the first part we will cover the basic notions of computability theory and study in detail the Turing machine approach to computability. The second part of the course will give a detailed presentation of Gödel’s incompleteness theorems and related results. incompleteness theorems. Finally, we will look at the philosophical relevance of these logical results to various areas of philosophy.

**Prerequisite:** 12A (or equivalent) or permission from the instructor.

**Course requirements:** exercise sets approximately every ten days (counting for 60% of final grade) and a philosophical paper due at the end of the semester (40% of final grade).

## Textbooks:

Boolos, Burgess, *Jeffrey, Computability and Logic*, 5th ed., Cambridge University Press, 2007.

Reader on the philosophical significance of Turing’s computability and Gödel’s incompleteness theorems for several areas of philosophy (to be chosen among philosophy of mind, philosophy of logic, philosophy of language, philosophy of science, philosophy of mathematics).

## Program:

### Part I: Turing Machines and computability

Week 1: Enumerability and Diagonalization, chs.1 and 2

Week 2: Turing machines, chs.3 and 4

Week 3: First order logic, ch. 9

Week 4: First order logic, ch. 10

Week 5: First order logic is undecidable, ch. 11

### Part II: Gödel’s incompleteness theorems

Week 6: Recursive Functions, ch. 6

Week 7: Recursive Sets and Relations, ch. 7

Week 8: Arithmetization and representability in Q, chs. 15 and 16

Week 9: Indefinability, Undecidability and Incompleteness, ch. 17

Week 10: The unprovability of consistency, ch. 18

### Part III: Philosophical consequences

Details t.b.a.

Updated on 2016-08-13 15:48:34 -0700 by Paolo Mancosu