Phil 140B

Intermediate Logic

Fall 2020

Professor Paolo Mancosu

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

Office hours: F 11.00-12.30

Email: mancosu@socrates.berkeley.edu

Lecture: Tu, Th 9.30-11.00,

GSI: Patrick Ryan, patrick.j.ryan@berkeley.edu

Office hours: Tu 11.00-13.00

Sections: Th 11:00-12:00, 12:00-13:00, 13:00-14:00.

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.

This course does not satisfy the “Philosophy and Values” breadth requirement. Graduate students in philosophy may use this course for satisfying the formal philosophy course requirement (i.e. a course in the 140 series or equivalent).

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).

Attendance to lectures: Attendance to the online lectures is mandatory. You will have to log in on Zoom with the video on at the beginning of the lecture and log out at the end of the lecture. Should you be unable to attend a lecture on a given day you should send me an email before the lecture with the reasons why you are not attending. You will be granted at most three absences from lectures during the entire semester (unless there is written medical justification).

Attendance to sections: While not mandatory it is highly recommended and you will skip it at your own peril.

Course Webpage: bcourses.berkeley.edu

You will have to log in with Calnet. Once you log in you should be able, if you are enrolled or on the waiting list, to see the web page for “Intermediate Logic (140B)” under “Courses”. We will use the bcourses page to post reading materials, assignments, grades, and other information relevant to the course.

Textbooks:

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

Articles 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). These readings will be made available on our web site in bcourses.

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.