Class Times: Tuesdays and Thursdays, 2.30pm-4pm
Location: Wilson Hall, 104
Course Website: http://www.artsci.wustl.edu/~grussell/Phil403.html
Instructor: Professor Gillian Russell
Office hours: Tuesdays 4.15-5.15pm or by appointment
Office Location: 209 Wilson Hall
Email: grussell – at – wustl – dot – edu
This is a course in mathematical logic for those who are already familiar with first-order symbolic logic. The main results are Goedel’s incompleteness theorems. The course assumes some basic set theory and faciliity with informal proof methods, such as proof by induction. Students are strongly advised to take Phil 100 Introduction to Logic and Phil 301: Symbolic Logic before attempting this more advanced course.
The textbook for this course is the 5th edition of Boolos, Burgess and Jeffrey’s Logic and Computability, published by Cambridge. It is the only text you need to buy. Second hand copies are fine.
Enumerability
Reading: Chapter 1 of the textbook.
Diagonalisation
Reading: Chapter 2
Exercises (1): 1.3, 1.5, 2.2
Turing Computability
Reading: Chapter 3
The Halting Problem
Reading: section 4.1
Exercises (2): 3.3, 3.5, 4.1, 4.2
Abacus Computability
Reading: chapter 5
Recursive Functions
Reading: chapter 6
Exercises (3): 5.1, 5.6, 6.1, 6.4
Recursive Sets and Relations
Reading: chapter 7
Equivalent Definitions of Computability (I)
Reading: sections 8.1 and 8.2
Exercises (4): 7.1, 7.3, 7.12, 8.1
Equivalent Definitions of Computability (II)
Reading: section 8.3
Midterm Exam 1 (on chapters 1-8)
A Precis of First Order Logic: Syntax
Reading: chapter 9.
A Precis of First Order Logic: Semantics
Reading: chapter 10.
Exercises (5): 9.1, 9.4, 10.1, 10.6, 10.8.
The Undecidability of First-Order Logic
Chapter 11
Models
Chapter 12
Exercises (6): 11.1, 11.7, 12.3, 12.8, 12.9
The Existence of Models (I)
Reading: section 13.1
The Existence of Models (II)
Section 13.2
Exercises (7): 13.8, 13.9, 13.10, 13.11
SPRING BREAK
SPRING BREAK
Exercises (7): 13.8, 13.9, 13.10, 13.11
Proofs and Completeness
Reading: chapter 14
NO CLASS
Exercises (8): 14.1, 14.3, 14.5, 14.7, 14.9
Arithmetization
Reading: Chapter 15
Representability of Recursive Functions (I)
Reading: sections 16.1 and 16.2
Exercises (9): 15.1, 15.4, 16.1, 16.2
NO CLASS
MIDTERM EXAM II (on chapters 9-15)
Exercises (9): 15.1, 15.4, 16.1, 16.2
NO CLASS
Representability of Recursive Functions (II)
Reading: sections 16.3 and 16.4
Exercises (10): 16.3, 16.5, 16.9, 16.10
Representability of Recursive Functions (III)
Reading: No additional Reading.
Indefinability, Undecidability and Completeness (I)
Reading: section 17.1
Indefinability, Undecidability, Incompleteness (II)
Reading: sections 17.2
The Unprovability of Consistency
Take home final will be given out on 26th of April, and will be due at noon on the 4th of May 2012.
Homework exercises are listed on the syllabus. They will be due by noon on the Friday that falls 8 days after the date under which they are listed (e.g. the first homework is listed under Thursday 19th January and so it is due by noon on Friday 27th. Exercises should be completed on paper (i.e. don’t email me your homework) and turned in to the appropriate drawer of the "turn-in" filing cabinent in the philosophy department office (2nd floor of Wilson Hall, opposite my office.)
Please be considerate of the office staff – the office closes for lunch (12.30 – 1.30pm) and at 4pm; we try to discourage students from knocking on the door at 4.01pm and access to the filing cabinets is not allowed when the office is unattended.
You may handwrite your homework (in fact, this is often faster and less prone to unfortunate typing errors) but you should always turn in neat, legible work, clearly marked with your name. Do not turn in "rough" work, or work with lots of crossings-out. Any work that I can’t read will get a zero.
Solutions to the problem sets will be given out in class.
Any homework set received after the solutions have been given out will receive a grade of zero.
40% of the grade for this course will come from the homework exercises completed during the semester. (We will drop your worst homework grade and average the rest.) 40% will come from the two in class midterm exams (20% each) and the remaining 20% from a take home final exam, which will be given out on the last day of class. You will have 1 week to complete the final. If you decide to take this course, you will need to make sure that you are able to come to class on the days of the midterms.
For students taking the course pass/fail, the minimum letter grade required for a pass will be a D, which can be obtained with an overall percentage grade of 50%.
It is very important that you understand the rules for collaboration on this course. You may work with other students in order to work out solutions to the exercises in your take-home problem sets; in fact, this is encouraged. However, each student must write up his or her solutions to the exercises alone. You may not do it with another student looking over your shoulder to correct you. You may not write your homework from notes which another student has made, nor may you make notes on another student’s written solutions. You may not lend or copy digital or paper homework solutions – at any stage of completion.
Collaboration is not allowed during the midterm and final examinations.
Sometimes it is unclear whether a hypothetical case of collaboration is permissible according to these rules, or whether it counts as misconduct, but it is your duty to ensure that ALL your collaborations are clearly permissible. One good way to do this is not to write anything down on paper whilst investigating problems with other students: use a chalk board or white board to work out ideas, (or, if you use paper, dispose of the written solutions before you separate to write up your individual homeworks alone.)
Students suspected of plagiarism or any other form of academic dishonesty or misconduct will be reported to the academic integrity officer for Arts and Sciences (currently Dean Killen), so that the incident may be handled in a consistent, fair manner, and so that substantiated charges of misconduct may be noted in students’ records.