Basic Concepts in Mathematical Logic

Philosophy 159/Linguistics 135
Syllabus

Professors

Prof. Edward N. Zalta, Philosophy Dept. (2/3 of the lectures)
Office: Ventura Hall B1
Phone: 723-0345; Electronic Mail: zalta@csli
Mailboxes in 91L (Philosophy) and in Ventura Hall AB
Office Hours: Tu/Thurs 10:00-11:15
Prof. John Etchemendy, Philosophy Dept. (1/3 of the lectures)
Office: 92G
Phone: 723-0855; Electronic Mail: etchemendy@csli
Mailbox in 91L Office Hours: W/F 10:00-11:00

Class Meetings

Monday, Wednesday, and Friday: 9:00-9:50 in 60-61H

Course Description

An informal introduction to the basic concepts and techniques used in mathematical logic: sets, functions, propositional logic, predicate logic, representing English sentences in logical notation, proofs, and mathematical induction.

Required Text

Robert Wall, An Introduction to Mathematical Linguistics

Course Requirements

6 sets of homework exercises (50 pts. each)
1 midterm exam (150 pts.)
1 final exam (300 pts.)

COURSE SCHEDULE

NOTE: Students are expected to have read the material by classtime of the day indicated.

October

1
Basic Set Theory
3
Basic Set Theory
read: Chapter 1
6
Sentences, Propositions, and the Propositional Connectives
read: Chapter 2, pp. 12-25
8
Logical Truth and Logical Equivalence
read: Chapter 2, pp. 25-34
10
EXERCISE SET #1 DUE
Proofs in Propositional Logic
read: Chapter 2, pp. 34-50
13
Quantifiers and Predicate Logic
read: Chapter 3, pp. 51-57
15
Translating English into Predicate Logic
READ: Chapter 3, 57-65
17
EXERCISE SET #2 DUE
CLASS MEETS IN THE MACINTOSH TEACHING LAB
read: Tarski's World, handout
20
Interpretations and Logical Truth
read: Interpretations, handout
22
Logical Equivalence
24
EXERCISE SET #3 DUE
Proofs in the Predicate Calculus
read: Chapter 3, pp. 65-80
27
Special Problems in Translating English into Logic
29
Review Session
31
MIDTERM EXAM

November

3
Recasting Set Theory in Predicate Logic
read: Chapter 4, pp. 81-87
5
Set Theoretic Operations
read: Chapter 4, pp. 87-103
7
Return and Review the Exam
10
Ordered Pairs, Cartesian Products, and Relations
read: Chapter 5, pp. 104-110
12
Properties of Relations
read: Chapter 5, pp. 110-121
14
Equivalence Relations
read: Chapter 5, pp. 121-124
17
EXERCISE SET #4 DUE
Functions
read: Chapter 5, pp.124-136
19
Orderings
read: Chapter 6, pp. 137-144
21
Isomorphisms
read: Chapter 6, pp. 166-172
24
Cardinality and Infinite Sets
read: Chapter 7, pp. 174-177
26
EXERCISE SET #5 DUE
Denumerable and Non-denumerable Sets
read: Chapter 7, pp. 177-182
28
THANKSGIVING

December

1
Cantor's Theorem
read: Chapter 7, p. 182-187
3
Definition by Recursion
read: Chapter 8, pp. 188-193
5
Proof by Induction
read: Chapter 8, pp. 193-197
8
EXERCISE SET #6 DUE
DEAD WEEK WILL BE RESERVED FOR CATCHING UP AND REVIEW
10
Dead Week
12
Review for the Final Exam
15
FINAL EXAM

Grading Policies

1. The course schedule is tentative and the professors reserve the right to make changes in the schedule. All such changes will be announced in class.

2. NO LATE HOMEWORKS, NO MAKEUP EXAMS and NO INCOMPLETES, unless special permission is granted by one of the professors in advance. Such permission will be granted only in the case of exceptional circumstances (such as a genuine emergencies, etc.), though some leniency for late homeworks can be expected.

3. Participation in class and/or steady improvement will be considered in determining your final grade, especially in borderline cases.

4. Reevaluations: Students may request a reevaluation of any exam or homework set if they feel that it has been incorrectly graded. The work must be resubmitted within two weeks of the date the exam or exercise was graded and returned.


Copyright © 1994, by Edward N. Zalta. All rights reserved.