| Prof: Jonathan
Bain |
Spring 2006 |
Office: RH
201D
|
T/Th 9:00-10:50
|
| Off. hr: W 11-12pm |
phone:
260-3688 |
I. Description
Metalogic concerns the "logic of logic". Topics to be covered
include the soundness and completeness of 1st-order logic, the
Lowenheim-Skolem and Compactness theorems for 1st-order logic, the
Godel Incompleteness theorem for formal arithmetic, and Turing machines
and the notions of computability and undecidability. We will also
spend some time looking at Torkel Franzen's recent assessment of the
"uses and abuses" of Godel's Incompleteness Theorem. Prerequisites:
PL2104-Symbolic Logic, or a strong mathematics background (3rd/4th year
mathematics major).
II.
Required
Texts
- Hamilton, A. (1988), Logic
for
Mathematicians, Cambridge Univ Press.
- Franzen, T. (2005) Godel's
Theorem: An Incomplete Guide to Its Use and Abuse, AK
Peters.
III.
Course
Requirements
| 1. |
There will be a homework
assignment handed out each week, due the following week.
Your final assignment grade will be calculated from the highest 10 of
your 13 individual assignment grades. |
| 2. |
There will be one midterm
and a final. The final
will be minimally cumulative (i.e.,
it will emphasize the units not covered by the midterm, but may include
a few questions from previous material). |
| 3. |
There will be an optional
essay
assignment on the general topic of applications of Godel’s
Incompleteness Theorem. A list of more detailed possible topic
questions will be handed out over the course of the semester. |
IV.
Grade
Distribution
There will be two grading options:
Plan
1
|
|
Plan
2 (Essay option)
|
Attendance: 10%
|
|
Attendance: 10%
|
Assignments: 30%
|
|
Assignments: 15%
|
Exam: 30%
|
|
Exam: 20%
|
Final: 30%
|
|
Final: 25%
|
|
|
Essay: 30%
|
V. Class Schedule:
The following schedule may be subject to revision over
the course of the semester. Reading assignments must be completed
by the date on which they appear.
| Week 1 |
Tues |
Thurs 1/19
HCh 1: Informal
Statement Calculus - Semantics |
| Week 2 |
1/24
HCh 1, cont. |
1/26
HCh 2: Formal
Statement
Calculus - Soundness and Completeness
|
| Week 3 |
1/31
HCh 2, cont. |
2/2
HCh 2, cont. |
| Week 4 |
2/7
HCh 3: Informal
Predicate
Calculus - Semantics |
2/9
HCh 3, cont. |
| Week 5 |
2/14
HCh 3, cont. |
2/16
HCh 4: Formal Predicate Calculus - Soundness and
Completeness |
| Week 6 |
2/21
HCh 4, cont.
|
2/23
HCh 4, cont. |
| Week 7 |
2/28
HCh 4, cont. |
3/2
HCh 4:
Lowenheim-Skolem
and Compactness Theorems |
| Week 8 |
3/7
MIDTERM |
3/9
HCh 5: A Formal
System N
of Arithmetic
|
| Week 9 |
3/14
SPRING BREAK |
3/16
SPRING BREAK |
| Week 10 |
3/21
HCh 6: The Godel
Incompleteness Theorem for N |
3/23
HCh 6, cont. |
| Week 1 |
3/28
HCh 6, cont. |
3/30
FCh 1, 2: Godel - Uses and Abuses |
| Week 1 |
4/4
FCh 3, 4: Uses and Abuses, cont. |
4/6
FCh 5, 6: Uses and Abuses, cont. |
| Week 13 |
4/11
FCh 7, 8: Uses and Abuses, cont. |
4/13
NO CLASS |
| Week 14 |
4/18
HCh 7: Computability and Undecidability |
4/20
HCh 7, cont. |
Week 15
|
4/25
HCh 7, cont.
|
4/27
HCh 7, cont.
|
| Week 15 |
5/2
Reading Day |
|
| Week 16 |
Final (Date to be announced by Registrar) |
|