Undergraduate Course: Logic, Computability and Incompleteness (PHIL10133)
Course Outline
| School | School of Philosophy, Psychology and Language Sciences |
College | College of Humanities and Social Science |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 20 |
| Home subject area | Philosophy |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course will focus on key metatheoretical results linking computability and logic. In particular, Turing machines and their formalization in first-order logic, linking uncomputability and the halting problem to undecidability of first-order logic. We will then study recursive functions and their construction, followed by first-order formalizations of arithmetic, particularly Robinson arithmetic and Peano arithmetic. We will then turn to the topic of the arithmetization of syntax and the diagonal lemma, before proceeding to prove some of the main limitative results concerning formal systems, in particular G¿del's two incompleteness theorems, along with allied results employing the diagonal lemma, including Tarski's Theorem and L¿b's Theorem. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Mind, Matter and Language (PHIL08014) AND
Knowledge and Reality (PHIL08017) AND
Logic 1 (PHIL08004)
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | Students studying Mathematics and/or Informatics may be able to take this course without the pre-requisites; this must be discussed with the Course Organiser who can give the necessary permission. |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | Passes in second level courses in Philosophy |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2013/14 Semester 2, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: 25 |
Web Timetable |
Web Timetable |
| Course Start Date |
13/01/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Seminar/Tutorial Hours 22,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
174 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | Logic, Computability and Incompleteness | 2:00 | | |
|
| Delivery period: 2013/14 Semester 2, Part-year visiting students only (VV1)
|
Learn enabled: No |
Quota: 5 |
Web Timetable |
Web Timetable |
| Course Start Date |
13/01/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Seminar/Tutorial Hours 22,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
174 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | Logic, Computability and Incompleteness | 2:00 | | |
Summary of Intended Learning Outcomes
Upon successful completion of the course, students will be able to demonstrate:
¿ familiarity with the general philosophical/mathematical project of Hilbert's program and how this is impacted by the technical results explored in the course;
¿ thorough understanding of some key limitative results in logic and computability, including the halting problem, the undecidability of first-order logic, and the incompleteness of first-order arithmetic;
¿ ability to employ abstract, analytical and problem solving skills;
¿ ability to formulate clear and precise pieces of mathematical reasoning.
Also, students will demonstrate the following transferable skills:
¿ evaluating abstract theoretical claims;
¿ grasping and analysing complex metatheoretical concepts;
¿ deploy rigorous formal methods.
|
Assessment Information
| There will be an opportunity for formative assessment and guidance based on exercise sets assigned during the semester. The course will be assessed by a 2 hour degree examination. The final mark for the course will be based on this examination. |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
The following is a sample bibliography, intended to indicate the type of reading that will be covered in the course.
[1] Boolos, G.S., J.P. Burgess & R.C. Jeffrey (2002) Computability and Logic, 4th edition, Cambridge University Press.
[2] Machover, M (1996) Set Theory, Logic and Their Limitations, Cambridge University Press.
[3] Enderton, H. (2001) A Mathematical Introduction to Logic.
[4] Mendelson, E. (1987) An Introduction to Mathematical Logic.
[5] Smith, P. (2007) An Introduction to G¿del's Theorems, Cambridge University Press.
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| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Paul Schweizer
Tel: (0131 6)50 2704
Email: paul@inf.ed.ac.uk |
Course secretary | Miss Susan Richards
Tel: (0131 6)51 3733
Email: sue.richards@ed.ac.uk |
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