Postgraduate Course: Logic, Computability and Incompleteness (PHIL11114)
Course Outline
| School | School of Philosophy, Psychology and Language Sciences |
College | College of Humanities and Social Science |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | The 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 Gdel's two incompleteness theorems, and allied results employing the diagonal lemma, including Tarski's Theorem and Lb's Theorem.
Shared with the undergraduate course Logic, Computability and Incompleteness PHIL10133
Formative feedback available;
- guidance based on exercise sets assigned during the semester. |
| Course description |
Not entered
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Logic 1 (PHIL08004)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | Students must have passed Logic 1 or equivalent course in their previous undergraduate studies. |
Course Delivery Information
|
| Academic year 2014/15, Available to all students (SV1)
|
Quota: 10 |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 20,
Feedback/Feedforward Hours 2,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
174 )
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| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
The course will be assessed 100% by exam; the mark for the course will be based on this examination.
Date of exam: TBC by central university
Return deadline: within 3 working weeks |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | | 2:00 | |
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.
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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 Gżdel's Theorems, Cambridge University Press. |
Additional Information
| Course URL |
Please see Learn page |
| Graduate Attributes and Skills |
Students will demonstrate the following transferable skills:
- evaluating abstract theoretical claims;
- grasping and analysing complex metatheoretical concepts;
- deploy rigorous formal methods. |
| Additional Class Delivery Information |
Taught by Dr Paul Schweizer |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Paul Schweizer
Tel: (0131 6)50 2704
Email: paul@inf.ed.ac.uk |
Course secretary | Miss Lynsey Buchanan
Tel: (0131 6)51 5002
Email: Lynsey.Buchanan@ed.ac.uk |
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