Undergraduate Course: Logic, Computability and Incompleteness (PHIL10133)
|School||School of Philosophy, Psychology and Language Sciences
||College||College of Humanities and Social Science
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||This course examines some fundamental topics relating to first-order Logic and the theory of computability, with particular emphasis on key limitative results.
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 Lob's Theorem.
Entry Requirements (not applicable to Visiting Students)
|| It is RECOMMENDED that students have passed
Logic 1 (PHIL08004)
||Other requirements|| ***Mathematics and/or Informatics Secretaries - please contact Course Secretary prior to enrolling students onto this course***
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.
This is an advanced logic course and interested philosophy students are strongly recommended to take a look at Richard Jeffreys Formal Logic: Its Scope and Limits, particularly chapter 4 on Multiple Generality and chapter 5 on Identity, in advance of the course. If you have any doubts about the suitability of this course given your background, please consult the course organiser prior to enrolling.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Seminar/Tutorial Hours 22,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Final two hour examination in the May diet (100%)
||Hours & Minutes
|Main Exam Diet S2 (April/May)|| Logic, Computability and Incompleteness||2:00|
| 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.
|The following is a sample bibliography, intended to indicate the type of reading that will be covered in the course.|
 Boolos, G.S., J.P. Burgess & R.C. Jeffrey (2002) Computability and Logic, 4th edition, Cambridge University Press.
 Machover, M (1996) Set Theory, Logic and Their Limitations, Cambridge University Press.
 Enderton, H. (2001) A Mathematical Introduction to Logic.
 Mendelson, E. (1987) An Introduction to Mathematical Logic.
 Smith, P. (2007) An Introduction to G¿del's Theorems, Cambridge University Press.
|Graduate Attributes and Skills
|Course organiser||Dr Paul Schweizer
Tel: (0131 6)50 2704
|Course secretary||Miss Ann-Marie Cowe
Tel: (0131 6)50 3961