Module PHIL3201: FORMAL AND PHILOSOPHICAL LOGIC

Department: Philosophy

PHIL3201: FORMAL AND PHILOSOPHICAL LOGIC

Prerequisites

• Language, Logic and Reality (PHIL2021), Mathematics for Computer Science (COMP1021), Theory of Computation (COMP2181), or other appropriate evidence

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To introduce students in Philosophy, Mathematics, and Computer Science to non-classical logics, such as modal logic and relevance logic, which have developed out of philosophical analyses of such topics as time, knowledge, necessity and conditional statements.
• To introduce students to the developments in early 20th-century logic (stemming from Hilbert’s programme) which led to Gödel’s proofs of the completeness of first-order logic and the incompleteness of Peano Arithmetic, as well as provide them with the technical means necessary to prove these results for themselves.
• To teach students how to articulate in a clear and concise fashion the historical and philosophical aspects of the material covered.

Content

• Kripke models for propositional modal logic.
• Axiomatic proof systems for propositional modal logic
• Theoretical and philosophical issues related to quantified modal logic
• Proof systems for first-order logic
• Model theory for first-order logic
• A brief history of Hilbert’s problems and the context of Gödel’s theorems
• Completeness Theorems for first-order logic
• Peano Arithmetic and proof by mathematical induction
• Incompleteness Theorems for Peano Arithmetic

Learning Outcomes

• At the end of the module students should have:
• an understanding of the motivations for developments in philosophical logic (that is, logic applied to philosophical problems and issues)
• the technical skills to deploy these logics as well as prove results about them
• a grasp of the philosophical significance of completeness and incompleteness phenomena, the historical context in which these issues first arose, and the relevant proof and model theory for first-order logic and Peano Arithmetic.

• By the end of the module students should be able to:
• Correctly utilise specialist vocabulary
• Write formal logical proofs in a clear, rigorous style.
• Grasp, analyse, evaluate and deploy subject-specific concepts and techniques
• Locate, understand, assess and utilise pertinent philosophical and historical sources.

• By the end of the module students will be able to:
• Write clear and succinct formal proofs
• Comprehend complex ideas, propositions and theorems
• Seek out and identify appropriate sources of evidence and information
• Tackle problems in a clear-sighted and logical fashion

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• This module will be taught in weekly two-hour seminars, with weekly or bi-weekly homework assignments allowing the students to practice the technical skills they are being taught. Teaching and learning methods will support students in achieving the Subject-Specific Skills 1-4 above. The Subject-Specific Skills will be formally assessed by the end of year exam.enter text as appropriate for the module

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Weekly or bi-weekly homework assignments

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University