PHIL3201: Formal and Philosophical Logic

• PHIL 2181Fundamentals of Logic or COMP1051 Computational Thinking or other appropriate evidence.

• None.

• None

• To introduce students to philosophically important issues connected to formal and philosophical logic, including a subset of the following: philosophy of logic, logical modelling, non-classical logics, such as modal logic (including temporal, epistemic, deontic logic etc); relevance logic; many-valued logics; dynamic logics; game theoretic appropriates to logic; Gdel's proofs of the completeness of first-order logic and the incompleteness of Peano Arithmetic; different approaches to philosophy of mathematics and the foundations of mathematics.
• To provide them with the technical means necessary to prove these results for themselves, and the philosophical skills to engage with current the philosophical issues raised by the formal problems.

• A subset of the following:
• Kripke models for modal logic.
• Axiomatic proof systems for propositional modal logic.
• Soundness and completeness results for propositional modal logic.
• Applications of modal logic to philosophical issues and problems.
• Theoretical and philosophical issues related to quantified modal logic.
• Motivations for other non-classical systems.
• Philosophical foundations of logic.
• Logic(s) as formal modelling tools.
• Hilbert's problems and the context of Gdel's theorems.
• Peano Arithmetic and proof by mathematical induction.
• Incompleteness Theorems for Peano Arithmetic.
• Platonist, Intuitionist, Formalist, and Structuralists Philosophies of Mathematics.
• Intuitionistic logic and other subclassical logics.
• Dynamic logic, multi-agent logic, and other extensions of modal logic.
• Game Logics and game theoretic equivalences.
• Decidability, translations, and expressive power of logics (first-order, modal, etc.).

Subject-specific Knowledge:

• At the end of the module students should have a grasp of the philosophical significance of various developments in logic and mathematics, such as completeness and incompleteness phenomena; the historical context in which these issues first arose, the relevant proof and model theory for proving the necessary technical results, and how to apply these tools to philosophical problems.

Subject-specific Skills:

• By the end of the module students should be able to do a selection of the following:
• Prove completeness and canonicity of specific propositional modal logics.
• Prove correspondence results between properties of models and specific modal axioms.
• Prove theorems of first-order logic using mathematical induction.
• Explain the incompleteness theorem for Peano Arithmetic.
• Prove meta-level results about non-classical logics.
• Articulate the differences between different foundational approaches to logic and mathematics.
• Explain how modal logic can be applied to philosophical problems and issues.
• Apply logical systems to philosophical problems and issues.

Key Skills:

• Students will be able to do a selection of the following:
• Present logical proofs in a clear, rigorous style.
• Articulate in a clear and concise fashion the historical and/or philosophical aspects of the material covered.
• Be adequately prepared to go on to do further research in formal logic at the postgraduate level.

• This module will be taught in weekly two-hour seminars, in which core content will be delivered. This content will be supplemented with regular formative and summative assignments, including a final written report, allowing the students to practice the technical and philosophical skills they are being taught. Teaching and learning methods will support students in achieving the Subject-Specific Skills above. The Subject-Specific Skills will be formally assessed by the summative exercises.

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