Introductory description

This module provides a study of formal logic, covering both propositional and first-order logic. We will study formal languages, which will allow us to define precise notions of logical validity, and to develop methods to establish the validity or invalidity of arguments. In particular, we will introduce a system of proof (of the natural deduction kind) which can be used to establish that an argument is valid. We will also learn how to translate English sentences into formal language ones and vice versa.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module is based on Barwise & Etchemendy: Language, Proof and Logic (CSLI publications, Stanford)

Learning outcomes

By the end of the module, students should be able to:

• Subject knowledge and understanding: students should be familiar with the notion of a logically valid argument and related notions; they should understand various ways to establish the logical validity or invalidity of arguments; and they should understand how to form and evaluate sentences in the propositional and first-order languages.
• Key skills: students should be able to use logical notions and formal techniques (specifically truth tables and formal proofs) in assessing (or establishing) the validity of arguments; they should be able to construct counterexamples to arguments; and should be able to translate first order sentences – including sentences involving multiple quantifiers, identity and number – to and from English.

Subject specific skills

• An understanding of the notion of logical validity and related logical notions.
• Enhancement of the ability to articulate and evaluate arguments with clarity and precision by enhancing (a) the ability to identify and articulate structural logical relations between English sentences, and (b) the ability to detect and articulate structural ambiguities in English.

Transferable skills

Enhancement of analytic skills, in particular the ability to: (a) articulate ideas and arguments with clarity and precision, (b) analyse and assess complex reasoning, (c) pay careful attention to detail.