Module PHIL2181: Fundamentals of Logics

Department: Philosophy

PHIL2181: Fundamentals of Logics

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• None

Aims

• To provide students of philosophy with logical skills needed for working in the formal parts of the discipline.
• To provide students of all disciplines with skills in precision and clarity of thinking and expression through understanding the logical relationships between sentences and terms.
• To explore issues arising from the relationship between formal and natural languages, and the application of logical methods to philosophical and non-philosophical problems.
• To introduce students to the connections that logic makes between philosophy, mathematics, and computer science.
• To introduce students to the philosophical history and context of developments in logic.
• To provide students with an understanding of what logic as a research discipline is and what research within the field of logic looks like.

Content

• Topics covered will include a selection of the following:
• Logic in the "wild": Arguments, soundness, validity; weaponization of "reason", "rationality", "logical"; feminist logic; logic and generative AI.
• Non-symbolic logical traditions: Hindu and Buddhist logic, African logic.
• Syllogisms: Categorical propositions; the Square of Opposition; interpretations; proof theory; meta-theory; the limits of the syllogistic.
• Propositional logic: The Stoic roots of propositional logic; truth-functional connectives; truth tables; assessing truth-functional validity using truth tables; truth-functional consistency and inconsistency; tautologies and contradictions; proof theory; soundness and completeness; the limits of propositional logic.
• Predicate logic: Predicates, variables and quantifiers; relations; identity; syntax of predicate logic; semantics; proof theory; soundness.
• Translating between natural/ordinary language and formal and symbolic languages.

Learning Outcomes

• By the end of this module, students will have knowledge and understanding of:
• relations between central concepts of logic: truth, argument, consistency, proof, validity, soundness;
• properties and limitations of systems of symbolic logic including syllogistic logic, propositional logic, and predicate logic (with identity);
• philosophical issues arising from the application of symbolic logics to natural/ordinary with language inferences;
• aspects of the history and development of competing accounts of "good argument", and the philosophical issues which underlie these developments.

• By the end of this module, students will have the practical ability to:
• deploy symbolic methods, such as those provided by syllogistic logic, propositional logic, and predicate logic (with identity) for assessing truth, validity, consistency, logical equivalence, and derivability in particular cases;
• identify appropriate symbolic languages for representing arguments in natural/ordinary language.

• By the end of this module, students will be able to:
• comprehend complex ideas, propositions and theories;
• defend their opinions by reasoned argument;
• tackle problems in a clear-sighted and logical fashion;
• explain their answers to their peers.

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

• Lectures introduce the core concepts and definitions to the students along with worked out examples. Because lectures involve both student participation and exercises worked out on the whiteboard (rather than slides), they are not suitable for lecture capture and are opted out of it in accordance with Encore Lecture Capture Policy (2.6).
• Tutorials provide students with the opportunity to present their formative work in a collaborative setting and receiving feedback on their answers.
• The in-class participation component reinforces the importance of practicing the subject-specific skills on a regular basis.
• The take-home exercise and the final exam test the students' understanding of the core concepts and definitions and their ability to apply them.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Weekly formative exercises to be prepared in advance of every tutorial meeting.

■ Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.