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 tools they need when 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 basic issues arising from the relationship between formal and natural languages, and the application of logical methods to 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 the developments of logic.

Content

• Topics covered will include a selection of the following:
• Logic, arguments, soundness and validity.
• Syllogisms: Categorical propositions; the Square of Opposition; interpretations; proof theory; the limits of the syllogistic.
• Propositional logic: The Stoic roots of propositional logic; truth-functional connectives; formalisation; parse-trees; conjunctive and disjunctive normal form; truth tables; assessing truth-functional validity using truth tables; truth-functional consistency and inconsistency; tautologies and contradictions; proof theory; the limits of propositional logic; soundness and completeness.
• Predicate logic: Predicates, variables and quantifiers; relations; identity; syntax of predicate logic; semantics; proof theory; soundness and completeness.
• Feminist logic.
• Non-European logical traditions: Hindu and Buddhist logic, African Logic

Learning Outcomes

• By the end of this module, students will have knowledge and understanding of:
• relations between the central concepts of logic: truth, argument, consistency proof;
• the properties and limitations of systems of formal logic including the syllogistic, propositional logic, and predicate logic (with identity);
• basic philosophical issues arising from the application of classical propositional and predicate logics to ordinary-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 a practical ability to deploy formal methods, such as those provided by the syllogistic, propositional logic, and predicate logic (with identity) for assessing truth, validity, consistency, logical equivalence, and derivability in particular cases.

• 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.
• Discussion groups provide students with the opportunity to collaborate with each other to work through weekly formative assignments.
• The summative exercise and the final exam test the students' understanding of the core concepts and definitions and their ability to apply them.
• N.B. Lecture capture usually isn’t appropriate for the lectures, since (i) the lectures often involve student participation, (ii) PowerPoint slides usually are not used, and (iii) the whiteboard is regularly used. However, lecture material is made available via (i) the course textbook, and (ii) bitesize videos covering course topics and subtopics in detail.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Weekly formative exercises to be prepared in advance of every discussion group.

■ 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