PHIL2181: Fundamentals of Logics

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• 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 philosophical history and context of the developments of logic.

• 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.
• Predicate logic: Predicates, variables and quantifiers; relations; identity; syntax of predicate logic; semantics; proof theory.
• Non-European logical traditions: Hindu and Buddhist logic, African Logic

Subject-specific Knowledge:

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

Subject-specific Skills:

• 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.

Key Skills:

• 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.

• 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 problem sets.
• The summative assignments and the final exam test the students' understanding of the core concepts and definitions and their ability to apply them.

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