Course Details in 2024/25 Session

Module Title	LI Logic: Its Limits + Scope
School	Phil, Theology and Religion
Department	Philosophy
Module Code	08 26792
Module Lead	Simone Picenni
Level	Intermediate Level
Credits	20
Semester	Semester 2
Pre-requisites	LC Philosopher's Toolkit A - (09 33081)
Co-requisites
Restrictions	None
Exclusions
Description	Is there any way to make a mathematics of reasoning? If so, what would it look like? What would be its scope, and what would be its limits? One set of questions concern the extent to which we can adequately represent the subtleties of natural language reasoning in a regimented, mathematical language. Another is whether we can make a system which gives all and only the right results. We will see that we can accomplish much of what we would hope to, but not all of it. The module deals with two main formal systems, sentential logic and predicate logic. After introducing the formal languages, we characterize the logical notions of interpretation, entailment, and deducibility relative to each system. We then investigate how these notions are related, proving some fundamental metatheoretic results. In particular, we prove that both systems are sound and complete. Towards the end of the module, we will have the opportunity to discuss additional metatheoretic results, such as the incompleteness theorems.
Learning Outcomes	By the end of the module students should be able to: - formalize English sentences in propositional and first-order logical notation; outline the proof of the soundness and completeness theorems for propositional logic and first-order logic; manifest improvement in general philosophical and mathematical skills.
Assessment	26792-01 : In Class Exam : Class Test (50%) 26792-02 : CT Exam : Exam (Centrally Timetabled) - Written Unseen (50%)
Assessment Methods & Exceptions	Assessments: 1 x 110 minute in-class exam (50%) and 1 x 2 hour centrally-timetabled exam (50%). Reassessment: 1 x 110 minute in-class exam (50%) and 1 x 2 hour centrally-timetabled exam (50%).
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