2024/25 Undergraduate Module Catalogue

PHIL2635 Universal Science: Topics in Formal Logic

20 creditsClass Size: 100

Module manager: Alastair Wilson
Email: A.J.J.Wilson@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisites

PHIL1250	How to Think Clearly and Argue Well
PHIL1260	How To Do Philosophy

Module replaces

PHIL2122 Formal Logic

This module is not approved as a discovery module

Module summary

Deductive logic has been described as universal science; it aspires to identify the most general principles of reason which apply to all topics whatsoever and on which we can always rely. The formal study of logic is key to the foundations of mathematics, computer science, and scientific representation in general; it is also a tool for sharpening our own thinking. The study of logic can help us whenever it is important to critically evaluate arguments.

Objectives

In studying this module, you will learn the key concepts underlying deductive logic and will acquire the abilities to reason formally about formal systems and to prove within them whether a given deductive argument is valid or invalid.
The module is taught through lectures that introduce concepts and methods, and seminars in which students learn how to apply those concepts and methods for themselves, acquiring the skills to rigorously establish conclusions of arguments.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Formalize natural language arguments in first-order quantified logic.
2. Distinguish between different logical systems, and between syntactic and semantic approaches to deductive inference.
3. Use a proof system to complete derivations with formulas involving both connectives and quantifiers.
4. Correctly deploy model-theoretic definitions of validity and invalidity, and construct countermodels for invalid formulas and arguments.
5. Explain the content and significance of meta-logical claims about first-order proof systems, e.g. soundness and completeness.

Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
6. Communicate ideas and understanding clearly and concisely, using appropriate academic language. (Academic and Work Ready skill)
7. Explore multiple approaches to difficult problems where there is no straightforward algorithm to complete a task. (Academic and Work Ready skill)
8. Search for appropriate material to support knowledge and analysis of topics. (Academic and Work Ready skill)
9. Critically analyse material and demonstrate independence of thought. (Academic and Work Ready skill)
10. Conform to standards of academic integrity including when and how to appropriately acknowledge someone else’s work. (Academic and Work Ready skill)

Syllabus

Topics covered may include the following:
1. Modelling logical reasoning using multiple formal systems.
2. Using truth tables to establish validity and invalidity of sequents.
3. Introduction of a proof system for propositional first-order logic.
4. Introduction of a proof system for quantified first-order logic.
5. Basic meta-logic: statements of soundness and completeness theorems for first-order logic.
6. Philosophical reflection on the capacities and limitations of different formal systems.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	18	1.00	18.00
Seminar	9	1.00	9.00
Private study hours			173.00
Total Contact hours			27.00
Total hours (100hr per 10 credits)			200.00

Opportunities for Formative Feedback

In advance of each week’s seminar, students will be provided with exercise sets which they are advised to complete in advance of the seminar, amounting to around 2 hours work per week. At each seminar, feedback will be offered on this formative work, with model answers to the exercises made available after the seminar for reference. Office hours will also be available to provide additional feedback on student’s answers to these exercises. In total, formative feedback will be given on 8 sets of exercises and on 1 practice exam paper.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Online Assessment	Final assessment of student achievement across the topics of the module, including multiple-choice, problem-based and mini-essay-based sections.	100.00
Total percentage (Assessment Coursework)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 08/05/2024 17:09:09

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