## PHIL2122 Formal Logic

### 20 creditsClass Size: 80

Module manager: Professor John Divers
Email: j.divers@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2019/20

PHIL 1250

### Pre-requisites

 PHIL1250 How to Think Clearly and Argue Well

### This module is mutually exclusive with

 MATH2040 Mathematical Logic 1

Module replaces

PHIL2010 Formal Logic

This module is not approved as a discovery module

### Module summary

This module is only available as a discovery module for students studying on Linguistics, Mathematics and Computing modules with relevant prerequisites.Throughout the history of philosophy, philosophers have been keen to identify the principles of logic: those most general principles that we can always rely on not to take us wrong. You will learn about rigorous methods for proving whether an argument is valid or invalid. You will learn how to reason formally about a formal system. You will learn about modern developments in non-classical logic. This module will be of use and interest to mathematicians and computer scientists. But it should also be of use and interest to anyone who is interested in how we can rigorously establish conclusions: the formal study of logic is not some abstract technical theory, but a tool for sharpening our own thinking. There is no area of study in which argument is not important, and therefore no area of study in which knowledge of logic cannot help.The module is taught through lectures and tutorials and assessed by a final exam.

### Objectives

On completion of this module, students should be able to:

1. Formalize natural language arguments in first-order quantified logic.
2. Use a proof system (axiomatic, natural deduction, or truth trees) to complete derivations with formulas involving both connectives and quantifiers.
3. Demonstrate an understanding of model-theoretic notions like validity and invalidity, and be able to recognize a countermodel for invalid formulas and arguments.
4. Demonstrate an understanding of basic metatheoretical claims about first-order proof systems, like e.g. soundness and completeness.

### Syllabus

1. Revision: translation into a formal system and truth tables.
2. Introduction of a proof system for propositional first-order logic.
3. Introduction of a proof system for quantified first-order logic.
4. Basic metatheory: statement of soundness and completeness theorems for first-order logic.

### Teaching methods

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

### Private study

- Lecture preparation: 74 hours
- Tutorial preparation: 49 hours
- Exam preparation: 50 hours.

### Opportunities for Formative Feedback

There will be a mock exam paper distributed in eighth week for those who want one.

### Methods of assessment

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 00 mins 100.00 Total percentage (Assessment Exams) 100.00

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