# 2019/20 Taught Postgraduate Module Catalogue

## MATH5021M Philosophy of Logic and Mathematics

### 20 creditsClass Size: 30

Module manager: Professor Michael Rathjen
Email: M.Rathjen@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2019/20

### Pre-requisite qualifications

MATH2040 or PHIL2121 or PHIL2122.

### This module is mutually exclusive with

 MATH3021 Philosophy of Logic and Mathematics PHIL3123 Philosophy of Logic & Maths

This module is approved as an Elective

### Module summary

Mathematics contrasts with empirical sciences, at least at first glance. Mathematicians are not content with experiments that confirm their hypothesis, they seek proofs. Science is contingent, where mathematics, if true, is necessarily true. However, scientific theories are often framed in mathematical terms. So what's the connection? How can mathematics be relevant to empirical applications? These features of mathematics give rise to some deep and extremely interesting philosophical questions. We will discuss a number of classical and contemporary approaches to these questions and related ones.

### Objectives

On completion of this module, students should be able to:
- understand and discuss critically in detail the philosophical issues concerning the nature and application of logic or mathematics;
- read, interpret and criticise historical and contemporary research work on the subject.

### Syllabus

Students will study a selection from the following or relevantly similar topics:

Philosophy of Mathematics Logicism (Frege, Russell, etc) Intuitionism (Kant and Kantians, Brouwer, etc) Formalism (Hilbert) The metaphysics of mathematical objects: realism and nominalism The epistemology of mathematics The (unreasonable?) effectiveness of mathematics in the sciences.

Philosophy of Logic What is logic? Logical constants; the scope of logic; higher order logic. Logical concepts: philosophical analysis of one or more of: the conditional, quantifiers, negation, definite descriptions etc. Alternative logics: free logic; many-valued and fuzzy logics; intuitionistic logic; relevance logics. Modern theories of truth from Russell to the present: correspondence, redundancy, Tarski, minimalism, truthmaker theory. Theories of vagueness: fuzzy logic, supervaluation, epistemic theories. Intensional logics, their uses and justifications. Paradoxes: types and avoidance strategies. Expanding logic: Generalised Quantifiers; Indexicals; Tense; Logic Diagrams. Approached to logic: formalist; semantic; logic in use. Logic and ontology. Logic, cognition and natural language; non-monotonic logics. Logic and computing: paradigms and their motivation; dynamic logics. Logic: One or Many?

### Teaching methods

 Delivery type Number Length hours Student hours Seminar 27 1.00 27.00 Private study hours 173.00 Total Contact hours 27.00 Total hours (100hr per 10 credits) 200.00

### Private study

Reading & seminar preparation: 113 hours;
Essay preapration: 60 hours.

### Opportunities for Formative Feedback

Students will be asked to hand in work during one seminar each week which can form the basis of discussion with module leader in office hours. They will be invited to submit draft essay/mock exams prior to formal assessment. The module leader will comment on these on request. Students will be invited to prepare and present material during seminars.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Essay 3,000 words 50.00 Essay 3,000 words 50.00 Total percentage (Assessment Coursework) 100.00

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