MATH3021 Philosophy of Logic and Mathematics

Reading List
  • Taught: Semester 2 View timetable
  • Credits: 20
  • Class Size: 35
  • Module Manager: Professor Michael Rathjen
  • Email:
  • Pre-Requisite Qualifications: MATH2040 or PHIL2121 or PHIL2122.
  • This Module is approved as a Discovery Module
  • This module is mutually exclusive with:
    • MATH5021M Philosophy of Logic and Mathematics
    • PHIL3123 Philosophy of Logic and Mathematics

Discovery module overview

Module Summary

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.


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.


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?

Assessment and teaching

Assessment and teaching


Assesment type Notes % of formal assesment
Essay 2,000 words 50
Essay 2,000 words 50
Total percentages (Assessment Coursework) 100

Private Study

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

Progress Monitoring

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.

Teaching methods

Delivery type Number Length hours Student hours
Seminar 27 1 27
Private Study Hours 173
Total Contact Hours 27
Total hours (100hr per 10 credits) 200

Reading List

Reading List
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