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PHIL312 Advanced Formal Logic

Advanced applications of first-order logic. The logical structure of theories, including formal number theory. Proof of the completeness of first-order logic (everything provable in it is valid and everything valid in it is provable).

This paper is an introduction to non-classical logic, covering the basics of systems that go beyond "black and white" reasoning (e.g. modal, intuitionistic, relevant and many-valued logics). Philosophical issues are discussed alongside formal techniques.

Paper title Advanced Formal Logic
Paper code PHIL312
Subject Philosophy
EFTS 0.1500
Points 18 points
Teaching period Second Semester
Domestic Tuition Fees (NZD) $868.95
International Tuition Fees (NZD) $3,656.70

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PHIL 212 or PHIL 222 or PHIL 322
Schedule C
Arts and Music
Pre-requisites may be waived on a case-by-case basis.
Teaching staff
Dr Zach Weber
Paper Structure
Two 1-hour lectures per week and one tutorial

Weekly lectures expand on the basic material covered in readings. At a rate of approximately one topic per week, we examine modal logics, intuitionistic, paraconsistent, paracomplete, relevant and fuzzy logic. Each logic is motivated by philosophical problems, which challenge our intuitive notions of logical correctness. The relationship between model structures and proofs is emphasised throughout.

  • Weekly homework assignments collected and discussed in tutorials
  • Two in-class tests
  • Final exam
Teaching Arrangements
Learning logic is like learning a foreign language - you have to practice! Weekly homeworks are announced in class at the start of the week and collected and discussed in tutorials. These are exercises to help you keep up with the material, which is cumulative.
Introduction to Non-Classical Logic by Graham Priest
Graduate Attributes Emphasised
Lifelong learning, Scholarship, Critical thinking, Self-motivation.
View more information about Otago's graduate attributes.
Learning Outcomes
Students who successfully complete the paper will acquire
  • A working knowledge of several non-classical logics, including the philosophical motivations for these logics
  • Competence with checking the validity of arguments in different logics and constructing counterexamples to invalid arguments
  • Demonstrated ability to work with abstract models and understand their relationship to data

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Second Semester

Teaching method
This paper is taught On Campus
Learning management system


Stream Days Times Weeks
L1 Monday 10:00-10:50 28-34, 36-41
Tuesday 11:00-11:50 28-34, 36-41
Wednesday 14:00-14:50 28-34, 36-41