The Power and Limits of Logic (PHIL30043)

Undergraduate level 3Points: 12.5On Campus (Parkville)

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Overview

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Semester 2
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This subject deals with the power and limits of logic. We will cover some of the great conceptual advances in logic in the 20th Century, which have revolutionised our understanding of logic and language, of models and meaning, and of concepts and computation. We will examine the conceptual foundations of logic and the way it can be applied, not only to develop theories in other domains, but how we can learn the limits of logic when we attempt to apply its power to logic itself.

In the course we will examine fundamental results such as (1) the soundness and completeness of different proof systems of first-order predicate logic, (2) the boundary between the countably infinite and the uncountably infinite, and (3) the boundary between the computable and the uncomputable. Concepts and results will be approached via both practical exposure to formal techniques and proofs and theoretical and philosophical reflection on those techniques.

Students will be able to appreciate the philosophical importance of the major logical results and equipping them for further work in logic in philosophy, mathematics, linguistics, computer science and related fields.

Intended learning outcomes

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

  • Develop and demonstrate an understanding of the core features of first order predicate logic, including soundness and completeness, the compactness theorem, computability and decidability
  • Clearly state and prove results in and about first order predicate logic
  • Develop a command of the connections between the concepts of proof, model, completeness, computation, and decidability, and their applications to areas inside and outside philosophy
  • Critically reflect on the strengths and weaknesses of formal logic and the ways it can be applied and mis-applied in different fields of inquiry
  • Work individually, and in groups, to clarify problems, apply reasoning techniques to different issues, and to critically evaluate the results.

Generic skills

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

  • Think critically
  • Analyse and evaluate concepts, theories, and arguments
  • Develop and present arguments for or against a position
  • Consider multiple viewpoints and arguments for those viewpoints
  • Articulate ideas, concepts, and interpretations with clarity and coherence
  • Engage in critical reflection, synthesis, and evaluation of research-based and scholarly literature.

Last updated: 9 April 2025

Eligibility and requirements

Prerequisites


Corequisites


Non-allowed subjects


Recommended background knowledge

Some familiarity with predicate logic is assumed, and having taken PHIL20030 is desirable. 

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 9 April 2025

Assessment

DescriptionTimingPercentage

Four problem sets

  • 2000 words (equivalent)
Throughout the teaching period50%

Written assignment 1

  • 1000 words
Mid semester25%

Written assignment 2

  • 1000 words
During the examination period25%
Hurdle requirement: 1. Attendance hurdle requirement: This subject has a minimum requirement of 80% attendance at tutorials, seminars, or workshops. There is an expectation that students attend lectures. Throughout the teaching periodN/A
Hurdle requirement: 2. Late Penalty and Assessment hurdle requirement: Assessment submitted late without an approved extension will be penalised at five per cent (5%) of the possible marks available for the assessment task per day or part thereof. All pieces of assessment must be submitted to pass the subject. Each submitted assessment must be complete, constitute a genuine attempt to address the requirements of the task and will not be accepted after 20 University business days from the original assessment due date without written approval. Throughout the semesterN/A

Last updated: 9 April 2025

Dates & times

  • Semester 2
    CoordinatorTristan Grotvedt
    Mode of deliveryOn Campus (Parkville)
    Contact hours35 hours: 1 x 2-hour lecture per week for 12 weeks, and 1 x 1-hour tutoral per week for 11 weeks (Week 2-12).
    Total time commitment170 hours
    Teaching period28 July 2025 to 26 October 2025
    Last self-enrol date 8 August 2025
    Census date 1 September 2025
    Last date to withdraw without fail26 September 2025
    Assessment period ends21 November 2025

    Semester 2 contact information

    Dr Tristan Grotvedt: tristan.grotvedt@unimelb.edu.au

Time commitment details

170 hours

What do these dates mean

Visit this webpage to find out about these key dates, including how they impact on:

  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Last updated: 9 April 2025

Further information

Last updated: 9 April 2025