The Power and Limits of Logic (PHIL30043)

Undergraduate level 3Points: 12.5Dual-Delivery (Parkville)

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Overview

Availability
Semester 1 - Dual-Delivery
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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 (3) the boundary between the computable and the uncomputable, and (4) Gödel's incompleteness theorem and its consequences. 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

Students who successfully complete this class should:



  • develop and demonstrate an understanding of the core features of first order predicate logic, including soundness and completeness, the compactness theorem, computability, decidability and Gödel’s incompleteness theorems;
  • demonstrate an ability to 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, decidability, and incompleteness, 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.

Last updated: 4 April 2025

Eligibility and requirements

Prerequisites

None

Corequisites

None

Non-allowed subjects

None

Recommended background knowledge

Completion of at least one of the subjects listed as recommended is helpful, but is not required:

Code Name Teaching period Credit Points
UNIB10002 Logic: Language and Information
Semester 1 (Online)
 12.5
PHIL20030 Logical Methods
Semester 2 (Online)
 12.5
MAST10012 Introduction to Mathematics
Semester 1 (Dual-Delivery - Parkville)
 12.5

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: 4 April 2025

Assessment

DescriptionTimingPercentage

Four online quizzes

Throughout the teaching period50%

A written assignment

  • 800 words
Mid semester25%

A written assignment

  • 800 words
During the examination period25%
Hurdle requirement: Students must attend a minimum of 75% of tutorials in order to pass this subject. All pieces of written work must be submitted to pass this subject.Throughout the teaching periodN/A

Additional details

Note: Assessment submitted late without an approved extension will be penalised at 10% per day. After five days late assessment will not be marked. In-class tasks missed without approval will not be marked.

Last updated: 4 April 2025

Dates & times

  • Semester 1
    CoordinatorGreg Restall
    Mode of deliveryDual-Delivery (Parkville)
    Contact hours1 x 2 hour seminar/workshop each week and 1 x 1.5 hour video lecture in preparation for each seminar.
    Total time commitment170 hours
    Teaching period 1 March 2021 to 30 May 2021
    Last self-enrol date12 March 2021
    Census date31 March 2021
    Last date to withdraw without fail 7 May 2021
    Assessment period ends25 June 2021

Time commitment details

170 hours

Last updated: 4 April 2025

Further information

Last updated: 4 April 2025