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The Power and Limits of Logic (PHIL30043)
Undergraduate level 3Points: 12.5Not available in 2022
From 2023 most subjects will be taught on campus only with flexible options limited to a select number of postgraduate programs and individual subjects.
To learn more, visit COVID-19 course and subject delivery.
Overview
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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: 3 June 2023
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 | No longer available | |
| PHIL20030 | Logical Methods | Semester 2 (Dual-Delivery - Parkville) |
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: 3 June 2023
Assessment
| Description | Timing | Percentage |
|---|---|---|
Four online quizzes | Throughout the teaching period | 50% |
A written assignment
| Mid semester | 25% |
A written assignment
| During the examination period | 25% |
| 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 period | N/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: 3 June 2023
Dates & times
Not available in 2022
Time commitment details
170 hours
Last updated: 3 June 2023
Further information
- Texts
Prescribed texts
The coordinator will advise students of any required texts.
- Related Handbook entries
This subject contributes to the following:
Type Name Major History and Philosophy of Science Major Philosophy Major Philosophy Major - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Biomedicine
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- Bachelor of Science
- Links to additional information
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 3 June 2023