The Power and Limits of Logic

This subject has the following teaching availabilities in 2016:

170 hours

Completion of at least one of the following is helpful, but is not required:

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.

It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support: http://services.unimelb.edu.au/disability

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.

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.

• Four tutorial exercises with short answer questions, due throughout semester (50%)
• A 2 hour closed book, written examination, in the end of semester examination period (50%)

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.

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.

The coordinator will advise students of any required texts.

This subject potentially can be taken as a breadth subject component for the following courses:

• Bachelor of Biomedicine
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music
• Bachelor of Science
• Bachelor of Engineering

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.