MATH134-10SU1 (C)
Logic and Computability
This is a summer course worth 18 points.
Course Information
This course introduces you to reasoning with utmost clarity and rigour about what it is to reason carefully and well. In particular, we ask: what is it to deduce a conclusion validly from some premises? One purpose of the course is to articulate a precise and cogent answer to this question. Another purpose is to descry a way in which valid deduction is demonstrably limited, and so seems not a complete view of what reason or rationality is.
In brief, we will study formal logic, its scope and limits. Logic as an inquiry has changed profoundly in the last 150 years, very much because of investigations where philosophy and mathematics intersect. These changes are intellectually rich and exciting. They are also hugely consequential culturally. For without formal logic there would be no computers. And without computers, our social forms and ways of getting on in the world would be very different.
The present course surveys the discoveries about reason which made the computer revolution possible. It demonstrates the expressive superiority of the symbolic language of logic vis-á-vis human languages, like English, in the domain of reasoning and highlights some aspects of the intriguing and mysterious relationship between the two. In so doing it also surveys some fundamental insights regarding the limits of symbolical reasoning, and thus of logic itself. It introduces you to propositional and predicate logic, soundness and completeness notions and results, the undecidability of the self-halting problem and its philosophical significance, and the relations between formal logic and the theory of computation.
Text
Jeffery, Richard. Formal Logic: Its Scope and Limits, 3rd ed. McGraw-Hill, 1991. Republished by Hackett 2004.
Notes
MATH 134, MATH 144, PHIL 134 and PHIL 144 are equivalent courses.
Enquiries
Mathematics and Statistics Reception
Room 436 Erskine Building
Phone (03) 364 2600