Introduction to Logic and Computability

Description

This course introduces the students to reasoning with clarity and rigour. In particular, we ask: what is it to deduce a conclusion validly from some premises? Broadly, we will study the techniques, scope, and limits of formal logic.

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 of immense cultural importance: 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 course aims systematically to introduce the subject of formal logic, and thereby to acquaint the students with many key, canonical results and ideas that have emerged in this subject in the past 150 years. They will acquire an appreciation of (i) the significance of formal logic for the advent of computers, and (ii) the philosophical significance of the mathematically demonstrable limitations of logic.

Relation to other courses:
The course can be credited as either Arts or Science points and is potentially valuable within any undergraduate degree. Since everyone uses reasoning, the course addresses itself to a subject with which everyone has some informal familiarity. No prior learning in either mathematics or philosophy is presupposed. Students who come to the course knowing something (from mathematics or computer science) about symbolic reasoning will learn many new things about that subject. Students with little such prior familiarity will build their confidence with symbols, confidence that could generalise to other symbolically-oriented forms of study. In any case, all students in the course will discover that the course presupposes nothing except that they possess ingenuity, perseverance, care for detail, and curiosity about the nature of good reasoning.