Prof John Worrall LAK 3.02

This course is available on the MPhil/PhD in Philosophy and MPhil/PhD in Philosophy of the Social Sciences. This course is not available as an outside option.

The course is, in general, only aimed at those students who have never taken a course in formal logic before. For such students the course is compulsory.

The course aims to give a precise formulation of correct deductive reasoning- of what it means for a sentence to follow from a set of other sentences taken as premises- and to investigate on this basis other important logical notions such as that of consistency. The course will also investigate how these formal principles are of use in analysing informal argumentation. Mathematicians lay down certain axioms and establish theorems by deducing them as consequences of the axioms; scientists postulate certain theories and test them by deducing certain consequences from them that can be checked experimentally; ordinary reasoners try to win (intellectual) arguments by showing that some position that they favour follows deductively from assumptions that everyone accepts. This course studies what exactly is involved in correct deductive reasoning. It begins by considering certain very simple inferences that can be formalized in a system called propositional logic. The semantic notion of deductive validity is developed for this system and the truth table, "no counterexample" and tree methods for establishing validity in propositional logic are introduced. The connections between validity and other important logical notions such as equivalence, consistency and independence are precisely detailed. Some simple results about propositional logic are proved. More complex inferences require a system called (first order) predicate logic. The course shows how to formalize some ordinary informal sentences (and therefore ordinary informal inferences) in predicate logic; and introduces methods for establishing the validity or invalidity of predicate logic inferences: both a system based on rules of proof and one based on the tree method will be studied. Again the relationships between validity of inference, on the one hand, and the notions of the logical equivalence of two sentences, the consistency of a set of sentences or the independence of one sentence from a set of sentences, on the other, are investigated for the more powerful system of predicate logic. Both the systems that we shall study - of propositional and predicate logic - are entirely formal. Although we shall emphasize how some especially simple ordinary arguments can be 'captured' within such systems, it is of course true that 'ordinary reasoners' do not explicitly employ such formal techniques. How then, if at all, can formal logic help in assessing ordinary deductive reasoning in science, social science and elsewhere?

15 hours of lectures in the MT. 15 hours of lectures in the LT.

Appropriate back-up teaching will be arranged with individual students.

Regular exercises will be set on the basis of the material covered in lectures; students are required to complete these exercises and to be ready to present and discuss answers in the associated seminar, where applications of formal logic to informal reasoning will also be investigated.

Extensive lecture notes will be provided covering all aspects of the course. Students will however find it useful to consult C Howson, Logic with Trees. This text concentrates exclusively on the method of trees, while the lecture also introduces other equivalent methods.

Exam (100%, duration: 3 hours) in the main exam period.