Prof John Worrall LAK3.02

This course is compulsory on the BSc in Philosophy and Economics, BSc in Philosophy, Logic and Scientific Method and BSc in Politics and Philosophy. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

We reason or make deductions all the time - both in intellectual disciplines and in everyday life. For example, a scientist will test a particular theory by reasoning that if that theory were true then some other claim, one that can be checked observationally or experimentally, would have to be true as well - that is, by showing that some observationally testable claim is deducible from the theory. Mathematics is of course concerned with proofs and proofs are deductive inferences. Finally, philosophy is centrally concerned with arguments or deductions. To take one example, many have argued that the presence of evil in the world is incompatible with the existence of an all-powerful, all-knowing, all-merciful god as proposed in, for example, Judaeo-Christian theology. That is, they have claimed that if you assumed that there is such a god, then it would follow, or you could infer that, there would be no evil in the world. But since there is evil, it follows that there can be no such god. More mundanely, we reason, or make inferences, all the time - though we don't always think of it that way.

Deductive Logic is the study of such inferences - it therefore has an enormously broad scope. Different disciplines have different ways of garnering information in the first place (the way that we arrive at a scientific theory is different from the way that we arrive at an axiom in mathematics or a thesis in philosophy), but the way that we reason from that information is the same no matter what the discipline. The main task of logic is to give an explicit characterisation of those inferences that are correct, or as we shall say, VALID (and hence differentiate them from those that are invalid). Logic tells you exactly when some conclusion really does follow from some premises and when it does not.

The course begins with a simple system called propositional or truth-functional logic, which despite its simplicity captures a great range of important arguments. The system of predicate logic that we study next is, however, still more powerful and provides the logical basis not only for ordinary inferences but also for inferences in the sciences.  In both the case of propositional and of predicate logic, the course also covers other notions, such as the consistency of a set of sentences, and the independence of one sentence from a set of assumptions, that are closely related to validity of inference. Finally the course covers some issues in the foundations of logic - to do with truth and sets.

15 hours of lectures and 9 hours of classes in the MT. 15 hours of lectures and 10 hours of classes in the LT. 1 hour of lectures and 2 hours of classes in the ST.

Formative coursework will take the form of a number of computer based quizzes and a number of regular exercises. Both of these will be set on the basis of the material covered in lectures. In the case of the computer based quizzes, students are required to complete them before a specific deadline; these will be discussed in class. In the case of the regular exercises, students are required to complete these and to be ready to present and discuss answers in the associated class; some of these will be formatively assessed by the class teachers. Successful completion of both the quizzes and the regular exercises is regarded as a prerequisite for admission to the examination for this course.

Detailed course notes are provided and are intended to be sufficient reading for the course. However for those who like to have a book the one whose treatment is closest to that adopted in the lectures is P.Suppes Introduction to Logic (Van Nostrand).

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