Dr Owen Griffiths

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.

This course concerns formal methods of reasoning in philosophy.

1. Deductive Logic. Philosophy is centrally concerned with arguments. The first question to be asked of any argument (or inference) is whether or not it is valid: that is, does its conclusion really follow from its cited premises.Validity of inference is the central problem of deductive logic.Logic has universal scope: different disciplines have different ways of garnering information, but the way that we reason deductively from that information is the same no matter what the discipline.The key to answering some other formal questions that often arise in philosophy - such as whether some set of assumptions is consistent - is also provided by deductive logic.

This section of the course covers first a simple system called propositional or truth-functional logic, which, despite its simplicity, captures a great range of important arguments and provides a formal articulation of the notions of validity of inference and consistency of a set of sentences.The main system covered, however, is (first order) predicate logic, which is powerful enough to capture not only simple inferences but also those involved in philosophy and the sciences.

The final section of this first part of the course investigates more systematically how the formal techniques provided by these systems of logic relate to the more informal arguments found in philosophy (and ordinary discourse).

2. Probability. In a valid deductive argument, the conclusion must be true if the premises are. However many inferences conclude only that a certain claim is probable (or more probable than it would otherwise be). For example, we clearly cannot conclude from the premise that someone smokes 40 cigarettes a day that s/he will die early from a smoking-related illness, but we can infer that  such an early death is much more probable than if s/he did not smoke.

Issues about probabilities play many roles in current philosophical debates: in decision theory, philosophy of economics, philosophy of physics and many other areas. This section of the course introduces the axioms of probability theory and then turns to foundational issues. It turns out that there are different interpretations of the probability axioms: in particular, a subjective interpretation which sees probabilities as credences or degrees of belief in the truth of some proposition, and objective interpretations which see probabilities as properties of physical events (such as the decay of a particular radioactive molecule in a given time interval. Interesting difficulties arise with both interpretations. The subjective interpretation has been developed into a full-blown, general Bayesian account of theory-confirmation in science - the essentials of this account will also be covered.

3. Formal Philosophical Devices. The final section of the course covers some of the formal, technical ideas that are often presupposed in contemporary philosophical work: including the notions of sets and infinities;theories of truth (and partial truth);analyticity and the a priori; possibility and necessity; and conditionals. Some of these notions have been clarified via analyses of some celebrated 'paradoxes' that will also be covered in this section of the course.

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.

Extensive lecture notes will be provided covering the first part  of the course. Further reading for parts 2 and 3 will be listed on the weekly worksheets available on Moodle.

Exam (100%, duration: 3 hours, reading time: 15 minutes) in the main exam period.