Miklos Redei

MSc Economics and Philosophy, MSc Philosophy of the Social Sciences and MSc Philosophy and History of Science. The course is available as an outside option where programme regulations permit.

PH101 or equivalent

The aim of the course is to make students of philosophy familiar with the elements of naive and axiomatic set theory, classical mathematical logic and propositional modal logic. From set theory, two types of facts and results are covered: (i) the ones needed to understand the basic notions, constructions and the mode of thinking in mathematical logic (ii) the ones that have philosophical-conceptual significance in themselves (elementary theory of ordinals and cardinals, transfinite induction, Axiom of Choice and its equivalents, Continuum Hypothesis, Russell paradox). Formal languages, syntactic-semantic, theorem-metatheorem, soundness and completeness and some model theory are the main topics covered from classical first-order logic, together with an outline of Peano arithmetic, decidability and Gödel's incompleteness theorems. The idea of possible world semantic and the semantic characterization of the basic types of modal propositional logics are covered from modal logic. In both set theory and logic, emphasis is on the conceptual-structural elements rather than on technical-computational details. Not all theorems are proven and not all proofs are complete.

30 hours of lectures and 20 hours of classes across the Michaelmas and Lent Terms.

Students are required to write three 1,500 word essays during the year on a topic from a list and are to hand in two problem solutions each term.

Peter J. Cameron. Sets, Logic and Categories. Springer undergraduate mathematics series. Springer, London, Berlin, Heidelberg, 1999.(main text for set theory); Sider, Theodore. Logic for Philosophy. Oxford University Press 2010. (main text for logic); J. Crossley. What is Mathematical Logic? Oxford University Press, Oxford, 1972.; H.B. Curry. Foundations of Mathematical Logic. McGraw-Hill, New York, 1963;. L. Goble, editor. The Blackwell Guide to Philosophical Logic, Oxford, 2001. Blackwell.; G.E. Hughes and M.J. Cresswell. A New Introduction to Modal Logic. Routledge, New York, 1996. (main text for modal logic).; D. Lewis. Counterfactuals. Blackwell, Oxford, 2nd edition, 2001. First edition: 1979.; D. Makinson. Sets, Logic and Maths for Computing. Springer, London, 2008.

Three hour written examination in the ST (100%).