Prof John Worrall LAK 3.02

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

This course is compulsory on the BSc in Philosophy, Politics and Economics (2nd year). It is compulsory on the BSc in Philosophy and Economics for those students who do not take PH101 in their first year. It is available as a more demanding alternative to PH101 the BSc Philosophy and Economics (1st year); BSc in Philosophy, Logic and Scientific Method and the 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.

Students will be advised that it is a more demanding alternative to PH101. Only students with facility in formal reasoning (such as employed in mathematics or statistics) are advised to take this course rather than PH101.

1. Deductive Logic. Philosophy is centrally concerned with arguments – for or against the existence of God, for or against the idea that humans possess free will, for or against the idea of an objective and absolute system of morality, etc. 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 the cited premises?

Validity of inference is the central problem of deductive logic. Logic has universal scope: different disciplines have different ways of garnering information (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 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 a position (set of assumptions and claims) is consistent (let alone true) – 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 key notions of validity and consistency. 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 part of the course investigates more systematically how the formal techniques provided by these systems of logic relate to the invariably 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. Many inferences that we make, however, conclude only that a certain claim is probable (or more probable than it would otherwise be). For example, we clearly cannot infer from the premise that someone smokes 40 cigarettes a day (together with background medical theories and data), that s/he will die early from smoking-related illness, but we can infer that it is much more probable that she will 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. Building on the axiomatic development of probability that students will have covered in ST102, this section of the course will cover elements of probability logic together with some foundational issues.  For example, it turns out that there are importantly different notions of probabilities, that is, different interpretations of these axioms. In particular, a subjective interpretation which makes probabilities credences or degrees of belief and objective interpretations which see probabilities as properties of physical events (like the probability of a particular radioactive atom decaying in a given time interval). Some interesting difficulties arise with both interpretations.

The subjective interpretation has been developed into a full-blown and general “Bayesian” account of theory confirmation in science, the essentials of which will also be covered.

3. Formal Philosophical Devices. This final section of the course covers some of the formal, technical ideas that are often presupposed in contemporary philosophical work: this may include the notions of sets and infinities; theories of truth; analyticity and aprioricity; possiblity and necessity; and conditionals. Many of these notions have been clarified via analyses of various celebrated paradoxes that will also be covered in this section of the course.

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.

There are regular structured exercises on Moodle, as there are now for PH101.

Students will be expected to produce 10 quizzes and 10 exercises in the MT and LT.

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 later sections of the course, exercises will include questions requiring brief essay answers.

John Worrall; Deductive Logic (unpublished notes);

Colin Howson and Peter Urbach: Scientific Reasoning- the Bayesian Approach 3rd edition, Open Court, 2006.

Alan Hajek ‘Interpretations of Probability’ Stanford Encyclopaedia of Philosophy http://plato.stanford.edu/entries/probability-interpret. 

David Papineau, Philosophical Devices: Proofs, Probabilities, Possibilities and Sets. OUP 2012;

Mark Sainsbury Paradoxes, CUP.

For Part 1: extensive notes are provided that are intended to be sufficient reading for this section of the course. Patrick Suppes, Introduction to Logic (Van Nostrand) is the book that most closely follows the system developed in the lectures.

For Part 2: Further course notes; Colin Howson and Peter Urbach: Scientific Reasoning- the Bayesian Approach 3rd edition, Open Court, 2006. Entry on ‘Interpretations of Probability’ by Alan Hajek in the Stanford Encyclopaedia of Philosophy http://plato.stanford.edu/entries/probability-interpret

For Part 3: David Papineau, Philosophical Devices: Proofs, Probabilities, Possibilities and Sets. OUP 2012; Mark Sainsbury Paradoxes, CUP.

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