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PH104

Formal Methods of Philosophical Argumentation

**This information is for the 2019/20 session.**

**Teacher responsible**

Dr Laurenz Hudetz

**Availability**

This course is available on the BSc in Management, BSc in Philosophy and Economics, BSc in Philosophy, Logic and Scientific Method, BSc in Philosophy, Politics and Economics, BSc in Politics, BSc in Politics and International Relations 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.

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 for 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 are 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 (where regulations permit this choice).

**Pre-requisites**

Although there are no formal prerequisities, facility in formal reasoning (such as employed in mathematics or statistics) will be presupposed.

**Course content**

**Deductive Logic. **Arguments and inferences play a fundamental role in philosophy, science and many areas of everyday life. The main task of deductive logic is to define in a rigorous way under which conditions the conclusion of a given argument or inference follows logically from its premises. This yields an explicit characterisation of those arguments and inferences that are deductively valid (and hence differentiates them from those that are invalid).

This course provides answers to central questions such as the following:

1. What exactly are arguments and inferences and which quality criteria should they satisfy?

2. What exactly does it mean that the truth of a statement is guaranteed by the truth of other statements?

3. What exactly does it mean that a statement is true (given an interpretation of the language in which it is formulated)?

4. Is it possible to find a few manageable inference rules such that, given any valid argument, its conclusion can be derived from its premises using only these rules?

5. Is there a general method for checking whether a given argument or inference is valid?

The course begins with a simple system called propositional or truth-functional logic, which despite its simplicity captures a significant range of important arguments. The course then focuses on predicate logic, which is much more powerful and provides the logical basis for analysing a great variety of arguments and theories.

**Inductive Logic and Probability.** In the case of a deductively valid argument, it is utterly impossible that the conclusion is false if the premises are true. However, in practice it is often only improbable that the conclusion is false if the premises are true. In such cases, the premises only support the conclusion to some degree, but their truth would not guarantee the truth of the conclusion. Arguments of this kind are deductively not valid but may still be inductively strong. For example, it does not follow logically 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 it is much more probable that s/he will than if s/he did not smoke. Analysing this type of reasoning leads us to some fundamental issues concerning the notion of probability, which are relevant to many current philosophical debates (e.g. in epistemology, philosophy of science, decision theory, philosophy of economics, philosophy of physics and various other areas).

Building on the axiomatic development of probability theory (which students may be familiar with from ST107 or ST102), this course focuses on conceptual and foundational topics concerning probability. For example, it is important to distinguish between different concepts ("interpretations") of probability. On the one hand, one can understand probabilities as an agent's subjective degrees of belief. On the other hand, having a certain probability can be understood as an objective feature of events that is independent of what anyone believes. The subjective conception of probability has been developed into a full-blown Bayesian account of confirmation, the essentials of which will also be covered.

**Formal Frameworks for Philosophy.** In addition to logic and probability theory, the course also covers further formal frameworks and methods that are often presupposed in contemporary philosophical work. It introduces important concepts from set theory and presents formal accounts of possibility and necessity, conditionals, causation, qualitative and quantitative concepts of rational belief as well as preference and utility.

**Teaching**

15 hours of lectures and 10 hours of classes in the MT. 15 hours of lectures and 10 hours of classes in the LT.

**Formative coursework**

Formative coursework will take the form of a number of 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 quizzes, students are required to complete them before a specific deadline. 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.

**Indicative reading**

There will be comprehensive lecture slides covering the entire course content. Useful but not mandatory background readings include the following:

On Deductive Logic:

Halbach, V. (2010): The Logic Manual. Oxford University Press.

Magnus, P.D. and Button, T. (2017): forallx: Cambridge. (available online)

On Inductive Logic, Probability and Formal Frameworks for Philosophy:

Howson, C. and Urbach, P. (2006): Scientific Reasoning: The Bayesian Approach. Open Court.

Papineau, D. (2012): Philosophical Devices: Proofs, Probabilities, Possibilities and Sets. OUP.

Skyrms, B. (2010): Choice and Chance: An Introduction to Inductive Logic. Fourth edition. Wadsworth.

Various entries in the Stanford Encyclopedia of Philosophy. Links will be provided in the lecture slides.

**Assessment**

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

** Key facts **

Department: Philosophy, Logic and Scientific Method

Total students 2018/19: 45

Average class size 2018/19: 11

Capped 2018/19: No

Value: One Unit

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills