## PH502Logic and Probability

This information is for the 2022/23 session.

Teacher responsible

Dr Laurenz Hudetz

Dr Wesley Wrigley

Availability

This course is available on the MPhil/PhD in Philosophy. 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.

Course content

This course covers the following topics.

1. Introduction to classical logic

Logic is the study of arguments and inferences. Its main task is to give an explicit characterisation of those arguments and inferences that are logically valid. Logic tells you exactly when some conclusion follows from some premises and when it does not. The skill of devising logically valid arguments is very important for philosophers. We train this and related skills based on classical theories of logical consequence. The course covers sentential or propositional logic as well as (first-order) predicate logic.

2. The art of defining

The modern theory of definitions offers a precise definition of ‘definition’ as well as rigorous criteria for checking whether a definition is formally correct. The skill of defining in a correct way can hardly be overestimated in philosophy. It prevents misunderstandings and can drastically improve the clarity of concepts, claims and arguments. It is particularly important for philosophers because many philosophical questions require definitions as answers (e.g., ‘What is knowledge?’, ‘What is truth?’, ‘What is a just society?’, ‘Under which conditions is an act morally wrong?’).

3. Set theory and model theory

Scientists often use mathematical structures to model real-world systems and to predict or explain their behaviour. Model theory is the study of mathematical structures from a logical point of view. It rests on set theory, which can be viewed as the foundation of modern mathematics. Students will be introduced to core concepts of set theory and model theory that help to better understand the formal architecture of scientific theories and models.

4. Possible world semantics

Classical logic only deals with truth-functional logical connectives (e.g., ‘not’, ‘and’, ‘or’). However, there are also non-truth-functional connectives which play a central role in philosophical and scientific reasoning. Prime examples are counterfactual conditionals (‘if A were the case, then B would be the case’) and modal notions (such as ‘it is possible that A’ and ‘it is necessary that A’). But what exactly is the meaning of these notions? In other words: how could a semantics for such non-truth-functional connectives look like? This course introduces students to the basic ideas of possible world semantics.

5. Probability theory and inductive logic

In the case of a deductively valid inference, it is utterly impossible that the conclusion is false when the premises are true. However, many inferences we draw in practice do not satisfy this ideal of validity. In many cases, the premises support the conclusion to some degree, but their truth would not guarantee the truth of the conclusion. 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 they will die early from smoking-related illness -- but it is much more probable that they will than if they did not smoke. Inductive logic is the systematic study of inferences of that type. Students will be introduced to the fundamentals of inductive logic and probability theory.

Teaching

15 hours of lectures in the MT. 15 hours of lectures in the LT.

Teaching in Michaelmas Term is delivered following a flipped learning approach. There are online lecture videos that students can watch in their own time; and the timetabled lecture slot is used for Q&A sessions with the lecturer.

Teaching in Lent Term is delivered following the standard approach of in-person lectures.

Appropriate back-up teaching will be arranged with individual students.

This course includes a reading week in Week 6 of both MT and LT.

Formative coursework

Formative coursework will take the form of problem sets and online quizzes.

There will be comprehensive lecture slides and materials covering the entire course content. Indicative background readings include:

• Button, T. and Magnus, P.D. (2017): forall x: Cambridge, URL= < http://www.homepages.ucl.ac.uk/~uctytbu/OERs.html>
• Copi I.M., Cohen, C. and McMahon K. (2014): Introduction to Logic. Pearson.
• Gupta, A. (2015): “Definitions”, Stanford Encyclopedia of Philosophy, URL=<https://plato.stanford.edu/entries/definitions/>.
• Hodges, W. and Scanlon, T. (2018): “First-order Model Theory”, Stanford Encyclopedia of Philosophy, URL=<https://plato.stanford.edu/entries/modeltheory-fo/>.
• Papineau, D. (2012): Philosophical Devices: Proofs, Probabilities, Possibilities and Sets. OUP.
• Salmon, M.H. (2013): Introduction to Logic and Critical Thinking. Wadsworth.
• Sider, T. (2010): Logic for Philosophy. OUP.
• Skyrms, B. (2010): Choice and Chance: An Introduction to Inductive Logic. Fourth edition. Wadsworth

Assessment

Exam (50%, duration: 2 hours, reading time: 15 minutes) in the January exam period.
Exam (50%, duration: 2 hours, reading time: 15 minutes) in the summer exam period.

Key facts

Department: Philosophy, Logic and Scientific Method

Total students 2021/22: 1

Average class size 2021/22: Unavailable

Lecture capture used 2021/22: Yes (LT)

Value: One Unit

Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Personal development skills

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