Dr Laurenz Hudetz

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.

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. 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. Students will be introduced to core concepts of model theory. We address questions such as the following: What exactly is a structure or model? What is a theory? What does it mean that a structure satisfies a formula or theory? When are two models structurally the same (isomorphic)? Rigorous answers to these questions yield a proper semantics for classical predicate logic, shed light on the notion of truth and help to better understand the formal structure of scientific theories and models.

3. The theory of definitions

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 justice?’, ‘Under which conditions is an act morally wrong?’).

4. Extensions of classical logic

Classical logic only deals with truth-functional sentential 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’), causal notions (‘A causes B’) 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. Inductive logic and probability

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 probabilistic reasoning.

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

This year, lectures will be delivered online. 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 will take the form of problem sets. These will be set on the basis of the material covered in lectures. Students are required to complete problem sets before the associated class and to be ready to present and discuss their answers in class.

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/>.
• Fitelson, B. (2006): “Inductive Logic”, Sarkar, Sahotra and Jessica Pfeifer (eds.), The Philosophy of Science: An Encyclopedia, Routledge.
• Halbach, V. (2010): The Logic Manual. Oxford University Press.
• Hodges, B. (2013): “Model Theory”, Stanford Encyclopedia of Philosophy, URL=<https://plato.stanford.edu/entries/model-theory/>.
• Hodges, W. and Scanlon, T. (2018): “First-order Model Theory”, Stanford Encyclopedia of Philosophy, URL=<https://plato.stanford.edu/entries/modeltheory-fo/>.
• 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

Take-home assessment (90%) in the ST.
Quiz (10%) in the MT and LT.