Critical Reasoning and Logical Argument

The details
Colchester Campus
Full Year
Undergraduate: Level 4
Thursday 03 October 2019
Friday 26 June 2020
02 September 2019


Requisites for this module



Key module for


Module description

Logic comes in two main kinds: formal and informal. Formal logic attempts to express and evaluate arguments using a specialised logical notation or set of symbols, whereas informal logic does the same in natural language (although it does sometimes involve the use of technical terms that differ from ordinary, everyday English).

In the Autumn Term, the focus will be on informal logic (or ‘critical reasoning’). Even without knowing it, we all already use informal logic to some extent. We regard some arguments as successful and others as unsuccessful in establishing their conclusions, and we may be able to give reasons why some arguments succeed and others fail. We may also recognise and distinguish between different kinds of argumentative move: e.g. the 'slippery slope argument' or the ‘ad hominem’. However, our grasp of these is often vague or implicit. The aim of the Autumn part of the course is to develop and sharpen this implicit understanding of informal logic by subjecting to critical scrutiny a range of key concepts such as ‘validity’, ‘soundness’ and ‘inference’, as well as looking some of the ways in which arguments can go wrong (sometimes termed 'fallacies'). These concepts help to understand and classify the arguments we come across, whether in philosophical prose or in other forms (such as the newspaper article or the political speech). Since informal logic is closely related to the ability to organise and express complex ideas with clarity and precision, this part of the course will also involve some intensive work on writing skills and even some basic grammar.

It can be useful to approach informal logic by focusing discussion around a particular topic or theme. For the academic year 2019-20, the chosen theme will be: ‘the politics of the university’. Broadly understood, this refers to the set of issues having to do with relations of power as they manifest themselves in the context of higher education. For example, we may discuss the recent and on-going ‘marketisation’ of the sector, the introduction of fees, student protest, industrial action by university staff, or issues of ‘free speech’ on campus.

Building on some of the notions and skills introduced in the Autumn, in the second part of the course we will look at ways of formalising arguments. Logic, both formal and informal, is about good reasoning: reasoning that consists of valid arguments. What formal logic gives us is a way of modelling valid arguments so we can better understand the patterns of thought used in good reasoning. To do this, we first translate arguments written in English into an abstract, artificial language which makes their structure clear and unambiguous. We can then apply tests to see whether or not the arguments are valid. In the process, the formalised arguments tell us something about the arguments in English that we started from: in the case of a valid argument, formalisation enables us to study the form of inference that made the reasoning correct, while in the case of an invalid argument, it provides a useful diagnostic tool. We will look at two simple formal languages, those of ‘propositional logic’ and ‘predicate logic’. Students will practise moving between English and these formal languages, and they will reflect on the difficulties and limitations of the translation process. Using the formal notation, we will study different methods for testing the validity of inferences. We will also explore some of the philosophical history and significance of formal logic.

Why is it important to study formal logic?

First, any critical thinker needs to be familiar with valid forms of argument (as well as invalid ones) in order to be able to present their own arguments as clearly and rigorously as possible, and to critically assess arguments encountered in philosophical texts, in public debate and in other contexts. Acquiring a good understanding of logic is thus essential to becoming a well-rounded philosopher, no matter which philosophical tradition you find yourself drawn to.

Second, a reading knowledge of formal logical symbolism is essential because philosophers often use formal notations to clarify their arguments. The symbolism of formal logic appears in many different areas of philosophy, including epistemology, philosophy of science, philosophy of mathematics, philosophy of language, and metaphysics. A familiarity with formal languages is therefore essential to be able to read and understand many works of modern philosophy.

Thirdly, the subject matter of logic itself raises deep philosophical questions in its own right, which are the object of the philosophy of logic. Finally, formal logic provides modelling tools for many other disciplines, from mathematics to computing and linguistics.

Students taking this module are required to attend – in addition to lectures – weekly ‘tutorials’ or classes: one-hour sessions in very small groups (sometimes even in pairs or one-to-one). Students may be asked to submit homework in advance of these tutorials and/or to complete exercises during the tutorial itself. So, while the course aims to be accessible – starting from and reinforcing the basics – it is also intense, demanding a substantial commitment of time and effort from students and teachers alike.

Assessment for this module is 50% coursework, 50% examination (to be held in Summer). The coursework will consist of:

- (Autumn Term) Either two essays of 1500 words each, or one longer essay of 3000 words.
- (Spring Term) Weekly logic exercises, including some exercises to be done in class in addition to homework exercises.

Coursework will be due for submission at the end of the Autumn term and on a weekly basis during the Spring term. Any queries about coursework can be raised with teaching staff during either tutorials or office hours, as appropriate.

Module aims

The aims of this module are:

To develop the capacity to deconstruct and critically analyse argumentative strategies in any medium (from philosophical essays to political speech, media sources and oral debates);
To gain a capacity to use critical thinking reflexively, in order to improve your own writing;
To acquire a familiarity with basic methods in formal logic.

Module learning outcomes

By the end of the autumn term, students should:

1. be able to identify and articulate arguments as presented in philosophical and other forms of prose;
2. have developed a range of skills for the assessment of arguments;
3. be able to identify informal argumentative fallacies;
4. have enhanced and developed their ability to write clear, forceful, argumentative essays in which arguments from published works are presented and critically assessed, and in which a thesis is critically defended.

By the end of the spring term, students should:

1. Have acquired a broad understanding of the purpose of formal logic.
2. Be able to translate natural language arguments into two simple formal languages.
3. Have mastered a range of formal methods to test the validity of arguments.
4. Have a more complete understanding of a range of essential philosophical notions, including consistency, validity, soundness, deduction, and argument.
5. Have developed their capacity for philosophical analysis and argument through the study of what constitutes a valid argument.

Module information

No additional information available.

Learning and teaching methods

1 x one-hour lecture each week followed by a one-hour discussion class at which issues covered in the lecture will be discussed. In addition there will be weekly tutorials during the autumn term beginning in week 3. In the spring term, beginning in Week 17, there will be weekly one-hour exercise sessions conducted in small groups. Weeks 8 and 21 are Reading Weeks. There will be two revision sessions during the summer term.


  • Smullyan, Raymond M. (2014) A Beginners Guide To Mathematical Logic, Mineola, NY: Dover Publications Inc.
  • Zalta, Edward N. (1998/06/10) Frege’s Theorem and Foundations for Arithmetic.
  • Restall, Greg. (©2006) Logic: an introduction, Ithaca: McGill-Queen's University Press. vol. Fundamentals of philosophy

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework IGNORE - DO NOT USE
Coursework Wk 3: Weekly essay 0%
Coursework Wk 4: Weekly essay 0%
Coursework Wk 5: Weekly essay 0%
Coursework Wk 6: Weekly essay 0%
Coursework Wk 7: Weekly essay 0%
Coursework Wk 9: Weekly essay 0%
Coursework Wk 10: Weekly essay 0%
Coursework Autumn chosen assignment/s 16/12/2019 50%
Coursework Weekly Logic Exercise (Week 17) 0%
Coursework Weekly Logic Exercise (Week 18) 0%
Coursework Weekly Logic Exercise (Week 19) 0%
Coursework Weekly Logic Exercise (Week 20) 0%
Coursework Weekly Logic Exercise (Week 22) 0%
Coursework Weekly Logic Exercise (Week 23) 0%
Coursework Weekly Logic Exercise (Week 24) 0%
Coursework Weekly Logic Exercise (Week 25) 0%
Coursework Spring: Best logic exercise a 20/03/2020 25%
Coursework Spring: Best logic exercise b 20/03/2020 25%
Exam 180 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
50% 50%


Coursework Exam
50% 50%
Module supervisor and teaching staff
Autumn: Dr Matteo Falomi Dr Spring: Dr Marie Guillot



External examiner

Dr Thomas Joseph Stern
University College London
Senior Lecturer
Available via Moodle
Of 160 hours, 44 (27.5%) hours available to students:
96 hours not recorded due to service coverage or fault;
20 hours not recorded due to opt-out by lecturer(s).


Further information

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