How should we reason? An introduction to logic

What is the course about?

Consider the sentences:

(1) If it is raining, then I will get wet.

(2) It is raining.

From (1) and (2), I can infer ‘I will get wet’, whereas I cannot infer ‘All dogs bark’. So, there is a right way and a wrong way to reason. If you infer ‘All dogs bark’ from (1) and (2), then you are reasoning incorrectly.

Philosophical Logic is the study of the rules of correct reasoning. This course will introduce you to some widely accepted rules of correct reasoning and teach you how to describe these rules with mathematical precision. We will also examine some controversial rules of inference and probe the deeper question of why exactly we should accept some inferences and not others.

This is a live online course. You will need:
- Internet connection. The classes work best with Chrome.
- A computer with microphone and camera is best (e.g. a PC/laptop/iMac/MacBook), or a tablet/iPad/smart phone/iPhone if you don't have a computer.
- Earphones/headphones/speakers.
We will contact you with joining instructions before your course starts.

What will we cover?

In this course we will explore:

- The history of logic, from Aristotle to Frege.

- Key logical concepts such as truth, validity, soundness, and consistency.

- The relationship between formal languages, invented by logicians, and natural languages such as English.

- A language and proof system for Classical Propositional Logic, the simplest widely used and studied logic.

- Some major debates between classical and non-classical logicians.

What will I achieve?
By the end of this course you should be able to...

- Define key terms in the study of Logic.

- Determine whether an argument is valid or invalid in classical propositional logic..

- Assess the arguments for and against deviations from classical logic.

- Use logical methods to tackle philosophical puzzles and paradoxes.

What level is the course and do I need any particular skills?

The course is suitable for all levels, including those who have never studied philosophy before. Some elements of
the course will involve a little bit of basic mathematics, but you do not need to have studied any mathematics
previously. An open mind and a willingness to listen and respond to ideas with which you may not always agree are more important than specific levels of skill.

How will I be taught, and will there be any work outside the class?

A small amount of reading and a short problem sheet will be set for each class via a Google Classroom. It is highly recommended that students complete the reading and attempt the problems, as this will help them get the most out of the sessions. If they wish, students may submit their work to be marked, but this is entirely optional.

Are there any other costs? Is there anything I need to bring?

You will be provided with all of the necessary reading, so you do not need to purchase a textbook. A notepad and
pen to take notes during the classes will be essential.

When I've finished, what course can I do next?

You may be interested in HP214 Introduction to Marxist philosophy, starting in March 2025, which is also taught by Oliver Josiah. Please see City Lit's website for full details of all upcoming philosophy courses.