What do mathematicians do? An introduction to philosophy of maths
Time: 18:00 - 19:30
This course will be delivered online. See the ‘What is the course about?’ section in course details for more information.
Course Code: HP150
Duration: 6 sessions (over 6 weeks)
What is the course about?
Suppose I claim to possess a wonderful kind of knowledge with the following three characteristics: First, the knowledge is a priori, meaning that it can be arrived at without relying on sensory observations or experiments. Second, the knowledge is necessary, meaning that the truths which I know could not possibly have been false even if the world had been totally different. Third, the knowledge is of objects which are not located in space and time; objects which are abstract as opposed to physical or concrete.
It is tempting to think that you would laugh me out of court, but in fact it is precisely this sort of claim which is made by most mathematicians today. After all, mathematical knowledge appears to be a priori, necessary, and of abstract numbers, sets, functions, and so on.
Mathematics is a far too successful discipline to be dismissed out of hand, and so the philosopher is forced to confront the following two-part question: (1) Does mathematical knowledge really have these three features, and (2) if so, how is such a strange sort of knowledge possible?
This course offers the opportunity to explore these fascinating questions by providing an introduction to four major 19th and 20th century philosophies of mathematics; logicism, formalism, intuitionism, and nominalism.
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.
We will contact you with joining instructions before your course starts.
What will we cover?
This course is based on the first seven chapters of Øystein Linnebo’s Philosophy of Mathematics (Princeton University Press, 2017) and will cover four major early philosophies of mathematics:
There is also the potential to run a future course on the remaining five chapters which are devoted to more modern and technical material.
What will I achieve?
By the end of this course you should be able to...
- Explain why mathematical knowledge is philosophically puzzling
- Understand the early history of the philosophy of mathematics
- Assess the strengths and weaknesses of four major philosophies of mathematics
- Explain the significance of philosophically important mathematical results, including Russell’s Paradox and Gödel’s Incompleteness Theorems.
What level is the course and do I need any particular skills?
This course is suitable for students of all levels, though some familiarity with high school level mathematics and mathematical thinking will be useful.
How will I be taught, and will there be any work outside the class?
The course is based on the first seven chapters of Øystein Linnebo’s Philosophy of Mathematics. Each class will focus on one chapter, and will consist of short lecture-style presentations, pair, group and class discussion. There will also be opportunity to participate in online forums and to complete individual exercises in order to explore topics further.
Are there any other costs? Is there anything I need to bring?
A copy of Øystein Linnebo’s Philosophy of Mathematics (Princeton University Press, 2017).
When I've finished, what course can I do next?
You might be interested in HP151 Where is the future? An introduction to the philosophy of time, starting in January 2022, and HP153 - Cause and effect: a philosophical investigation, starting in May 2022.
Oliver holds a postgraduate degree in Philosophy from the University of Oxford. Since graduating, he has taught a wide variety of courses to a broad range of students, from adults and children exploring the subject for the first time through to advanced undergraduates. His main areas of interest are the Philosophy of Mathematics, Metaphysics, the Philosophy of Language, and Logic. Recently, his research has focussed on developing medieval approaches to semantic paradoxes using modern mathematical methods. When Oliver’s not teaching or writing up papers, he’s either lost in a good book or somewhere deep in the English countryside.
Please note: We reserve the right to change our tutors from those advertised. This happens rarely, but if it does, we are unable to refund fees due to this. Our tutors may have different teaching styles; however we guarantee a consistent quality of teaching in all our courses.