Doing UCL Philosophy as a Mathematics Student
Introduction
Before I begin, I think it's worth mentioning that I'm not comparing the quality between maths and philosophy modules. Both of them are exceptionally well taught. It is also worth mentioning that I am a mathematics student having audited a philosophy module, read up on another, and completed a third, and am going to complete a fourth. However, despite this, I mostly expected what I got, so this post ideally should not be read in a 'shocking things I never knew' respect.
Why I did philosophy?
In the mathematics world, a popular sentiment is that foundational mathematics (that is, mathematics concerning the initial assumptions we make about maths and the way we construct it) is unfulfulling, or doesn't bring out a mathematician's true potential. Exceptionally rare results that have a major significance, such as Gödel's Incompleteness Theorems, seemed to end around 80 or so years ago. Whilst I am very passionate about this topic, as an average undergraduate mathematician, I am in no position to dispute it; all I can say is that for now I want to learn it whilst keeping my options open.
The reason this is relevant is because it also means that the UCL maths department does not have many modules about foundational mathematics (most likely as their research interests are for applied areas). This is entirely fair, as it is a niche subject, but it means I have fewer opportunities to learn about this subject with a grade-related payoff. The best place to learn it is in the philosophy department, where formal logic has a wide array of modules.
Introduction to Logic 1 & 2
In general, I endeavoured to learn how to translate ideas into the symbols ¬, ∧, ∨, →, ∀ and Ǝ, in my own reading. This became formalised in term 1 in my algebra course, being able to manipulate it syntactically (e.g De Morgan laws). However for the concept of theories, models and domains and so on and so forth, I had no experience. Introduction to Logic 1 concerned itself with propositional logic (the first 4), and I did most of my learning through the book, 'The Logic Manual', Halbach. Whilst I learned a lot in terms of the relation to natural language, it didn't stick because I had no need to reaffirm it. All in all it felt like an easier experience for me when reading it. Especially so when considering the contact hours that a philosophy student would have.
Introduction to Logic 2 was a little harder. It had a lot more topics to cover. I auditted it in the first half of term 2, which was a fun experience in the classes. Again, it did not feel too difficult due to my advantages. Another reason may be because the formal aspects are more close to STEM mindsets than qualitative humanities ones, which are more common amongst philosophy students (not to say mathematically minded philosophers don't exist, but a module naturally should cater to all). Similarly, I felt less inclined when learning Russell's Theory of Definite descriptions. But as a mathematics oriented student, I didn't need to. I self studied the second half over the holidays using Forallx by Tim Button and P.D Magnus, such as the laws of natural deduction.
Philosophy of Arithmetic and Incompleteness
This was the first philosophy module I chose to take, grade and all. The first half covered attempts at formalising arithmetic, and the second covered Gödel's Incompleteness theorems. Compared to mathematics modules, it was far less intense. There were only half the contact hours, and all coursework was issued and due in the last 2-3 weeks of term. However, a lot of work leaked into the holidays, which lead to less time to revise for exams. This makes sense, as I expect a lot more philosophy is based around essays, and so what would be an intense 'revision period' for mathematicians would be an intense 'essay period' for philosophers.
Part of this module was the essay. Playing to my strengths, I wrote about a technical endeavour rather than a semantic one. Although I am only in my 2nd-3rd year, I do think this has allowed me to improve upon my academic writing skills for my upcoming dissertation in my 4th. I still think that trying to attain a good grade for the module is far easier here than for a maths module, but it would be at the cost of revision time for other modules. You can find lecture notes I wrote whilst taking the module here.
Other Philosophy Modules
In the philosophy department, there are four main modules (I would expect) that would appeal to mathematicians (beyond the basically-required introductory ones):
- Philosophy of Arithmetic and Incompleteness (T2)
- Worlds, Sentences and Measures [mostly modal logic] (T2)
- Paradoxes (T1)
- Logic and its Limits (T1)
Closing Remarks
A drawback to philosophy modules is that all marks are scaled to be below 80. But before you get scared thinking you need 87.5% correct marks to get a first, the raw percentage of whatever grade you get for coursework, exams etc do not necessarily correlate linearly. e.g if you earn 40% in courseworks and 60% in an essay (with a 50/50 split between them) you will not necessarily get 40 out of 80. The problem, however, is that for a philosophy student, this is fine as all your marks will be below 80, whereas it looks bad on a transcript if you are a high achieving maths student.
In general, there are fewer contact hours for philsophy modules than there are for maths modules (roughly half). This sounds good if you want a less intense timetable, but that does mean that philosophy modules feel more empty. The plus side is that you can further engage with your topic more and perhaps some of your other subjects. (The moral dilemma of taking it to coast I will leave to the reader).
All in all, I would definitely recommend taking a philosophy module, so long as you are willing to understand prerequisites, and are willing to engage.