# Beginning maths, beginning philosophy

Tim Gowers has begun what he plans to be a long series of posts on his blog giving advice for beginning Cambridge mathmos. But the posts should of course be of great interest for new undergraduate mathematicians anywhere. So spread the word.

And already some of his advice seems pretty applicable to beginning philosophers too. That shouldn’t be too surprising: in both cases, what we are trying to teach isn’t a body of facts so much as an understanding of argumentative moves. In both cases, students need to learn how to see how to fillet out the key ideas (and tell what’s just joining-up-the-dots).

So I might be inspired to do what I have meant to do for a while and put together some how-to-get-started-thinking-philosophically and how-to-approach-your-work notes for new philosophers. It shouldn’t be made a mysterious business, whether it’s maths or philosophy. But meanwhile, read Gowers!

### 6 thoughts on “Beginning maths, beginning philosophy”

1. That sounds like a wonderful idea! I took a look at what Gowers is up to. It would be excellent if you could do the equivalent for new philosophers. Also, I’ve been meaning to brush up on my logic more generally and I was curious as to whether you suggest Sider’s Logic for Philosophy or Garson’s Modal Logic for Philosophers for someone trained primarily in classical philosophy and continental philosophy with an analytic orientation. Thanks!

1. Well, I’ll see how much energy I’ve got for Gowers-style postings!

As for books for brushing up logic, it depends how much logic you already have. I’d have thought that both Sider and Garson would be quite tough going if you had only done a one-semester intro formal logic course. Both are pretty respectable, as far as I know (I haven’t tried teaching from either), so all I can say is try them and see. If one or both seems heavy going, then don’t worry — it just means that you need to try something rather more elementary/slow going first.

Which reminds me of another thing I ought to do …i.e. write a guide to some of the logic books out there!

2. As someone starting Maths & Philosophy in a week, this feels conveniently serendipitous, and I shall both take it as a good omen and eagerly await any guidance.

3. This is not directly relevant, but I’ve noticed that Halmos, Naive Set Theory and (even better from my POV), Judith Roitman’s Introduction to Modern Set Theory, have recently become available as inexpensive paperbacks.

Since Roitman’s book is one of the most interesting set theory intros, and the hardcover edition costs over £100, I think that’s good news. There’s no excuse for such books being so expensive.

4. I look forward to both series of post: the one on getting started to think philosophically and the other on the logic books.

In the last few years I have seen quite a lot of books on logic. The one that attracks me the most –but I haven’t read yet– is «A concise introduction to logic» written by Wolfgang Rautenberg. It says that it brings a proof of the second incompleteness theorem, which is something omitted in most textbooks.

1. Re proof of the second incompleteness theorem, George Tourlakis’s Lectures in Logic and Set Theory: Volume 1, Mathematical Logic also has one, iirc.

Scroll to Top