This course has concessions available

Mathematics and Philosophy – and their Differences

How different are the worlds opened up by mathematics and philosophy, and how does difference itself make its presence felt within each? For example, do the apparently fixed and stable identities of numbers perhaps arise from their need to differ? And if, with the passage of time, I am no longer the person I once was, how come, is it still me that is different, and not you?

Who is this course for

No specific mathematical knowledge is required - just curiosity! The philosophical level will be reasonably advanced, and should suit students who would like to be challenged by what some of the big names from the history of philosophy - Plato, Spinoza, Kant, Wittgenstein, amongst others - themselves had to say.

What does this course cover

Throughout history, philosophers have called upon the evident authority of mathematics to lend support and plausibility to their claims. Plato, Spinoza and Kant, to name just three, each regarded the existence, and even the very possibility, of mathematics as fundamentally significant. Plato saw geometry as exemplifying a realm of eternal truth; Spinoza actually wrote his Ethics as an ordered sequence of explicit propositions and meticulous proofs; and Kant went so far as to assert that, in approaching the general question of how there can be any knowledge at all, we must address the particular question: 'how is pure mathematics possible?'.

Yet mathematics and philosophy are surely different; and the nature of their difference is presumably more a philosophical than a mathematical problem. On the other hand, what about difference as such, difference 'in itself'? Does its extreme abstractness ultimately lend itself more naturally to mathematical reflection? Is, for example, the humble sequence of whole numbers 1, 2, 3, 4, 5, ..., despite the ocean of marvels concealed beneath its bland surface, essentially an expression of how things can merely differ from one another?

But what of the thinker thinking these thoughts? In thinking about thinking, must an even more fundamental difference open up: a difference within thought, a 'self-distancing' that makes reflection, including self-reflection, even possible? And where is that self-distancing difference situated? Which brings us on to time as a possible source of what (continuously) binds 'me' across that self-distancing difference. And would that suggest that identity in general could in some sense be 'personal' - a question perhaps worth spending a few moments pondering!

Ultimately, since this is a philosophy course, your time will have been well spent if your appreciation of the questions raised has been enhanced, no matter which 'solutions' have been proposed.

What will it be like

The course material will be introduced with the help of handouts provided at the start of each class. For a short course such as this, assessment of your progress can most appropriately be made on the basis of your participation in the discussions arising from the ideas and themes presented.

What else do you need to buy or do

The course is completely self-contained. Apart from pen and paper, no extra materials are required, and nor is any particular preparation. However, should you wish to whet your appetite, the following three (very different!) books can be recommended, although none of them cover the course content as such. They can all be previewed on Google Books ( and are available to buy online for around £15.

How Mathematicians Think - William Byers - 2007 - Princeton University Press - ISBN 9780691145990
Meaning in Mathematics - ed. John Polkinghorne - 2011 - Oxford University Press - ISBN 9780199605057
Why Is There Philosophy of Mathematics At All? - Ian Hacking - 2014 - Cambridge University Press - ISBN 9781107658158

The open-access Stanford Encyclopedia of Philosophy ( contains a huge number of up-to-date articles covering topics at varying levels of generality and specialisation across the whole range of philosophical traditions past and present.

What this course could lead to

Further study in philosophy, including its overlaps and points of intersection with other related areas of interest and enquiry.

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This course has concessions available for people who meet certain criteria

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