Monday, 17 October 2011

Introducing myself

My name is David Corfield and I'm very grateful to have been invited to join this blog as a contributor. With five years of blogging behind me at the n-Category Café, I relish the opportunity to talk with a new audience. My rate of blogging may have slowed, especially as my adminstrative load has increased - I'm now Head of Philosophy at the University of Kent - but I'm looking forward to writing some posts here.

I have interests in a variety of approaches to mathematical philosophy, including the statistical learning theory I picked up from my time at the Max Planck Institute for Biological Cybernetics in Tübingen, but the main idea I would like to promote to the audience here is that category theory is worth exploring as a resource for the mathematical philosopher.

I have recently published a couple of articles which examines the light category theory can throw on familiar infinite structures. In Understanding the Infinite I: Niceness, Robustness, and Realism, I look at the phenomenon where an infinite entity is defined by a universal property, and through this inherits 'for free' a range of other nice properties. In Understanding the Infinite II: Coalgebra, I look at the duality between minimally and maximally defined entities in the context of the duality between 'algebra' and 'coalgebra'.

Perhaps had I known of Shaughan Lavine (1994) Understanding the Infinite, Harvard University Press, I might have opted for a different title.

There's much to do to understand the relationship between category theory and the traditional foundational branches, which have drawn most philosophical attention. Recently, I posed a question on MathOverflow concerning category theory and Joel Hamkins' set theoretic multiverse. The answer by Joel there shows just the sort of joint investigation needed. A few years ago at the Café, we had a discussion on the relationship between category theory and model theory.

Category theory also has an interface with proof theory, but I know less about this. Something to look out for in the future is the new Homotopy type theory , and associated Univalent foundations.

8 comments:

  1. Cool! Glad to have you as a contributor, David

    - Jeff

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  2. Welcome, David! So this is at least one fruitful outcome of our meeting in Gent last month :) (Hopefully, there will be others...) I look forward to your M-Phi posts!

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  3. Could this post be tagged "PlanetMO" so that it can be found at mathblogging.org/planetmo ?

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  4. The views of my MO question have risen to 997, only 3 more for a badge. Sad how enjoyable these pointless rewards are.

    Peter, I'm not sure what you're asking for.

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  5. David, I think on blogspot tags are called "labels", they can be added in the "edit post" page.
    http://www.mathblogging.org/planetmo came out of a discussion on meta.MO, cf. http://meta.mathoverflow.net/discussion/1002/should-there-be-a-corner-for-discussion-close-to-mo/

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  6. The Introduction "Introducing Myself" does not have any name.
    How does one know who is being introduced here?

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  7. Anonymous, the answer was only one click away, but why should you have to do that, so I've added some words at the start of the post so you know who I am.

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  8. David, thanks for adding the label!

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