### 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.

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.

Cool! Glad to have you as a contributor, David

ReplyDelete- Jeff

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!

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

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

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

David, I think on blogspot tags are called "labels", they can be added in the "edit post" page.

ReplyDeletehttp://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/

The Introduction "Introducing Myself" does not have any name.

ReplyDeleteHow does one know who is being introduced here?

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.

ReplyDeleteDavid, thanks for adding the label!

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ReplyDelete