## October 17, 2014

### ‘Competing Foundations?’ Conference

#### Posted by David Corfield

FINAL CFP and EXTENDED DEADLINE: SoTFoM II Competing Foundations?’, 12-13 January 2015, London.

The focus of this conference is on different approaches to the foundations of mathematics. The interaction between set-theoretic and category-theoretic foundations has had significant philosophical impact, and represents a shift in attitudes towards the philosophy of mathematics. This conference will bring together leading scholars in these areas to showcase contemporary philosophical research on different approaches to the foundations of mathematics. To accomplish this, the conference has the following general aims and objectives. First, to bring to a wider philosophical audience the different approaches that one can take to the foundations of mathematics. Second, to elucidate the pressing issues of meaning and truth that turn on these different approaches. And third, to address philosophical questions concerning the need for a foundation of mathematics, and whether or not either of these approaches can provide the necessary foundation.

Date and Venue: 12-13 January 2015 - Birkbeck College, University of London.

Confirmed Speakers: Sy David Friedman (Kurt Goedel Research Center, Vienna), Victoria Gitman (CUNY), James Ladyman (Bristol), Toby Meadows (Aberdeen).

Call for Papers: We welcome submissions from scholars (in particular, young scholars, i.e. early career researchers or post-graduate students) on any area of the foundations of mathematics (broadly construed). While we welcome submissions from all areas concerned with foundations, particularly desired are submissions that address the role of and compare different foundational approaches. Applicants should prepare an extended abstract (maximum 1,500 words) for blind review, and send it to sotfom [at] gmail [dot] com, with subject SOTFOM II Submission’.

Notification of Acceptance: Late November 2014

Scientific Committee: Philip Welch (University of Bristol), Sy-David Friedman (Kurt Goedel Research Center), Ian Rumfitt (University of Birmigham), Carolin Antos-Kuby (Kurt Goedel Research Center), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Goedel Research Center), Neil Barton (Birkbeck College), Chris Scambler (Birkbeck College), Jonathan Payne (Institute of Philosophy), Andrea Sereni (Universita Vita-Salute S. Raffaele), Giorgio Venturi (CLE, Universidade Estadual de Campinas)

Organisers: Sy-David Friedman (Kurt Goedel Research Center), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Goedel Research Center), Neil Barton (Birkbeck College), Carolin Antos-Kuby (Kurt Goedel Research Center)

Conference Website: sotfom [dot] wordpress [dot] com

Further Inquiries: please contact Carolin Antos-Kuby (carolin [dot] antos-kuby [at] univie [dot] ac [dot] at) Neil Barton (bartonna [at] gmail [dot] com) Claudio Ternullo (ternulc7 [at] univie [dot] ac [dot] at) John Wigglesworth (jmwigglesworth [at] gmail [dot] com)

The conference is generously supported by the Mind Association, the Institute of Philosophy, British Logic Colloquium, and Birkbeck College.

Posted at October 17, 2014 2:09 PM UTC

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### Re: ‘Competing Foundations?’ Conference

Funny how even the url sotfom [dot] wordpress [dot] com was obfuscated. To prevent robots from visiting the site? Google has already indexed it …

more on topic: I hope they will provide some of the outcomes for non-visitors, such as videos of lectures and downloadable slides.

### Re: ‘Competing Foundations?’ Conference

The interaction between set-theoretic and category-theoretic foundations has had significant philosophical impact, and represents a shift in attitudes towards the philosophy of mathematics. This conference will bring together leading scholars in these areas

I don’t see many (if any!) category theorists listed…

Posted by: David Roberts on October 18, 2014 11:27 PM | Permalink | Reply to this

### Re: ‘Competing Foundations?’ Conference

David wrote:

I don’t see many (if any!) category theorists listed…

Yeah, really. This looks like a “competition” where one team wasn’t invited. Too bad: it will be much more boring than if they also brought in Voevodsky, Awodey, McClarty and Corfield.

However, I also think the idea of “competing foundations” needs to be criticized (and I’m sure some of these people could do it).

The metaphor of “foundation” makes it sound like there should be just one foundation, on which the building of mathematics rests. But that’s just not how it works. A better terminology would be “portal” or “entrance”: there are various ways to get into mathematics starting from simple assumptions, but once you’re in you can study all the entrances. You don’t have to choose one entrance as the “correct” one. There’s still a competition, but we shouldn’t expect or hope for a single winner.

Posted by: John Baez on October 24, 2014 11:53 PM | Permalink | Reply to this

### Re: ‘Competing Foundations?’ Conference

There’s a thread taking place at the list FOM (Foundations of Mathematics) where this same theme of competition can be found. Urs has recently posted on this matter at Google+.

The FOM thread is archived here and gets under way approximately here in this post by Harvey Friedman where Voevodsky’s name was brought up. (The posts can be sorted by thread which seems to be easiest way of following the flow of discussion.) This is the initial post to which Urs responded at FOM.

Almost immediately hackles seem to have been raised, with talk of “throwing down the gauntlet” and various “challenges” being issued. If I may speak frankly, I don’t hold out hope that this sort of atmosphere will lead to much enlightenment. Certainly not if past history has been any guide (and already I see people talking past one another).

Urs did (in his Google+ post) helpfully point to a minicourse by Mike Shulman on for anyone wishing an introduction to HoTT. Really, though, if people at FOM want to know the point of HoTT, I’d say they should pick up the book and start reading.

Alternatively, if “traditional logicians/set theorists” don’t want to pick up the book and start reading, they could ask someone in their community such as François G. Dorais, who has made an effort to understand and could help explain. But of course this is predicated on the assumption that people want to learn and not just have a fight or “defend turf”.

Posted by: Todd Trimble on October 25, 2014 6:42 AM | Permalink | Reply to this

### Re: ‘Competing Foundations?’ Conference

Yes, I felt the discussion was going nowhere. I’ve bowed out of the discussion, and unsubscribed from the list, to preserve my sanity.

Posted by: David Roberts on October 26, 2014 10:46 AM | Permalink | Reply to this

### Re: ‘Competing Foundations?’ Conference

I guess they’re largely recruiting from the local population, and there aren’t too many category theoretic philosophers in the UK.

To the extent I get invited to conferences, it’s not as someone working on any foundations. The introduction to The Philosophy of Mathematical Practice falsely presents me as opposed to foundational work.

On the other hand, James Ladyman is invited and he’s working with Stuart Presnell on a three year project ‘Applying Homotopy Type Theory in Logic, Metaphysics, and Philosophy of Physics’.

Posted by: David Corfield on October 26, 2014 8:36 AM | Permalink | Reply to this

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