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May 26, 2015

SoTFoM III and The Hyperuniverse Programme

Posted by David Corfield

Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, September 21-23, 2015.

Here are the details:

The Hyperuniverse Programme, launched in 2012, and currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna, aims to identify and philosophically motivate the adoption of new set-theoretic axioms.

The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the conceptual and epistemological status of new axioms and their alternative justificatory frameworks.

The aim of SotFoM III+The Hyperuniverse Programme Joint Conference is to bring together scholars who, over the last years, have contributed mathematically and philosophically to the ongoing work and debate on the foundations and the philosophy of set theory, in particular, to the understanding and the elucidation of the aforementioned topics. The three-day conference, taking place September 21-23 at the KGRC in Vienna, will feature invited and contributed speakers.

I wonder if anyone will bring some category theory along to the meeting. Perhaps they can answer my question here.

Further details:

Invited Speakers

  • T. Arrigoni (Bruno Kessler Foundation)
  • G. Hellman (Minnesota)
  • P. Koellner (Harvard)
  • M. Leng (York)
  • Ø. Linnebo (Oslo)
  • W.H. Woodin (Harvard) and
  • I. Jané (Barcelona) [TBC]

Call for papers: We invite (especially young) scholars to send their papers/abstracts, addressing one of the following topical strands:

  • new set-theoretic axioms
  • forms of justification of the axioms and their status within the philosophy of mathematics
  • conceptions of the universe of sets
  • conceptions of the set-theoretic multiverse
  • the role and importance of new axioms for non-set-theoretic mathematics
  • the Hyperuniverse Programme and its features
  • alternative axiomatisations and their role for the foundations of mathematics

Papers should be prepared for blind review and submitted through EasyChair on the following page:

https://easychair.org/conferences/?conf=sotfom3hyp

We especially encourage female scholars to send us their contributions. Accommodation expenses for contributed speakers will be covered by the KGRC.

Key Dates: * Submission deadline: 15 June 2015 * Notification of acceptance: 15 July 2015

For further information, please contact:

sotfom [at] gmail [dot] com

or alternatively one of: 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)

Posted at May 26, 2015 2:50 PM UTC

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5 Comments & 0 Trackbacks

Re: SoTFoM III and The Hyperuniverse Programme

I’ve not found out yet what SoT stands for. Is it Sets or Types? Or what?

Posted by: Todd Trimble on May 28, 2015 3:17 AM | Permalink | Reply to this

Re: SoTFoM III and The Hyperuniverse Programme

“Symposia on the foundation of Mathematics”

Posted by: David Roberts on May 28, 2015 3:32 AM | Permalink | Reply to this

Re: SoTFoM III and The Hyperuniverse Programme

Huh. So the t in ‘the’ is capitalized? That’s strange.

Posted by: Todd Trimble on May 28, 2015 3:47 AM | Permalink | Reply to this

Re: SoTFoM III and The Hyperuniverse Programme

So why is it called the “Hyperuniverse Programme”?

Sure, it sounds cool — but I don’t see a clear explanation of the term “hyperuniverse”:

The Hyperuniverse Programme, launched in 2012, and currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna, aims to identify and philosophically motivate the adoption of new set-theoretic axioms.

The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the conceptual and epistemological status of new axioms and their alternative justificatory frameworks.

Is the “hyperuniverse” the same as the “set-theoretic multiverse”?

I gather that the “set-theoretic multiverse” is a way of talking about the idea that we should accept the truth that’s been staring us in the face since Gödel: we should stop talking about “the” universe of sets, since any reasonable axiom system for set theory admits many different models, which aren’t even elementarily equivalent. But terms like “multiverse” and “hyperuniverse” suggest that we should simultaneously study all the models of a given set of axioms for set theory — or indeed, all the models of many different axiom systems.

Since each such model gives a category of sets, all these categories fit together to form a 2-category of some very special sort, which in some sense is parametrized by our choice of axiom systems. If one understood this well enough, the term “hyperuniverse” could become a precise thing that people could prove theorems about, instead of just an advertising gimmick.

Posted by: John Baez on June 3, 2015 8:28 PM | Permalink | Reply to this

Re: SoTFoM III and The Hyperuniverse Programme

As far as I can tell, “hyperuniverse” is due to Sy Friedman, and refers to finding new axioms among statements that hold in extensions of ‘the’ set-theoretic universe (by forcing, class forcing and basically any means possible). This is apparently along Goedel’s suggested programme of finding stronger and improved axioms for set theory.

The multiverse view seems to be more about finding out is is true in various universes, or how different universes relate (and here the methods are more restrained: one does not seem to use much class forcing, so more things are preserved).

(As an aside, forcing is, as you know, about looking at the internal logic in categories of sheaves on posets (or small sites more generally). Class forcing is (I claim) about taking small sheaves on large sites. This has only been explored, generally speaking, where such large sites are large sequential limits of posets.)

Some references: Multiverse conceptions and the hyperuniverse program and this description of a postdoc position within the project (unfortunately both very verbose).

Posted by: David Roberts on June 4, 2015 4:57 AM | Permalink | Reply to this

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