Variable Set Theory?

Mike Barr posted in the cats mailing list the following:
Around 1986, Colin McLarty, Charles Wells, and I noticed that Scientific American had recently published a few articles on subjects mathematical
and decided to try to write one on variable set theory, AKA topos theory.
Unfortunately, that particular window at Sci Am quickly closed.  Our article was turned down and we forgot about it.  More recently, I decided it might be interesting, or at least amusing to throw it open to the
categorical community.  The result can be found at
ftp://ftp.math.mcgill.ca/barr/pdffiles/vst.pdf

(the picture is apparently Grothendieck lifting Michael Atiyah, from facebook, so who knows if it's real...)


Further news: Since the ftp site in Montreal is having some issues at the moment, Mike Barr was kind enough to send us a copy of the paper, which I'm posting here. Thanks Mike!

Set Theory for the Masses

So I've posted something about the two currents in Set Theory trying to add more axioms to solve the Continuum Hypothesis and the guys had more than a hundred comments on the post, so they are even starting to write a new paper on the subject, yay!

In some ways this is all I have always advocated for: maths needs to be done collectively, social networks can have an effective role in creating new knowledge by putting people in contact with others, etc..

But the Facebook post is not ideal: you cannot write maths properly, you cannot comment where you want, and let's face it, I cannot cope with the speed that they're producing ideas/thesis/hypotheses and demolitions. Maybe this is because I'm not a set-theorist, maybe it's because my full time job is not as a mathematician, maybe is just because I'm getting old. Who knows?
Anyways in an attempt to parse their conversation and get my own ideas straightened I've created another blog http://settheory4themasses.blogspot.com/2013/12/all-you-didnt-want-to-know-about-set.html

Long Mathematical Proofs?...

There is a Wikipedia page for them...

List of long proofs

Wish someone would organize a sensible collection of of Large Theories Common Sense problems, a bit like the TPTP collection. Also need to check out the Intuitionistic Logic benchmarks, the ILTP Library.

8th Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2013)

The Workshop on Logical and Semantic Frameworks is a series of conferences in Brazil that I like to support.

As I read in their 'about us' page:

"LSFA is a series of Meetings on Logical and Semantic Frameworks with Applications. Logical and semantic frameworks are formal languages used to represent logics, languages and systems. These frameworks provide mathematical foundations for formal specification of systems and programming languages, supporting tool development and reasoning. The objective of this series is to put together theoreticians and practitioners to promote new techniques and results, from the theoretical side, and feedback on the implementation and use of such techniques and results, from the practical side."

It could've been be a bit less underspecified, methinks.

I have never been invited speaker or even invited for their programme committee, which is a surprise, as it is exactly my kind of work.
and many of the organizers are my long-standing friends...

But still I think the idea is a good one, so once again I "paid to work", instead of being paid to do it.
hmm, this is not strictly true, as I guess this is what the Brazilian CAPES funding agency  gave me a "Ciencia Sem Fronteiras" award for.
Vagaries of the Brazilian funding system and its implementation, perhaps.

I  talked about work that I did with mathematicians Charles Morgan and Samuel Gomes da Silva on Natural Numbers Objects in Dialectica Categories.

This is very interesting stuff, and the guys promised that they're writing up a more mathematical version of our content.
From my part I'd like to do the other two bits of work that we thought we would do; applications of the Dialectica construction
1. to cardinalities of the continuum and
2. to the 'laxification' of topological spaces.

Yep, I definitely need to write some of this work up and I need to put up, somewhere, all the dozens of other talks I've given that I have not written up. yet.
I guess discarded slides might end up being the notebooks of the scholars of the future.

Ilha Grande and All That....

Over the summer I went to this most wonderful place in Brazil, Ilha Grande. The meeting was called

Ilha Grande 2013: II Workshop on Logic and Semantics

and I talked about versions of constructive modal logics. The slides are here and the discussion was pretty good.

Type Theory at EACL, yay!

Another fun event announced this week. In Gothenburg:
http://clt.gu.se/event/2014-04-27/type-theory-workshop-eacl-2014
(they probably need a picture in their page, I chose one at random, as I've never been there...)

Belated Happy Halloween...

Spending a weekend in New York with my best friend was brilliant. We went to the theater, to the High Line Park and Chelsea Market, to lots of museums, where the highlight was the Frick Collection, with its amazing free audioguides spoken by the curators themselves. This was fantastic! the best museum experience ever.

Since I also had two papers accepted for the Global WordNet Conference in Estonia and one submitted for LREC in Iceland I should be feeling pretty stoked about work, shouldn't I? But I feel that it's going too slow, that we're not making progress as fast as we need to. Oh well, let me remind myself that I have been invited to review papers for LREC and that I've been invited to the Program Committee of the EACL 2014 Type Theory and Natural Language Semantics Workshop (TTNLS), whose deadline is 23rd January 2014. Got to get the stuff working and the papers written...

(Historical note on this photo: The Ladies of Trinity Hospital at Castle Rising, Norfolk, England taking afternoon tea over 100 years ago. Single ladies (spinsters) still live in this almshouse today, and it is a condition of their residency that they wear this 17th century costume on Sundays and Open Days. This is what they say in the ebay posting that allows you to buy the full picture for 5 dollars)