BEST 2013

February 19, 2013

After a short hiatus, the BEST conference is back this year: The 20th BEST will take place at the University of Nevada, Las Vegas during June 16–19, 2013, as part of the 94th Annual Meeting of the AAAS Pacific Division.

Please email me or Marion Scheepers for further details, and let people who may be interested know. We expect we will be able to offer some (limited) financial support for students and postdocs. I will be posting more details as they materialize.

6th Young set theory workshop

February 19, 2013

The 6th Young Set Theory Workshop will take place this year at the Santuario di Oropa, in Biella, Italy, on June 10th – June 14th.

There will be tutorials by James Cummings, Sy Friedman, Su Gao, and John Steel, and invited talks by Tristan Bice, Scott Cramer, Luca Motto Ros, Victor Torres Perez, and Trevor Wilson.

Here is the official page for the workshop. (I am part of the scientific committee.)

Is mathematics created or discovered?

February 19, 2013

Last Friday, Feb. 15, I had the opportunity to host a Friday Forum discussion at the Honors College on whether Mathematics is created or discovered.

One can address the question from a technical metaphysical point of view, but currently I do not find this approach too illuminating or interesting. This was the path followed by Kit Fine in a talk he gave here about two years ago (April 15, 2011). I commented briefly on Fine’s talk on Twitter: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11:
I attended yesterday a public lecture by Professor Fine, entitled “Mathematics: Invented or discovered”. The auditorium was packed.
I didn’t like some of the points Fine made, and the direction in which he took the discussion, but there were some interesting highlights.
His conclusion: The heart of mathematics is not axioms but procedures for extending the domain of discourse.
For example, we extend the concept of “number” from “natural” to “integer”, “rational”, “real”, …
Fine introduced a calculus based on dynamic logic for “extension procedures”.
This was the core of his talk, one of the parts I mostly disagreed with. Another: Fine seems to think there “is”, e.g., a unique “number 1”.
(As opposed to: this makes no sense, but there are many essentially equivalent representations.)
A cute detail was his portrayal of constructivism, equating it with writers creating fictional characters.
(It made me think all I do is write fan fiction, which made me smile (snicker?).)
I guess Fine’s conclusion is that mathematics is both invented and discovered as they are different parts of his “extension procedures”.

The Friday Forum was a very nice experience. The problem is complex and has a long history. One of the questions it leads to is how to explain the applicability of mathematics. I consulted several references while preparing for the forum, and I think someone else may find at least some of them useful. Let me list a few. Books: