A Chance to Win €20,000

The Gödel Centenary Conference will include a competition for “young scholars” (born on or after 1/1/1970). “Submitted projects should be strongly connected to the scientific achievements (including recent applications) and/or life of Kurt Gödel. Projects can cover any of the disciplines, such as: logic, mathematics, physics, computer science, theology or philosophy.” 10 finalists will get a paid trip to present their projects at the conference in Vienna, first prize is €20,000 (in words: twenty thousand euros! Second and third prize: €5,000 each). Crazy!

Logician Action Figures

They’ve been around for a while, but one of the students in my Logical Positivism class made copies of them and passed them out (I suggested they start their final presentations with a joke), which reminded me: Ian Vandewalker‘s “Philosophical Powers” mock action figures of philosophers include four logicians:

“Ferocious” Frege (includes Morning Star® and Evening Star® accessories)

“Vindictive” Wittgenstein (with language game action)

“Rough” Russell (powers: comprehension of sets)

Quine “The Quasher” (aka Stormin’ Van Orman)

I wish these were real, they’d make such good presents (for me)!

PS: I forgot Aristotle and Leibniz.

New Stuff from Jeremy Avigad

Jeremy posted this to FOM yesterday:

I’d like to announce a review I have written of two books that deal with logic and foundations in the early twentieth century: Calixto Badesa’s The Birth of Model Theory and Dennis Hesseling’s Gnomes in the Fog. The review, which will appear in the Mathematical Intelligencer, can be found on my web page under “Reviews.”

While I am at it, I’d like to mention two other papers, still in preprint form, that may be of interest to the FOM audience. Both can be found on my web page, under “Research.”

The first, “A formally verified proof of the prime number theorem,” describes a formalization of the PNT using a mechanized proof assistant, Isabelle. The formalization was joint work with Kevin Donnelly, David Gray, and Paul Raff.

The second, “Quantifier elimination for the reals with a predicate for the powers of two,” [with Yimu Yin] is a syntactic proof of a result due to van den Dries, namely, that the theory of the reals as an ordered field with a predicate for the powers of two is decidable. This result is interesting in that it subsumes two of the most important decidability results of the last century: the decidability of real-closed fields, due to Tarski, and the decidability of the additive theory of the integers, due to Presburger. It turned out to be rather difficult to extract an explicit quantifier-elimination procedure from van den Dries’s proof; the best we could do is an algorithm that runs in iterated-iterated-exponential time!

In an MS thesis that he is close to finishing, Yin has also determined a novel equivalence between two q.e. tests which seem to be strictly stronger than q.e. For fun, he has also extended the decidability results to the reals with a predicate for the Fibonacci numbers, and predicates for other sequences defined by appropriate recurrence relations. I will add a link to my web page when he has posted it online.

[Reposted with permission]

Carnap, Quine, Tarski: 1940-1941

If you’re reading Obscure and Confused Ideas or the comments to this post on logicandlanguage.net, then you probably know that Greg Frost-Arnold is working on a book about what went on at Harvard in 1940/41, when Carnap, Quine, and Tarski were hanging out there. While you’re waiting for that book to come out, you could look at Paolo Mancosu‘s paper on some of the same stuff, hot off the presses of HPL:

Paolo Mancosu, Harvard 1940–1941: Tarski, Carnap and Quine on a finitistic language of mathematics for science. History and Philosophy of Logic 26/4 (2005) 327-357

Tarski, Carnap and Quine spent the academic year 1940–1941 together at Harvard. In their autobiographies, both Carnap and Quine highlight the importance of the conversations that took place among them during the year. These conversations centred around semantical issues related to the analytic/synthetic distinction and on the project of a finitist/nominalist construction of mathematics and science. Carnap’s Nachlaß in Pittsburgh contains a set of detailed notes, amounting to more than 80 typescripted pages, taken by Carnap while these discussions were taking place. In my article, I present a survey of these notes with special emphasis on Tarski’s rejection of the analytic/synthetic distinction, the passage from typed languages to first-order languages, Tarski’s finitism/nominalism, and the construction of a finitist language for mathematics and science.

Maybe Greg wants to follow up?

(PS: The new issue of HPL also includes the full review of Torkel Franzén’s book Use and Abuse of Gödel’s Theorem announced previously.)