Proof Formalization in Mathematics: Guest Post by Jeremy Avigad

There's a discussion going on at the Foundations of Mathematics mailing list about the purpose and value, actual and potential, for formalized proofs in mathematics.  Harvey Friedman asked Jeremy Avigad to comment; he sent this super-useful list of references, republished here with his approval. John Harrison and I recently wrote a survey on formalized mathematics, … Continue reading Proof Formalization in Mathematics: Guest Post by Jeremy Avigad

Edward Nelson, 1932-2014

Just found out that Edward Nelson died last month. http://www.princeton.edu/main/news/archive/S41/11/36I14/index.xml http://en.wikipedia.org/wiki/Edward_Nelson

SotFoM II: Competing Foundations

The second installment of SotFom (Symposium on the Foundations of Math) is asking for papers by Halloween: http://sotfom.wordpress.com/2014/10/14/final-cfp-and-extended-deadline-sotfom-ii-competing-foundations-12-13-january-2015-london/ 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 … Continue reading SotFoM II: Competing Foundations

Free Schlick!

Did you know? The Moritz Schlick Gesamtausgabe is available for free at the Moritz-Schlick-Forschungsstelle! Just click on the cover image to download the PDF (instead of the "order online" link).  Alas, it's only in German.

Cambridge Graduate Conference on the Philosophy of Mathematics and Logic

If you're in that part of the world (or will be in January), you might be interested to know that registration for the 8th Annual Cambridge Graduate Conference on the Philosophy of Mathematics and Logic (17-18 January 2015) is now open: The conference will be held in St. John's College, Cambridge. There will be two … Continue reading Cambridge Graduate Conference on the Philosophy of Mathematics and Logic

Putnam Blogging on Tarski on Truth

Hilary Putnam is writing on Tarski's theory of truth (and Field's analysis of it) at Sardonic Comment. First two blog posts are up: http://putnamphil.blogspot.ca/2014/09/first-of-series-of-posts-on-tarski-i-am.html http://putnamphil.blogspot.ca/2014/09/a-second-post-on-tarski-this-post.html

Steve Awodey gives inaugural Calgary Mathematics & Philosophy Lecture

I'm very excited that Steve Awodey is on his way here to deliver the first Calgary Mathematics & Philosophy Lecture tomorrow! He's speaking on "Univalence as a New Principle of Logic." If you're in Calgary, you should come.  It'll be exciting. Thursday, 3:30 pm, in Engineering Building A aka ENA 101 on the UofC campus. … Continue reading Steve Awodey gives inaugural Calgary Mathematics & Philosophy Lecture

Milton Friedman and Gödel

I've been having a conversation with Alex Douglas and Eric Schliesser on their posts (Alex's, Eric's) about Milton Friedman's footnote about observer-dependence and Gödel's incompleteness theorem.

John Venn Day

John Venn would have been 180 today (August 4). In celebration, Google put up an interactive Venn Diagram doodle, which is pretty amazing.

Also, TIL that it's not a Venn diagram if it doesn't contain all possible intersections, a restriction that doesn't apply to Euler diagrams.  So representing an empty intersection by two non-intersecting regions is, technically, not a Venn diagram; and Venn diagrams for more than three sets get harder and harder to draw. Check out the informative Wikipedia entry.

I have a previous entry on humorous Venn (and Euler) diagrams around the Internets.

Gödel’s Vienna: Finding Café Reichsrat

The Café Reichsrat in Vienna is notable as the place where Gödel, on August 26, 1930, first announced the incompleteness theorem to Carnap, Feigl, and Weismann. The members of the Vienna Circle had met there to prepare for the trip to the "Zweite Tagung für Erkenntnislehre der Exakten Wissenschaften," a satellite meeting to the congress of the German Society of Mathematicians organized by the Vienna Circle. This was where the famous symposium on the foundations of mathematics took place, with Carnap representing logicism, Heyting intuitionism, and von Neumann speaking for Hilbert's school of formalism -- the contributions are reprinted in Benacerraf's anthology Philosophy of Mathematics. From Carnap's diary: "6-1/2 9 [6pm to 8:30pm] Cafe Reichsrat ... preparations for the trip to Königsberg. Gödel's discovery: incompleteness of the system of Principia Mathematica ... difficulties of the consistency proof."  In February 1930, Gödel and Tarski discussed logic here during the latter's first visit to Vienna.

The Reichsrat no longer exists, and the only picture that's around shows just the top of one of its doors (from Jimmy Schimanovich's photo gallery).

The window atop the door, columns, and stucco match the entrance to the Konditorei Sluka at Rathausplatz 8, and presumably on the basis of this it's long been believed that the Reichsrat used to be located where the Sluka is now. But the Sluka has been around since 1891, which led Paul Raymont to speculate that it expanded into the Reichsrat's space after the latter closed down. In 2010, Karlis Podnieks noticed that on the other side of the main driveway to Rathausplatz 8 there's another door that also looks like the one in the picture, and conjectured that the Reichsrat might have been located there. But Vienna's Kaffeehäuser were cavernous establishments and also almost all located at corners. So I asked Karl Sigmund, co-editor of Kurt Gödel: The Album and creator of the Gödel Exhibition, for help, and he suggested to check the phone book!  And indeed, Adolph Lehmann's allgemeiner Wohnungs-Anzeiger : nebst Handels- u. Gewerbe-Adressbuch für d. k.k. Reichshaupt- u. Residenzstadt Wien u. Umgebung gives the address for the Reichsrat as Stadiongasse 2.

Phone book entry for Kaffeehaus Reichsrat

The Café Reichsrat was thus located at the north-west corner of Stadiongasse and Reichsratsstraße/Rathauspark, and the archive picture probably shows the mid-block back entrance facing the Rathauspark identified by Podnieks. A bank now occupies the space:

Location of the former Café Reichsrat in Vienna

If you go visit, do have a coffee and cake at the Sluka!  I also made a map for all you Gödel pilgrims.

And here is some background reading:

John W. Dawson, Jr., Karl Sigmund, 2006. Gödel’s Vienna. The Mathematical Intelligencer 28(3), 44-55

For an almost complete list of people and places from the time of the Vienna Circle, consult:

Volker Thurm, 2003. Wien und der Wiener Kreis: Orte einer unvollendeten Moderne: Ein Begleitbuch, Vienna: facultas.wuv / maudric

Bleg: Philosophy survey for mathematicians

A group of researchers in philosophy, psychology and mathematics are requesting the assistance of the mathematical community by participating in a survey about mathematicians’ philosophical intuitions. The survey is here: http://goo.gl/Gu5S4E. It would really help them if many mathematicians participated. Thanks.

The Place of Logic in Computer Science Education Followup

The Special Session on "The Place of Logic in Computer Science Education" took place at the Logic Colloquium on Tuesday. It was well attended and, I think, overall a successful session.  The newly-formed ACM Special Interest Group on Logic and Computation (SIGLOG) was represented by its chair Prakash Panangaden. He stressed the importance of logicians … Continue reading The Place of Logic in Computer Science Education Followup

Getting Excited about the Computational Logic Olympics

So while everyone is following the World Cup, I'm getting excited about the FLoC Olympic Games to be held at the Vienna Summer of Logic this year.  Still doing my research to pick favourites, but here are some of the disciplines:

plus a few others.  There will even be live viewing and a medal ceremony!