An article just published in Quanta Magazine by Natalie Wolchover covers a recent result from reverse mathematics. Keita Yokoyama and Ludovic Patey showed that Ramsey’s theorem for pairs is finitistically reducible, i.e., it is \(\Pi_3\) conservative over \(I\Sigma_1\). The article explains Ramsey’s theorem, but also Hilbert’s program and its more recent relativizations, i.e., the reverse mathematics program.
12-14 October 2016
Munich Center for Mathematical Philosophy, LMU Munich
In the course of the last century, different general frameworks for the foundations of mathematics have been investigated. The orthodox approach to foundations interprets mathematics in the universe of sets. More recently, however, there have been other developments that call into question the whole method of set theory as a foundational discipline. Category-theoretic methods that focus on structural relationships and structure-preserving mappings between mathematical objects, rather than on the objects themselves, have been in play since the early 1960s. But in the last few years they have found clarification and expression through the development of homotopy type theory. This represents a fascinating development in the philosophy of mathematics, where category-theoretic structural methods are combined with type theory to produce a foundation that accounts for the structural aspects of mathematical practice. We are now at a point where the notion of mathematical structure can be elucidated more clearly and its role in the foundations of mathematics can be explored more fruitfully.
The main objective of the conference is to reevaluate the different perspectives on mathematical structuralism in the foundations of mathematics and in mathematical practice. To do this, the conference will explore the following research questions: Does mathematical structuralism offer a philosophically viable foundation for modern mathematics? What role do key notions such as structural abstraction, invariance, dependence, or structural identity play in the different theories of structuralism? To what degree does mathematical structuralism as a philosophical position describe actual mathematical practice? Does category theory or homotopy type theory provide a fully structural account for mathematics?
- Prof. Steve Awodey (Carnegie Mellon University)
- Dr. Jessica Carter (University of Southern Denmark)
- Prof. Gerhard Heinzmann (Université de Lorraine)
- Prof. Geoffrey Hellman (University of Minnesota)
- Prof. James Ladyman (University of Bristol)
- Prof. Elaine Landry (UC Davis)
- Prof. Hannes Leitgeb (LMU Munich)
- Dr. Mary Leng (University of York)
- Prof. Øystein Linnebo (University of Oslo)
- Prof. Erich Reck (UC Riverside)
Call for Abstracts
We invite the submission of abstracts on topics related to mathematical structuralism for presentation at the conference. Abstracts should include a title, a brief abstract (up to 100 words), and a full abstract (up to 1000 words), blinded for peer review. Authors should send their abstracts (in pdf format), together with their name, institutional affiliation and current position to firstname.lastname@example.org. We will select up to five submissions for presentation at the conference. The conference language is English.
Dates and Deadlines
Submission deadline: 30 June, 2016
Notification of acceptance: 31 July, 2016
Registration deadline: 1 October, 2016
Conference: 12 – 14 October, 2016
For further details on the conference, please visit: http://www.mathematicalstructuralism2016.philosophie.uni-muenchen.de/
The European Meeting of the ASL will be held in Leeds this year, July 31 to August 6. The deadline to submit a contributed talk is tomorrow!
For details, see the conference website!
My friend and colleague Helmut Veith died yesterday. His death is a great and shocking loss to his family and friends, and the logic community, especially in Austria.
I’ve known Helmut since we were undergraduates in computer science at Vienna Technical University in the early 1990s. We shared a passion for theoretical topics in computer science, a love of Robert Musil; we took many courses together. In fact, we liked logic so much that together we created a specialized course of study (a studium irregulare) in computational logic. At the time this still required approval by the federal ministry of science and research, and it was a lot of work, but we got it approved. It has since morphed into a standard stream in the computer science curriculum at the TU Vienna, and more recently a doctoral program, all in no small part due to Helmut’s tireless organizational work. I was a year ahead of him, but he was the better student. He literally had straight As throughout high school and university. In Austria, that earns you a doctorate sub auspiciis praesidentis, and the president of the republic himself hands you your diploma. His Diplom was on finite model theory; his dissertation on the complexity of database query languages (supervised by Georg Gottlob). Helmut had a stellar career: appointments at TU Munich, TU Darmstadt (two of the centers of computer science in Germany), and finally a full professorship at our alma mater in 2010; add to that an adjunct professorship at Carnegie Mellon. Not only was he the better student, he had the better sense to stay in computer science, and to do something useful with logic. He was one of the leading experts in computer aided verification, especially model checking, with over 120 papers to his name. After his return to Vienna, he was instrumental in getting the Vienna Center for Logic and Algorithms off the ground, led the organization of the Vienna Summer of Logic, and helmed the Austrian doctoral program on logical methods in computer science. Helmut wasn’t just an outstanding researcher, he was also passionate about improving undergraduate education in logic and computer science (he served on the ASL’s Logic Education committee, and we co-organized a special session at the 2014 Logic Colloquium), about diversity in the field, and about science policy.
We need more people like him. I miss him.
- TU Vienna obituary in German and English.
- A scholarship fund in Helmut’s honour is being set up. Contributions to the Helmut Veith Award can be made to “Zentrum für Informatikforschung”, IBAN: AT36 1200 0515 8258 2701, BIC: BKAUATWW, reference: “Helmut Veith Award”
[Photo credit: Nadia Meister/VSL]
(Cross-posted from the Open Logic Project)
Two exciting new things from the Open Logic Project. The first one is another sample textbook. I’ve previously written about how to get your textbook to print, and for my course “Logic II (Phil 379)” this term, I’ve done that. Properly: perfect bound paperbacks, with a nice cover, proper front and back matter, professional illustrations, and an (I think) appealing book design. The source for generating it is on GitHub (of course):
github.com/rzach/phil379. If you want to compile it, just clone that repository into the
courses/ subdirectory of your local OLP clone. It should compile out of the box. There are three files you can compile:
phil379-screen.tex makes a multi-color PDF suitable for on-screen reading;
phil379-print.tex makes a black-and-white PDF suitable for printing via lulu.com. The third is
cover-lulu-quarto.tex, which generates the PDF lulu.com uses for the cover. You can see the product on the builds site:
The second exciting thing is that we’ve started to put photos of logicians into the text. Right now, they’re imported into the biographies. The photos themselves are not in the main repository, however. We have a separate repository for them:
github.com/OpenLogicProject/photos. We’ve separated them because (a) the licensing issues are more complicated: some of the photos are under copyright, and we wanted everything in the main repository to be available under a Creative Commons license; (b) the main repository would become very large if it included all these pictures. To use the pictures, clone the photos repository into the
assets/ subdirectory of your local OLP clone. (If the files aren’t there, the biographies including them will happily compile but leave out the photos.) There’s a PDF with all the photos also on the build site.
(PS: If you want to buy an actual copy of the Sets, Logic, Computation book, go here. It sells for CAD 9.42 (USD 8.36, EUR 8.55). But be warned; we’ve already corrected a bunch of typos and errors, so that version is not up-to-date.)