12-14 Oct 2016
Munich, Germany
CFR: Foundations of Mathematical Structuralism 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? Programme: Day 1 - Wednesday 12 October 2016 9:00 - 9:15 Welcome and introductory remarks 9:15 - 10:45 Steve Awodey ?Univalence and Structuralist Foundations of Mathematics? 10:45 - 11:00 Coffee break 11:00 - 12:30 Øystein Linnebo ?Structure Abstraction? 12:30 - 12:45 Coffee break 12:45 - 13:45 José Ferreirós ?On Feferman's Conceptual Structuralism? 13:45 - 15:00 Lunch break 15:00 - 16:30 James Layman ?Does the Univalence Axiom in Homotopy Type Theory Encode Mathematical Structuralism?? 16:30 - 16:45 Coffee break 16:45 - 17:45 Dan Waxman ?Structuralism and the Epistemology of Coherence? Day 2 - Thursday 13 October 2016 9:00 - 10:30 Hannes Leitgeb ?A Theory of Unlabeled Graphs as Ante Rem Structures? 10:30 - 10:45 Coffee break 10:45 - 12:15 Erich Reck ?Towards a New Taxonomy for Mathematical Structuralism? 12:15 - 12:30 Coffee break 12:30 - 13:30 Francesca Boccuni & Jack Woods ?Structuralist (Neo-?)Logicism? 13:30 - 15:00 Lunch break 15:00 - 16:30 Mary Leng ?An ?i? for an i, a truth for a truth?? 16:30 - 16:45 Coffee break 16:45 - 17:45 Josef Men?ík ?Mathematical Structuralism: Internal and External? 18:00 Conference dinner Day 3 - Friday 14 October 2016 10:00 - 11:30 Jessica Carter ?Structuralism and Mathematical Practice? 11:30 - 11:45 Coffee break 11:45 - 13:15 Gerhard Heinzmann ?The Structuralist Roots of Mathematical Understanding: Early French Structuralism Reconsidered? 13:15 - 14:45 Lunch break 14:45 - 15:45 Francesca Biagioli ?Structuralism and Mathematical Practice in Felix Klein's Work on Non-Euclidean Geometry? 15:45 - 16:00 Coffee break 16:00 - 17:30 Geoffrey Hellman ?Modal-Structural Mathematics for a Multiverse? Call for Registration: To register for the conference, please email your name and affiliation to mathematicalstructuralism2016@lrz.uni-muenchen.de. There will be a conference dinner on Thursday 13 October 2016. We would be grateful if you could let us know if you plan to attend. For further details on the conference, please visit: http://www.mathematicalstructuralism2016.philosophie.uni-muenchen.de/index.html Organisers: Georg Schiemer (MCMP & University of Vienna), John Wigglesworth (MCMP) -- John Wigglesworth Ludwig-Maximilians-Universität München Munich Center for Mathematical Philosophy (MCMP) www.wigglesworth.org -- [LOGIC] mailing list http://www.dvmlg.de/mailingliste.html Archive: http://www.illc.uva.nl/LogicList/ provided by a collaboration of the DVMLG, the Maths Departments in Bonn and Hamburg, and the ILLC at the Universiteit van Amsterdam