20-21 Jun 2022
CONF Engineering the Concept of Collection, Oslo/Zoom, 20-21 June Engineering the Concept of Collection Time and place: June 20, 2022–June 21, 2022, Georg Morgenstiernes hus, University of Oslo room 452, and on Zoom Web: https://www.hf.uio.no/ifikk/english/research/projects/infinity-and-intentionality-towards-a-new-synthesi/events/conferences/engineering-the-concept-of-collection.html Speakers: Carolin Antos (Universität Konstanz), Neil Barton (University of Oslo), Tim Button (University College London), Herman Cappelen (University of Hong Kong and University of Oslo), Laura Crosilla (University of Oslo), Kentaro Fujimoto (University of Bristol), Luca Incurvati (University of Amsterdam), Øystein Linnebo (University of Oslo), Stewart Shapiro (Ohio State University and University of Oslo) The workshop will be hybrid (in-person and online). Registration is free but is required to attend the workshop. Please fill in this form to register: https://docs.google.com/forms/d/e/1FAIpQLSfmNtoV8hHbZWGxQFcjPYyhM65060zheM8C7KfSZ_GYSqguJg/viewform Registration deadline: 19th of June 2022, 5 pm (CET). You will receive the Zoom invite by email in the evening of the 19th of June. If you plan to attend in person in Oslo, please let the organisers know by the 10th of June at the latest. Program 20th June 1030-1145 Herman Cappelen and Øystein Linnebo: Engineering the concept of collection: introductory remarks 1145-1200 Break 1200-1315 Luca Incurvati: Inferential deflationism about objectified properties 1315-1415 Lunch 1415-1530 Kentaro Fujimoto: Plural, infinity, and impredicativity 1530-1545 Break 1545-1700 Laura Crosilla: On Weyl’s predicative concept of set 21st June 1030-1145 Tim Button: MOON theory: Mathematical Objects with Ontological Neutrality 1145-1200 Break 1200-1315 Carolin Antos: Engineering the concept of set - in practice 1315-1415 Lunch 1415-1530 Neil Barton: Engineering Set-Theoretic Concepts 1530-1545 Break 1545-1700 Stewart Shapiro: Semantic indeterminacy, concept sharpening, set theories Description: The history of mathematics and philosophy have seen many different concepts of collection: a set (understood as a gathering into one of previously available objects), a class (understood as defined by its membership condition, not by its members), a mereological sum, etc. Indeed, even a plurality (i.e. many objects) and a concept can be seen as a collection, since it makes sense to talk about their members (or instances). Alongside these longstanding debates about the nature of collections, there are also questions of how exactly each conception should be made precise. Recent attempts to make sense of the ontology of combinatorial sets, for example, have proposed very different pictures of what they are like. This is especially clear in the debates on the nature of our thought concerning `the’ universe of sets: Does our concept of (combinatorial) set suffice to determine a unique and maximal universe, or does our concept and talk of sets admit of different multifarious interpretations? These observations raise some general philosophical-mathematical questions. What concepts of collection do we have? Which, if any, of these concepts should we use? Or should we “(re-)engineer” one or more concepts of collection to produce concepts that are fit for purpose? Further questions may include: Should we use a single concept of collection or different concepts for different purposes? (Remember George Boolos: “I thought that set theory was supposed to be a theory about all, `absolutely' all, the collections that there are”.) Specifically, do we need both a combinatorial concept of set and a logical concept of class (cf. Parsons 1974, Maddy 1983, Linnebo 2006)? Should we strive for a single true theory based on one or more “correct” concepts of collection, or be pluralists and accept a multitude of equally legitimate, but often competing, theories? Can recent views on the nature of combinatorial sets (e.g. Hamkins, Linnebo, Woodin) be understood as instances of conceptual engineering? -- Dr. Neil Barton Postdoctoral Researcher IFIKK, Universitetet i Oslo Web: https://neilbarton.net/ -- [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