Seminars
PoSeT G runs a monthly online seminar with the aim of creating a place of encounter for philosophers of set theory and set-theorists. We want to foster interaction and cooperation between the two disciplines as we think they can both benefit from each other.
If you would like to attend the seminar, please subscribe to our mailing list or send us an email [poset.group@gmail.com].
2025
JANUARY: 31st January
Sandra Müller (Vienna)
Title: Scenarios for attacking Gödel's Problem
Abstract: After proving that not all statements in mathematics can be proven or disproven from the accepted ZFC axioms, Gödel raised the question whether natural statements, such as Cantor’s continuum hypothesis, can be decided via extending the axiomatic framework by axioms of large infinities. While this question has been answered in the negative, the problem of finding good axioms that decide natural mathematical statements remains open. There is a compelling candidate for an axiom that could solve Gödel’s problem: V = Ultimate L. We motivate and describe this candidate together with the Sealing scenario as well as recent set theoretic advances in this area.
Time: 4:30pm CET (UTC +1)
2024
DECEMBER: 12th December
Chris Scambler (Oxford)
Title: Cardinality Relativism
Abstract: I will discuss three types of argument for cardinality relativism: those from the Lowenheim Skolem theorems, from predicativity considerations, and finally some more recent arguments I’ve been developing related to the theory of forcing. I will argue that the latter are the most persuasive, and that they provide a decidedly countabilist perspective on the independence phenomenon in set theory that differs in significant ways from Hamkins-style pluralism.
Time: 4:30pm CET (UTC +1)
NOVEMBER: 11th November
Joan Bagaria (Barcelona)
Title: On the truth of large cardinal axioms of set theory
Abstract: If we understand set theory as the theory of the set-theoretic universe, given by the cumulative hierarchy of sets that is obtained inductively along the class of all ordinal numbers, then all Zermelo-Fraenkel (ZF) axioms are true. The axiom of Choice is usually taken also to be true, for a variety of reasons that we will not address in this talk. But as ZFC (ZF plus Choice) leaves many fundamental questions about the set-theoretic universe unanswered, further axioms are needed. Beyond the ZFC axioms, the axioms asserting the existence of large cardinals are the best studied and the most widely accepted. But are they true? In recent years, different forms of varying strength of a very general reflection principle, known as Structural Reflection, have been shown equivalent to many of the known large cardinal axioms, thus providing evidence that all large cardinal axioms are in essence strong reflection principles of this sort. We shall discuss to what extent these Structural Reflection principles can be justified as being true axioms of set theory.
Time: 4:30pm CET (UTC +1)
OCTOBER: Monday 14th
Luca Incurvati (Amsterdam)
Title: Conceptual engineering and conceptual genealogy: sets vs properties
Abstract: I will start by clarifying the extent to which the defence of the iterative conception in Incurvati 2020 is compatible with pluralism. The idea is that some conceptions are better than others for certain goals. The approach is functionalist about concepts: sharpenings of concepts are selected on the basis of how well they fullfill a certain function. I will then move on to discuss the case of objectified properties. I will again start from a functionalist approach and take as a starting point the expressive function of objectified-property talk. I will then report work in progress on a theory of objectified properties which is motivated by the functionalist approach and takes the meaning of objectified-property talk to be completely explained in terms of its inferential relation to property talk. I will discuss formal and philosophical aspects of the theory, in particular its relationship with Maddy's work on classes and the question of realism about objectified properties.
Time: 4:30pm CEST (UTC +1)
TIME ZONES
Most seminars take place at 4:30pm CET (UTC +1, Rome, Vienna, Oslo), here's the conversion with some other time zones:
London (UTC + 0): 03:30pm
New York (UTC -5): 10:30am
Chicago (UTC -6): 09:30am
Los Angeles (UTC -8): 7:30am
Singapore (UTC +8): 10:30pm
Tokyo (UTC +9): 11:30pm
Sydney (UTC +10): 00:30am
We are grateful to the Circle-U Alliance network for their support in organizing these seminars.