It is our pleasure to announce that starting this October the Department of Philosophy, University of Warsaw will host a new mathematical logic seminar devoted to formal truth theories and implicit commitments of foundational theories as well as their conceptual surroundings. At least until the end of the year, the seminar will be held utterly virtually on a bi-weekly basis. We have the following permanent link to seminar meetings:
If you wish to be put on the mailing list, please contact Mateusz Łełyk (mlelyk(at)uw.edu.pl).
Time: Friday, Jan 22nd, 8 pm (CET, GMT+1)
Speaker: Joel David Hamkins
Title: Definability and the Math Tea argument: must there be numbers we cannot describe or define?
According to the math tea argument, perhaps heard at a good afternoon tea, there must be some real numbers that we can neither describe nor define, since there are uncountably many real numbers, but only countably many definitions. Is it correct? In this talk, I shall discuss the phenomenon of pointwise definable structures in mathematics, structures in which every object has a property that only it exhibits. A mathematical structure is Leibnizian, in contrast, if any pair of distinct objects in it exhibit different properties. Is there a Leibnizian structure with no definable elements? We shall discuss many interesting elementary examples, eventually working up to the proof that every countable model of set theory has a pointwise definable extension, in which every mathematical object is definable.
Time: Friday, Feb 05th, 8 pm (CET, GMT+1)
Speaker: Leon Horsten
Title: Reflection and epistemic warrant
Over the past years, philosophers of mathematics have started to reflect on the epistemology of proof theoretic reflection. A central philosophical question that is being addressed in the emerging (small) body of literature on this theme is: what is the nature of the epistemic warrant that we have for proof theoretic reflection principles for (mathematical) knowledge (or justified beliefs) that we already have, and how can we come to acquire this epistemic warrant? I will start by giving an opinionated overview of recent work in this area. Subsequently, I will discuss some philosophical questions that, in my view, bear further philosophical investigation. One general message that I will aim to get across is that a deeper engagement with general accounts of epistemic warrant is needed in order to make philosophical progress in the area under consideration.