Collection
What Can Philosophy Do for Set Theory?
In recent times, there’s been a significant increase of the interest in the philosophical aspects of set theory, reflected by a vast production addressing themes such as pluralism, realism, the nature (and justification) of the axioms, potentialism, set theory’s connections with science, and others. The correct relationship between philosophy and set theory has itself been the subject of intense debate, and there seems to be no broad consensus on how it should be articulated. One way of seeing the role that philosophical reflection plays in set theory is simply to view the research itself, on things like the inner model program, Ultimate-L, forcing axioms, and so on, as philosophy itself. Under this view, this is what the exploration of, e.g., set-theoretic truth is and should look like. Alternative to this form of set-theoretic naturalism is the view that broader philosophical perspectives, including metaphysical ones, not only play an important role in guiding the research programmes of the field but can also shed new light on set theory itself. Of course, these two approaches do not, nor are meant to, exhaust all options. This volume will bring together both practising set-theorists and more philosophically oriented scholars for the purpose of thinking about the question what philosophy can (and should) do for set theory, as well as that of how set theory could make the most of a broad range of additional logical and philosophical tools.
Editors
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Joan Bagaria bagaria@ub.edu
Joan Bagaria: Fulbright Fellow UC Berkeley, 1985-87. PhD in Logic and the Methodology of Science, UC Berkeley, 1991. Postdoc. researcher, UC Berkeley, 1991-92. Assoc. Prof. at Catalonian universities, 1992-2001. ICREA Research Prof. at Univ. Barcelona since 2001. Invited researcher at UC Berkeley, CalTech, Hebrew Univ., Harvard Univ. President of the European Set Theory Society, 2007; Chairman of INFTY ESF-Research Networking Program, 2009-14; Simons Foundation Fellow at Isaac Newton Inst., Univ. Cambridge, UK, 2015. Director of the Barcelona Research Group on Set Theory (BCNSETS), and coordinator & PI of the Barcelona Logic Group (BCNLOGIC).
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Juliette Kennedy juliette.kennedy@helsinki.fi
Juliette Kennedy received her Ph.D. in mathematics in 1996 from the C.U.N.Y. Graduate Center. After post-doctoral years at Stanford and Bucknell Universities, she joined the Department of Mathematics at the University of Helsinki in 1999. Kennedy works in set theory and set-theoretic model theory. She has also worked extensively in the early 20th century foundations of mathematics. Her recent books include Gödel’s Incompleteness Theorems, and Gödel, Tarski and the Lure of Natural Language (Cambridge University Press). Kennedy also works as a curator. Her most recent exhibitions have featured the American minimalist artist Fred Sandback.
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Claudio Ternullo claudio.ternullo@ub.edu
Claudio Ternullo (PhD, Liverpool, 2012) is currently a Postdoctoral Fellow in the Department of Mathematics and Computer Science of the University of Barcelona. Previously, he was a Postdoctoral Fellow at the KGRC, University of Vienna, at the University of Tartu and a Beatriu de Pinós (Marie-Skłodowska Curie COFUND) Fellow at the University of Barcelona. His research interests lie in logic and the philosophy of mathematics (in particular, in the philosophy of set theory). His work focuses on the set-theoretic multiverse, the justification of new axioms, mathematical platonism, abstraction principles, and the history of logic.
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Giorgio Venturi gio.venturi@gmail.com
Giorgio Venturi is Associate Professor at the University of Pisa and before that he worked as Assistant Professor at the University of Campinas. He has a background in both philosophy and mathematics and he received a PhD in Mathematics at the Université Paris Diderot and a PhD in Philosophy from the Scuola Normale Superiore, in 2014. His research interests are in set theory and philosophy of mathematics, with a focus on forcing and its role in the foundations of mathematics, but they also extend to the modal and non-classical logics. He is currently secretary of the European Society for the Philosophy of Mathematics.
