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                                                       7-8 November, 2011


 Maximalist and Minimalist Perspectives on Infinity: A meeting on set theory and its philosophy

Speakers:Tatiana Arrigoni (Fondazione Bruno Kessler, Trento & Kurt Gödel Centre, Vienna); Joan Bagaría (Universitat de Barcelona); Laura Crosilla (University of Leeds); Sy Friedman (Kurt Gödel Centre for Mathematical Logic, Vienna); Ignasi Jané (Universitat de Barcelona)

Timetable and Abstracts


   




 

 

 

 


It has been argued that set theoretic developments are guided by two key methodological criteria: maximize and unify (Maddy 1997). The first criterion in particular has been central to some of the most successful developments of the last 50 years, namely those having to do with large cardinal hypotheses. And it is certainly the case that ZFC plays the role of a unifying framework in contemporary mathematics (regardless of considerations of evidence and of obscurities which may still be lurking behind its most basic principles). Yet there are different sources of concern with the two maxims singled out by Maddy, ranging from the need to supplement them with other criteria, to – more interestingly – the possible ambiguities in their practical application (i.e. the need to consider more specific versions of each one of them, which might then orient research along different directions).
 It is certainly the case that not all experts in set theory agree on the desired “maximality” that the theory ought to incorporate or implement. While some of them emphatically adopt the most encompassing large cardinal axioms, some set theorists have expressed a preference for the constructible universe or else for inner models that share some of its characteristics (see Arrigoni 2011, Friedman 2002). Moreover in recent decades there have emerged proposals for a “constructive set theory” that creates links with ideas and approaches that have established themselves successfully in other areas of recent mathematics, e.g. with intuitionistic type theory (see Crosilla 2009).  In accordance with the situation just sketched, the aim of our meeting is to try to clarify the aims and goals involved in several minimalistically- and maximalistically-oriented research programs that are pursued in current work, as well as the criteria to be employed in judging the success of such programs. The workshop will feature talks both by some prominent set theorists and experts in the philosophy of set theory. 

References:
Tatiana Arrigoni. V = L and intuitive plausibility in set theory. A case study. Bull. Symbolic Logic 17, Issue 3 (2011), 337-360.
 Sy David Friedman. Cantor’s set theory from a modern point of view. Jahresbericht der Deutschen Mathematiker–Vereinigung 104: 165–70, 2002.
Crosilla, Laura, "Set Theory: Constructive and Intuitionistic ZF", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.).
URL = <http://plato.stanford.edu/archives/spr2009/entries/set-theory-constructive/>. Penelope Maddy. Naturalism in mathematics. Oxford University Press, 1997.
 



Organizado con la colaboración del IMUS
(Instituto de Matemáticas, Univ. Sevilla)
y el
patrocinio de la Sociedad de Lógica, Metodología
y Filosofía de la Ciencia en España.