Everything you needed to know about forcing, but were afraid to ask Alain Badiou

Hat tip to Fabio at Hypertiling and Tzuchien Tho for bringing this to my attention. Wish I could be there. If the reason you can't attend this magnificent, London-based workshop is that you'll be in Mexico City this May, stay tuned...

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A Set Theory Postgraduate Workshop for Readers of Being and Event or: Everything You Needed to Know about Forcing but were Afraid to Ask Alain Badiou

24 May, 31 May and 7 June 2011 in Room G03, 28 Russell Square

As part of its ongoing Seminar Series on Mathematics for the Humanities and Cultural Studies, the London Consortium will hold a series of three postgraduate students workshops that aims to discuss and provide a quick overview of some of the mathematics that needs to be known in order to follow the use of set theory
in Alain Badiou’s Being and Event [L'Être et l'Événement]. The main focus of these ‘bootcamps’ will be on introducing and discussing, in a friendly manner, the technicalities concerning the “mathematical bulwarks” mentioned in Badiou’s philosophical masterpiece:
(1) the Zermelo-Fraenkel Axioms of Set Theory
(2) the Theory of Ordinal and Cardinal Numbers
(3) Kurt Gödel and Paul Cohen’s work on Consistency and Independence.

Particular attention will be paid towards providing a sufficiently detailed, rigorous and clear explication of Paul Cohen’s technique of forcing and generic models, a mathematical result that Peter Hallward has called “the single most important postulate” in the whole of Being and Event. If time permits, we might also be touching on some recent mathematical developments in the field as well as trying to understand how Badiou contributes towards the contemporary re-intervention of mathematical thinking into philosophy.

The workshops will be held in room G03 at 28 Russell Square, Bloomsbury, London. The intended audience are postgraduate students or researchers who are interested in understanding Badiou’s philosophy but who lack the mathematical background. There are no assigned compulsory readings for the bootcamps,
and there are no pre-requisites save for some minimal familiarity with mathematics at the pre-university level. The sessions are free and open to the public but please register by sending your name, email and affiliation to forcing.badiou@gmx.com so as to give us an idea of the numbers since the classroom size, unfortunately, will be limited.

Workshop Convener: Burhanuddin Baki

Schedule and List of Topics

Session I (Tuesday, 24 May)

2-4pm – Basic Mathematics and Short Introduction to Forcing
Short Introduction to Badiou’s Being and Event; Basic Arithmetic, Abstract Algebra and First-Order Logic;
Idea of Mathematical Proof; Induction; Naïve Set Theory, Cantor’s Theorem and Russell’s Paradox

6-8pm – Zermelo-Fraenkel Set Theory
Zermelo-Fraenkel Axioms plus the Axiom of Choice (ZFC); Peano Axioms of Arithmetic; Gödel’s
Incompleteness Theorems; Being and Event Parts I, II, IV and V; Some Alternative Axiomatizations of
Mathematics and Set Theory

Session II (Tuesday, 31 May)

2-4pm – Cardinal and Ordinal Numbers
Cardinal Numbers; Well-Orderings; Ordinal Numbers; Continuum Hypothesis; Being and Event Part III
and Meditation 26; Introduction to Surreal Numbers

6-8pm – Kurt Gödel and the Constructible Hierarchy
Some Relevant Model Theory; Formal Semantics of Situations; Formal Semantics of Events; Gödel’s
Completeness Theorem; Compactness Theorem; Löwenheim-Skolem Theorem and Paradox; Transfinite
Induction; Cumulative and Constructible Hierarchies; Axiom of Constructibility; Gödel’s Proof of
Consistency; Being and Event Meditation 29; Introduction to Large and Inaccessible Cardinals

Session III (Tuesday, 7 June)

2-4pm – Paul Cohen, Forcing and Generic Models
General Machinery of Forcing; Analogy between Forcing and Field Extensions; Cohen’s Proof of
Independence

6-8pm – Beyond Cohen’s Forcing
Cohen’s Proof of Independence (con’t); Being and Event Meditations 33, 34 & 36; Forcing in terms of
Kripkean Semantics; Forcing in terms of Boolean-valued models; Forcing Axioms and Generic
Absoluteness; Introduction to Categorial Logic and Topos Theory; Forcing in terms of Topos Theory;
Short Introduction to Forcing in Badiou’s The Logics of Worlds

Suggested Introductory Reading List

Avigad, J. (2004). “Forcing in Proof Theory”. http://www.andrew.cmu.edu/user/avigad/Papers/forcing.pdf.
Badiou, A. (2007). Being and Event. Translated by Oliver Feltham. London: Continuum.
Badiou, A. (2007). The Concept of Model. Translated by Zachary Fraser & Tzuchien Tho. Victoria: re:press.
Badiou, A. (2008). Number and Numbers. Translated by Robin Mackay: Cambridge: Polity.
Badiou, A. (2009). The Logics of Worlds. Translated by Alberto Toscano. London: Continuum.
Bowden, S. (2005). “Alain Badiou: From Ontology to Politics and Back”.

http://jffp.pitt.edu/ojs/index.php/jffp/article/view/244/238.

Chow, T. (2004). “Forcing for Dummies”. http://math.mit.edu/~tchow/mathstuff/forcingdum.
Chow, T. (2008). “A Beginner’s Guide to Forcing”. http://arxiv.org/abs/0712.1320.
Cohen, P. (2002). “The Discovery of Forcing”.

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181070

010.
Cohen, P. (2008). Set Theory and the Continuum Hypothesis. New York: Dover.
Crossley, J., et. al. (1991). What is Mathematical Logic?. Mineola: Dover.
Devlin, K. (1991). The Joy of Sets: Fundamentals of Contemporary Set Theory. New York: Springer.
Doxiadis, A., et. al. (2009). Logicomix: An Epic Search for Truth. Bloomsbury Publishing PLC.
Easwaran, K. (2007). ” A Cheerful Introduction to Forcing and the Continuum Hypothesis”.

http://arxiv.org/abs/0712.2279.

Fraser, Z. (2006). “The Law of the Subject: Alain Badiou, Luitzen Brouwer and the Kripkean Analyses of
Forcing and the Heyting Calculus”. http://www.cosmosandhistory.org/index.php/journal/article/view/30.
Goldblatt, R. (2006). Topoi: The Categorial Analysis of Logic. Mineola: Dover.
Hallward, P. (2003). Badiou: A Subject to Truth. Minneapolis: U. of Minnesota Press.
Halmos, P. (1974). Naive Set Theory. New York: Springer.
Jech, T. (2004). Set Theory: The Third Millennium Edition, Revised and Expanded. New York: Springer-Verlag.
Jech, T. (2008). “What is Forcing?”. http://www.ams.org/notices/200806/tx080600692p.pdf.
Kanamori, A. “Cohen and Set Theory”. Bull. Symbolic Logic 13(3) (2008), 351-78.
Kunen, K. (1992). Set Theory: An Introduction to Independence Proofs. New York: North Holland.
Norris, C. (2009). Badiou’s Being and Event. London: Continuum.
Pluth, E. (2010). Badiou: A Philosophy of the New. Cambridge: Polity Press.
Potter, M. (2004). Set Theory and its Philosophy. Oxford: Oxford U. Press.
Smullyan, R. & M. Fitting. (2010). Set Theory and the Continuum Problem. Mineola: Dover.
Tiles, M. (1989). The Philosophy of Set Theory. Mineola: Dover.

The London Consortium is a multi-disciplinary graduate programme in Humanities and Cultural Studies. We are a collaboration between five of London’s most dynamic cultural and educational institutions: the Architectural Association, Birkbeck College (University of London), the Institute of Contemporary Arts, the Science Museum, and Tate.