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Aus Bartlett und Clemens - Neither Nor

"Neither Nor" ist eine polemische Replik auf eine Kritik von Richardo und David Nirenberg - Badiou’s Number: A Critique of Mathematics as Ontology, beides im Critical Inquiry. Sie weisen dort auf Sekundärliteratur zum Verhältnis von Ontologie und Mathematik bei Badiou, die die Nirenbergs nicht beachtet hätten.

Madison Mount 2005 - Cantorian revolution

B. Madison Mount: Cantorian revolution" In: Polygraph 17. The Philosophy of Alain Badiou. Ed. by. Matthew Wilkens, 2005

Aus der Einleitung von M. Wilkens, S.2f:

"A number of the contributions to this volume take up Badiou’s use of set theory and its connection to ontology as a step toward examining other aspects of his thought. B. Madison Mount’s essay on the “Cantorian revolution,” however, is the lone direct and sustained engagement with his philosophy of mathematics, and is perhaps the best such treatment yet to have appeared in English or in French. Mount begins by situating Badiou’s ontology within and against the historical development of theories of the infinite through Cantor and Gödel, with particular attention to issues surrounding the Continuum Hypothesis. He then goes on, in the second section, to analyze the ways in which Badiou seeks to develop a line of thought “transverse” to what he calls the grammatical or constructivist, generic, and prodigal orientations of contemporary philosophy of mathematics. Specifically, Mount reads at length meditations 28−30 of L’être et l’événement in order both to show the ways in which Badiou derives a closed or nonevental understanding of constructivist thought from Leibniz’s metaphysics and to suggest the alternate conceptions that might be drawn from — or in alignment with the same source. Mount’s essay will thus be of particular relevance to those interested in Badiou’s generally dismissive treatment of constructivism past and present, as well as to those seeking a more complete understanding of his position vis-à-vis other mathematical philosophies (and philosophies of mathematics). Finally, it provides a useful complement to and extension of Hallward’s appendix to his Badiou on the technical details of Badiou’s mathematical thought; see especially sections 1.2 and 2.2, which treat the Continuum Hypothesis and the large cardinal axioms in meaningful and comprehensive detail."

Brassier 2007 - Unbinding the Void

Ray Brassier. Nihil Unbound - Enlightenment and Extinction. Chapter 4: Unbinding the Void (PDF)

Gillespie 2008 - The Mathematics of Novelty

Sam Gillespie. The Mathematics of Novelty: Badiou's Minimalist Metaphysics (PDF)



Fraser 2006 - Badious Subjekt, Kripke zu Forcing und das Heyting-Kalkül

Zachary Fraser: Alain Badiou, Luitzen Brouwer and the Kripkean Analyses of Forcing and the Heyting Calculus. In: Cosmos and History: The Journal of Natural and Social Philosophy, vol. 2, no. 1-2, 2006 (PDF)

Norris 2008 - Badiou für analytische Philosophen?

Christopher Norris: Some Versions of Platonism: Mathematics and Ontology According to Badiou. In: Philosophical Frontiers - A Journal of Emerging Thought, vol. 3, no. 1, 2008 (Abstract)

Kadvani 2008 - Review of Number and Numbers

John Kadvani hat ein Review von Badious "Number and Numbers" im "Notre Dame Philosophical Reviews" geschrieben: Online-Version

Hersh 2009 - Review of Number and Numbers

Reuben Hersh: Review of Number and Numbers. In: THE MATHEMATICAL INTELLIGENCER. Volume 31, Number 3 (PDF)

"This seems to me to be the key fallacy of Badiou: This bare statement that the general form of every presentation is multiplicity. Badiou seems to actually say that the Multiplicity of a Situation is a complete description or specification of it! On the contrary, even a mathematical situation beyond abstract set theory is described mainly by the relations, the operations, which are defined on some set. So much more so is any ‘‘real-world’’ situation described by many more attributes than its mere multiplicity!"
"To my mind, this one-dimensional reduction of reality to a well-ordered set is embarrassingly simplistic. Indeed, it is in essence already too familiar, as a way of caricaturing reality. Anyone acquainted with Marxist analysis will recognize its similarity to the one-dimensional universal ranking of everything by Price, which is the essence of the ‘‘Free Market,’’ the reign of Capital."
"Real situations are not one-dimensional, they are multi-dimensional, even infinite-dimensional. Mathematics used in a serious way to study non-mathematical reality cannot limit itself to any one-dimensional scale, no matter how extended or how refined!"

Hersh - Paul Cohen and Forcing in 1963

Reuben Hersh: Paul Cohen and Forcing in 1963. In: THE MATHEMATICAL INTELLIGENCER. Volume 33, Number 3, p. 138-140 (Preview)

mathematisches Basiswissen

Chow 2008 - A beginner's guide to forcing

Website des Texts inkl. PDF - von Timothy Y. Chow

"This expository paper, aimed at the reader without much background in set theory or logic, gives an overview of Cohen's proof (via forcing) of the independence of the continuum hypothesis. It emphasizes the broad outlines and the intuitive motivation while omitting most of the proofs. The reader must of course consult standard textbooks for the missing details, but this article provides a map of the forest so that the beginner will not get lost while forging through the trees."