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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)

Recherche

Weblinks

Fraser 2006 - The Law of the Subject

Zachary Fraser: The Law of the Subject: 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)

Badiou - The Concept of Model

Zachary Fraser ist außerdem Herausgeber/Übersetzer von einem sehr frühen Text von Badiou - Le concept de modèle (1969) - "The Concept of Model" (2007) (PDF), das als Open Access E-Book verfügbar ist: "Written on the eve of the events of May 1968, The Concept of Model provides a solid mathematical basis for a rationalist materialism. Badiou’s concept of model distinguishes itself from both logical positivism and empiricism by introducing a new form of break into the hitherto implicated realms of science and ideology, and establishing a new way to understand their disjunctive relation."

Peter Dews 2008 - Review of Being and Event

Der Review von Dews ist in Notre Dame Philosophical Reviews verfügbar.

"Badiou's whole philosophy, we could say, is generated by the tension between his basic claim that mathematics is ontology, and his equally fundamental claim that, as he puts it, 'ontology is a situation' (p. 25). For this means that, although ontology exhausts what there is, it cannot capture everything which occurs: there can be other situations, regardless of how difficult it may be to portray them theoretically. So despite his hostility to the 'anti-philosophical' tradition in post-Hegelian thought, Badiou himself plays his own version of that tradition's typical game. What cannot be known is what it is most urgent to know, what really matters, politically and existentially. Badiou -- and here he differs from his post-structuralist contemporaries -- is inclined to call it 'truth'."

[...]

"Badiou's transposition of the notion of fidelity from the sphere of love (to which he concedes that it directly refers (p. 232)), the misdirection of his passion for the unconditional towards happenings in the mutable socio-historical world, brings with it the dangers of dogmatism and exclusivism, if not worse. And it also raises one final issue. Badiou repeatedly declares that God 'does not exist' (e.g., p. 277). But the whole of Being and Event is an intense and intricate exploration of what does not exist -- namely the event, for which there is 'no acceptable ontological matrix' (p. 190). Furthermore, Badiou's own thinking cannot help but lead towards the question: why ought we to become subjects, why should we commit ourselves to a life of fidelity? Indeed, Badiou himself later poses this question in terms of the 'fidelity to fidelity that defines ethical consistency' (Ethics, pp. 49-50). And although this may not be Badiou's answer, it is not clear what aspect of his system would rule it out as a response: because we are called by God, who is the event of events."

Paul Livingston 2008 - Being and Event

  • Livingston, Paul (2008) 'Review of Being and Event ', Inquiry,

51:2, 217 - 238

  • Verfügbar [1.pdf als 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

"Anti-constructivist bias distorts Badiou's history of mathematics, in which virtually nothing happens vis à vis number after around 1900. In particular, he ignores Alan Turing and related theories of symbolic processing (Post, Church, Chomsky, et al.), from which came modern computing and its world historical consequences. Of course, Badiou detests such "constructive" thought, so he ignores its milestones, including equivalencies of many mathematical theories and computational procedures."

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."

Cohen 2002 - The discovery of forcing

Paul J. Cohen, The discovery of forcing, Rocky Mountain J. Math. 32 (2002), 1071–1100 (PDF)