- 1 Aus Bartlett und Clemens - Neither Nor
- 2 Recherche
- 2.1 Weblinks
- 2.2 Fraser 2006 - The Law of the Subject
- 2.3 Peter Dews 2008 - Review of Being and Event
- 2.4 Paul Livingston 2008 - Being and Event
- 2.5 Paul Livingston 2009 - Agamben, Badiou, and Russel
- 2.6 Paul Livingston 2012 - The Politics of Logic: Badiou, Wittgenstein, and the Consequences of Formalism
- 2.7 Norris 2008 - Badiou für analytische Philosophen?
- 2.8 Kadvani 2008 - Review of Number and Numbers
- 2.9 Hersh 2009 - Review of Number and Numbers
- 2.10 Hersh - Paul Cohen and Forcing in 1963
- 3 mathematisches Basiswissen
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 hin 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)
- Review zu "Number and Numbers" von bat020: http://bat020.com/2011/02/17/review-of-badious-number-and-numbers/. Der Beitrag ist auch in der Zeitschrift "Radical Philosophy", issue 156 (2009) erschienen.
- In MathOverflow "a place for mathematicians to ask and answer questions" wurde gefragt, ob Badiou interessant zu lesen ist für die Mathematikerin mit einer interessanten Antwort.
- Blog article about the Badiou-Nirenberg-debate: http://academiclogbook.blogspot.ch/2012/02/nirenberg-badiou-debate-over-being-and.html
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 als PDF
"Yet as much as it may give grounds for hope, there is also reason to doubt that Being and Event will succeed in providing a project that can be continued, even with significant critical adjustments and limitations, by members of the (at present extremely disjoint) audiences it addresses. For those students of continental philosophy who, drawn by its rhetoric of activism and militancy, see in Being and Event a manifesto for activism or radical exercises of the political imagination, it is doubtful whether its appeal to set theory can be, at present, much more than an empty gesture toward a largely uncomprehended source of doctrinal authority. There is aneminent danger, in particular, that these students, lacking a detailed understanding of Badiou’s formal apparatus, will take up his terminology as jargon, and thus lose the clarity with which Badiou himself employs it. Coming from the other side, as well, it seems likely that analytic philosophers may find Badiou unrigorous, if not in his development of the details of set theory themselves, then certainly in his application of them to the murky questions of being, event, and subject; as imaginative and innovative as these connections can be, their necessity is not always obvious, and the particular results that Badiou reaches depend in detail on the rich but dense matrix of concepts he draws from Lacan and other poststructuralist philosophers of a more ‘‘literary’’ bent."
"If there is any hope for the continuance of these methods, it will indeed be important that continental philosophers learn logic and set theory, and that analytic philosophers learn Lacan, Deleuze, and Derrida; this will require, clearly, that both groups give up deeply-held prejudices and methodological assumptions. It is thus certainly to be hoped that the current translation of Being and Event helps to create an audience that can read it; nevertheless the development of such an audience may take a long time, and it will take more than one book, no matter how imaginative, to anchor it."
Paul Livingston 2009 - Agamben, Badiou, and Russel
Paul Livingston (2009). Agamben, Badiou, and Russell. Continental Philosophy Review 42 (3). Verfügbar als DOC
- "I document [..] implications of Russell’s paradox in the texts of Agamben and Badiou and suggest that they point the way toward a reconfigured political life, grounded in a radical reflective experience of language."
Paul Livingston 2012 - The Politics of Logic: Badiou, Wittgenstein, and the Consequences of Formalism
- 5 von 10 Kapitel sind auf Livingstons Homepage als Download verfügbar.
- "Badiou develops a dramatic interpretation of the implications of mathematical set theory for contemporary thought about the very structure of being and the most fundamental possibilities of political change and transformation. More recently, in the 2006 sequel Logics of Worlds, Badiou has supplemented this investigation with a detailed analysis, grounded this time on the formalisms of mathematical category theory, of the relationship between being as it is in itself (and is treated by "ontology") and appearances or phenomena, the subject of "phenomenology". Together, the two books thus comprise a highly sophisticated manifestation (probably the most highly developed to this date) of what I am here calling the "politics of logic". One main purpose of this book is thus to examine Badiou‘s system, both in its formal and its political registers. But while this demands some exegesis of Badiou‘s complex work, my aim here is not simply exegetical, but also evaluative and critical."
- "[O]ne of the most innovative and helpful features of Badiou‘s thought is his ability to draw specific and determinate ontological and political results from the formal structures. However, his specific ways of interpreting formalisms nevertheless involves, at several points, fundamental interpretive choices which he often leaves unmarked. This leads Badiou repeatedly to reject positions and orientations of thought with which he might otherwise be much more sympathetic, and which we ought to consider in the course of an investigation of the consequences of formalism for questions of political life."
Levi R. Bryant: Review of "The Politics of Logic
"Prospective readers of The Politics of Logic will find this book to be of great importance and interest for three reasons. [...]
- First, those interested in the Continental/Analytic divide will be impressed by how Livingston deftly weaves together the work of thinkers as diverse as Deleuze, Derrida, Lacan, Badiou, Gödel, Wittgenstein, Russell, Turing, Quine, and Carnap, demonstrating both how Continental thinkers have a great deal to teach us about logic and formalism, and how Analytic thinkers have a great deal to teach us about politics. [...]
- Second, for those situated in the French Continental tradition such as myself, Livingston brings into relief a common thematic, present in highly diverse thinkers, and demonstrates the political implications that follow from this theme. Increasingly, Continental thought has become occupied with issues of sovereignty and what I call "logics of exception". These themes can be traced in thinkers as diverse as Lacan in his graphs of sexuation, Derrida in his meditations on incompleteness, Badiou in his reflections on events and truth-procedures, Žižek in his reflections on the Real and the Act, Agamben in his work on sovereignty and homo sacer, and many others. [...]
- Third, and most importantly, through his meditations on formalism and logic, Livingston is able to open new vistas for critique and resistance. In doing so, he generates hope that resistance and change are indeed possible -- and that they are possible for necessary structural reasons, not contingent historical reasons -- thereby contributing to the revitalization of political engagement. If there is one lesson to draw from Livingston's book, it is that there are always and necessarily resources available for resistance: change is necessarily possible.
John Protevi: Spotlight on "The Politics of Logic"
- Verfügbar im New APPS blog
- "Livingston is after how formal structures of sets (the various ways of relating the one and the many) illuminate not just the (conceptual or logical) relation of objects and predicates or properties but also the (political) relation of states or communities to their members: how they include them in a whole and also how the excluded can lead to their rupture or transformation."
- "What Livingston means by the contemporary “consequences of formalism” are the ways formalist advances make possible not just information technologies but also the very bureaucratic / administrative forms of government and social organization which they subtend. So we have to investigate two grounds: 1) how any kind of collective life can be reflected in formal structures and 2) how our collective life is being transformed by these information technologies and political rationalities."
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)
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)