Mathematics of the Transcendental

ISBN-13: 9781441189240 / Angielski / Twarda / 2014 / 296 str.

Alain Badiou; A. J. Bartlett; Alex Ling

Opis

In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of Category Theory, demonstrating their internal logic and veracity, their derivation and distinction from Set Theory, and the 'thinking of being'. In doing so he sets out the basic onto-logical requirements of his greater and transcendental logics as articulated in his magnum opus, Logics of Worlds. This important book combines both his elaboration of the disjunctive synthesis between ontology and onto-logy (the discourses of being as such and being-appearing) from the perspective of Category Theory and the categorial basis of his philosophical conception of 'being there'.Hitherto unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use of Category Theory. The book is an essential aid to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.

Recenzje

[Badiou's] mathematics is precise and correct ... I am impressed by the lucidity of [his] remarks on the philosophical significance of category theory, especially in relation to set theory, and I invite philosophically minded mathematicians to be so too. Notices of the AMS 20151031

Spis treści

Translator's Introduction Preface Part I: Topos, or Logics of Onto-logy: An Introduction for Philosophers 1. General aim 2. First definitions 3. The size of a category 4. Limit and universality 5. Some fundamental concepts 6. Duality 7. Isomorphism 8. Exponentiation 9. Universe 1: closed Cartesian categories 10. Structures of immanence 1: philosophical grounds 11. Immanence 2: sub-object 12. Immanence 3: elements of an object 13. 'Elementary' clarification of exponentiation 14. Logic 1: central object (or sub-object classifier) 15. True, false, negation and more 16. Central object as linguistic power 17. Universe 2: the concept of Topos 18. Ontology of the void and of difference 19. Mono., Epi., Iso., Equa., and other arrows 20. Topoi as logical places 21. Internal algebra of 1 22. Ontology of the void and excluded middle 23. A classical miniature 24. A non-classical miniature Part II: Being-There Introduction A. Transcendental structures B. Transcendental connections B2. Of transcendental connections and logic in its usual sense (propositional logic and first order logic of predicates) B3. Transcendental connections and the general theory of localisations: topology C. Theory of appearing and of objectivity D. Transcendental projections: theory of localisation E. Theory of relations. The status of worlds Index

O autorze

Alain Badiou is a world-renowned French philosopher, formerly chair of the École Normale Supérieure in Paris, France, and founder of the faculty of Philosophy at the University of Paris VIII with Gilles Deleuze, Michel Foucault, and Jean-François Lyotard. Badiou has authored multiple major works of philosophy, many of which have been published in English by Bloomsbury, including Being and Event (2005), Logics of Worlds (2009), and The Immanence of Truths (forthcoming, 2021). A. J. Bartlett is an Adjunct Research Fellow at the Research Unit in European Philosophy at Monash University, Australia. He is the author of Badiou and Plato: An Education by Truths (2011), and with Justin Clemens and Jon Roffe author of Lacan, Deleuze, Badiou (2015). Alex Ling is Senior Research Lecturer in Communication and Media Studies at Western Sydney University, Australia. He is the author of Badiou Reframed (2016) and Badiou and Cinema (2011) and co-editor and translator of Mathematics of the Transcendental (Bloomsbury, 2014).