Plotnitsky A, 2012, "Experimenting with ontologies: sets, spaces, and topoi with Badiou and Grothendieck" Environment and Planning D: Society and Space 30(2) 351 – 368
Download citation data in RIS format
Experimenting with ontologies: sets, spaces, and topoi with Badiou and Grothendieck
Received 29 April 2010; in revised form 16 May 2011; published online 19 January 2012
Abstract. The paper explores the ontology and logic of the irreducibly multiple in set theory and in topos theory by considering the differences between Badiou’s logical and Grothendieck’s ontological approach to topos theory. It argues that Grothendieck’s ontological program for topos theory leads to a more radical concept of the multiple than does the set-theoretical ontology, which defines Badiou’s view of ontology even in his later, more topos theoretically oriented work. Extending Grothendieck’s way of thinking to other fields enables one to give ontological multiplicities—no longer bound by the set-theoretical ontology or ultimately by any mathematical ontology, even in mathematics—a great diversity and richness. It follows that the set-theoretical ontology is not sufficiently rich to accomplish what Badiou thinks it could accomplish even in mathematics itself, let alone elsewhere; and Badiou wants it to work elsewhere—indeed, wherever it is possible to speak of ontology. I shall also consider, in closing, some implications of the arguments for the workings of the multiple in ethics, politics, and culture.
Keywords: logic, mathematics, multiplicity, ontology, philosophy, set theory, topos theory
Full-text PDF size: 229 Kb
References 15 references, 0 with DOI links ()
Your computer (IP address: 220.127.116.11) has not been recognised as being on a network authorised to view the full text or references of this article. If you are a member of a university library that has a subscription to the journal, please contact your serials librarian (subscriptions information).