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Some Versions of Platonism: Mathematics and Ontology According to Badiou

Author(s): Christopher Norris

Journal: Philosophical Frontiers : A Journal of Emerging Thought
ISSN 1758-1532

Volume: 3;
Issue: 1;
Start page: 1;
Date: 2008;
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Keywords: Badiou | Platonism | Mathematics | Ontology

In this article I offer some perspectives on the work of Alain Badiou, a thinker whose sheer ambitiousness and speculative range have perhaps conspired against his achieving wider recognition amongst Anglophone, analytically trained philosophers. Badiou’s thinking is remarkable chiefly for taking so strong and principled a stand against just about every major direction of the present-dayphilosophic tide. He has affirmed the absolute priority of ontology over epistemology, truth over knowledge, knowledge over the means or mode of its linguistic representation, and the claim of mathematics as prima philosophia over those of various currently favoured rival candidates. This involves a far-reaching conception of set theory and its ontological bearings, one that – if valid – bids fairto redefine the very terms and conditions of rational enquiry across the whole range of the natural and social or human sciences. Badiou starts out from a rigorous distinction between being and event, or ontology and that which exceeds or disrupts the existing ontological order. Such episodes occur through the advent of some wholly unprecedented claim on the allegiance of subjects – whether scientists, artists, political activists, or ethical agents – who most clearly perceive its challenge and who resolve to pursue its implications to the utmost of their intellectual,creative or investigative powers. Thus Badiou sees the constant extension andrefinement of set-theoretical concepts from Cantor to the present as an objectlesson in the way that knowledge typically accrues through successive encounters with a limit on its present-best powers of rational comprehension. This sense of falling-short, or presumptive anomaly, in turn provides the impetus that ‘forces’ thought (through a formal operation that Badiou lays out in precisely specified set theoretical terms) to move beyond its current, restricted stage of development and achieve what was hitherto a strictly inconceivable advance. As well as describing these technical aspects of his work in philosophy of mathematics, logic and the formal sciences I explain – for the benefit of those trained up in the more compartmentalized mindset of analytic philosophy – how these aspects relate to Badiou’s thinking in the fields of ethics, politics, aesthetics, and psychoanalysis. Above all I stress his singular capacity to combine the most adventurous and widerangingforays into realms of speculative thought with the highest degree ofconceptual rigour and logical precision.
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