The Place of Mathematics in Badiou’s Ontology: A First Look

Being and Event

(Note: I have changed my view on this topic considerably. Please scroll down or click this link to see a video of a talk I gave on this topic which ends on a more skeptical note.)

It is well-known that Badiou proposes a new connection between mathematics and ontology. In the first place, this is a move internal to the field of philosophy, as his work does not aim to actively contribute theorems and proofs to mathematics proper. Rather, the aim is to show how certain classical ontological/philosophical questions can be approached by examining abstract (but foundational) mathematical theories. This examination remains distinctly philosophical; insights are lifted from the strictly mathematical language and interpreted ontologically. How is this move justified? Perhaps most importantly: How is the relation between mathematics and philosophy understood here? In this short text, I aim to explain how this new assembly of mathematics and ontology is motivated, how it works and why it contributes something to the philosophical field.
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What is Possible with Heidegger? Remarks on the Relation Between Modality and Time in Sein und Zeit

Ekstatikon

The ekstatikon, from my notes to Sein und Zeit

Heidegger’s Sein und Zeit is famous for pushing the question of being (“der Sinn des Seins überhaupt”) to the forefront of philosophical inquiry – and for offering as a preliminary horizon for answering this question an investigation into the threefold structure of time (past, present, future). For Heidegger, every explicit or implicit interpretation of being (Seinsverständnis) held by a human being (Dasein) can and must be explained on the basis of a deeper systematic account of the temporal structure of being. To render the thesis of being as time plausible, Heidegger spends most of the book reinterpreting a host of typical, but also atypical, subjects of ontological inquiry, like things, signs, world, space, sociality, normativity, emotion, understanding, language, truth, silence, fear, conscience, and death. This paper asks what role logical modality (possibility, actuality, necessity) plays in his account of temporality (Zeitlichkeit), and argues that the link between the two provides an important insight in the systematic nature of his philosophical operation.

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