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The Mathematical in Heidegger and Badiou Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2008 The am thematical in Heidegger and Badiou Dylan Armstrong Wade Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Arts and Humanities Commons Recommended Citation Wade, Dylan Armstrong, "The am thematical in Heidegger and Badiou" (2008). LSU Master's Theses. 4201. https://digitalcommons.lsu.edu/gradschool_theses/4201 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. THE MATHEMATICAL IN HEIDEGGER AND BADIOU A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Arts in The Department of Philosophy and Religious Studies by Dylan Armstrong Wade B.A. Tulane University, 2006 August 2008 TABLE OF CONTENTS ABSTRACT ............................................................................................................................. iii CHAPTER 1: FACTICITY AND INTERPRETATION ..............................................................1 1.1 Introduction .......................................................................................................................1 1.2 The Facticity of a Thing .....................................................................................................1 1.3 The Interpretive Structure of Dasein ..................................................................................4 1.4. Language and the Formalization of Facticity ................................................................... 11 CHAPTER 2: THE MATHEMATICAL IN MARTIN HEIDEGGER ....................................... 15 2.1 Introduction ..................................................................................................................... 15 2.2 Mathematical as Pre-theoretical Understanding ................................................................ 16 2.3 Nature in Aristotle and Newton ........................................................................................ 19 2.4 The History of Transcendental Reasoning ........................................................................ 23 2.5 Ontology as Standing-Reserve ......................................................................................... 28 CHAPTER 3: THE MATHEMATICAL IN ALAIN BADIOU.................................................. 31 3.1 Introduction ..................................................................................................................... 31 3.2 Mathematics as Ontolgy................................................................................................... 32 3.3 Truth and Subject ............................................................................................................. 38 3.4 Conclusion ....................................................................................................................... 45 REFERENCES ......................................................................................................................... 48 VITA ........................................................................................................................................ 49 ii ABSTRACT In this thesis I am tracing the historical development of subjectivity from its skeptical foundation in Descartes to Alain Badiou’s subject as fidelity to truth. Drawing from Martin Heidegger’s What is a Thing? , this history begins with the turn from an Aristotelian to a Newtonian apprehension of motion, turning towards an a priori mathematical projection of spatial uniformity, such that there are no longer different places – only quantifiable distance. It is on the basis of this turning away from tradition, or ordinary experience of different phenomena, that Descartes posits the self-certain I-pole. Heidegger criticizes modernity, defined as the merging of the metaphysical and the mathematical, for apprehending the relationship between man and world in only one way, as things. I hope show that this development does not derive from the mathematical alone, but from the project of objects against an objective background secured in an I-pole, further advanced by Kant’s transcendental reflection of the thing-in-itself over this project. I do this by following Alain Badiou’s assessment of Zermelo-Fraenkel’s axiomatic set theory, a particular mathematical model that self-destructs, meaning it cannot become absolute or dogmatic. With this thesis I hope to contribute to the scholarship of facticity, the existential thinking that begins with doubt. If we can dissociate in our ordinary language claims that utilize transcendental reasoning from claims concerning mathematical projection based on speculation alone, perhaps we might find some basis to make existential claims independent of perspective, or subjectivism. iii CHAPTER 1: FACTICITY AND INTERPRETATION 1.1 Introduction In What is a Thing? Martin Heidegger criticizes the heirs of Kant’s legacy, neo-Kantians or positivists, for failing to understand Kant’s original ontological inquiry. While positivists maintained a scientific attitude by holding that the only meaningful assertions were those that could be falsified by experience, Heidegger criticizes this particular school of materialism for a dogmatism of its own, in seeing the relationship between man and world as only describable in terms of discreet units or particular things, that is, mathematically. In order to disclose the historical situation in which thing-ness has come to be apprehended in terms of quantifiable things, I will follow Heidegger’s history of subjectivity as a reaction to the speculation of mathematics, secured in the presentation of the I-pole for Descartes, and formalized in the consistent representation of phenomena as spatial for Kant. By dismissing the thing-in-itself as an object of knowledge, the thing-in-itself becomes the determinate apprehension of thing-ness as a limit for speculation. Yet the question of thing-ness can again be raised by returning to the speculative foundation, pure reason, which Kant critiques. In the second half of this thesis, I hope to demonstrate that the speculation of modernity motivates Alain Badiou’s claim that the one-is-not, promoting a form of non-dogmatic mathematics that may turn our understanding of existential claims away from subjectivism, by returning to the factical situation of pure reason, or doubt. 1.2 The Facticity of a Thing By disclosing the historical situation upon which the linguistic assumptions of our ordinary language are made possible (specifically the subject/object relation), Heidegger thereby underscores the degree to which our everyday approach to things has been historically 1 determined and thus grounded on nothing besides its own history. The question that Heidegger raises to begin paragraph 58 of Being and Time is how Dasein can be called to be itself, defined as care, care for both things and others. In other words, how can we come to recognize that we are involved in a world, not as some merely present object, determined either by external forces or human nature? Moreover, how can we come to recognize this situation, our facticity, without being informed of it – subjecting that information to a general knowledge of objective facts? Heidegger answers that we must begin with the general knowledge, our ordinary way of talking about ourselves as subjects to objects, given in our relationships with the world and others. Take any object given as present, some X. Generally, we would speak of this X as pertaining to a certain category or kind. We would say that X is of a certain kind, distinct from some other kind Y. By categorizing these distinct kinds, we suppose a universal schema for their ordering, thus grounding these present objects in a transcendent structure or logos –a logos of objectivity for the positivists or neo-Kantians. Heidegger opposes to category the notion of the existential. In category, the question of being has been distorted, such that being has been thought of as a universal and a-temporal order. This inauthentic distortion prevents any experience of beings except through that supposed universal ordering. By means of a regressive logic,1 Heidegger opens the relational structure between different kinds of beings, positing existential kinds, that is, different kinds of relations. Existentials relate the whole of being, the facticity of the Dasein,2 while categories may certainly be appropriate for the particular relationship to objects present-at-hand. Heidegger defines Dasein as a thrown project, existing temporally with no before or after, groundless aside from its own history and direction. 1 One example takes place in the third chapter of Martin Heidegger’s Being and Time where the present-at-hand, or useless objects, derives from the breakdown of circumspective concern, or the practical relationship between man and world. 2 Literally translated as being-there, or what we might call the relationship between man and world. 2 In What is a Thing? Heidegger contrasts the two modes (existential and categorical) in terms of the philosopher and the nursemaid. It has been said that one day while
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