The Law of the Subject: Alain Badiou, Luitzen Brouwer, and the Kripkean analyses of

Por • 13 ene, 2020 • Sección: Leyes

Olivia Lucca Fraser

Abstract : One of the central tasks of Badiou’s; Being and Event; is to elaborate a theory of the subject in the wake of an axiomatic identification of ontology with mathematics; or; to be precise; with classical Zermelo-Fraenkel set theory. The subject; for Badiou; is essentially a free Project that originates in an event; and subtracts itself from both being qua being; as well as the linguisticand epistemic apparatuses that govern the situation. The subjective project is; itself; conceivedas the temporal unfolding of a ‘truth’. Originating in an event and unfolding in time; the subject cannot; for Badiou; be adequately understood in strictly ontological; i.e. set-theoretical; terms; insofar as neither the event nor time have any place in classical set theory. Badiou neverthelessseeks to articulate the ontological infrastructure of the subject within set theory; and for this hefastens onto Cohen’s concepts of genericity and forcing: the former gives us the set-theoretic structure of the truth to which the subject aspires; the latter gives us the immanent logic of the subjective procedure; the ‘law of the subject’. Through the forcing operation; the subject is capable of deriving veridical statements from the local status of the truth that it pursues. Between these set-theoretic structures; and a doctrine of the event and temporality; Badiou envisions the subject as an irreducibly diachronic unfolding of a truth subtracted from language; a subject which expresses a logic quite distinct from that which governs the axiomatic deployment of his classical ontology. This vision of the subject is not unique to Badiou’s work. We find a strikingly similar conception in the thought of L.E.J. Brouwer; the founder of intuitionist mathematics.Brouwer; too; insists on the necessary subtraction of truth from language; and on its irreduc-ibly temporal genesis. This genesis; in turn; is entirely concentrated in the autonomous activityof the subject. Moreover; this activity; through which the field of intuitionistic mathematics is generated; expresses a logical structure that; in 1963; Saul Kripke showed to be isomorphic withthe forcing relation. In the following essay; I take up an enquiry into the structure of these two theories of the subject; and seek to elucidate both their points of divergence and their strangecongruencies; the former; we will see; primarily concern the position of the subject; while the latter concern its form. The paper ends with an examination of the consequences that this study implies for Badiou’s resolutely classical approach to ontology; and his identification of ontologyas a truth procedure.

Keywords : Badiou; Brouwer; Intuitionism; Forcing; Genericity; Subjec

 https://www.academia.edu/199620/The_Law_of_the_Subject_Alain_Badiou_Luitzen_Brouwer_and_the_Kripkean_analyses_of_Forcing_and_the_Heyting_Calculus

 

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