From Godel to Derrida: Undecidability, indeterminacy, and infinity

David King

The purpose of this thesis is to argue for a textualist view of reality. By 'textualist view of reality’ is meant a standpoint whereby any subject position can be seen to be only provisional, not absolute. It is established early in the thesis that only an approach that draws on both the analytic and the continental schools of philosophy is adequate for such a project; roughly speaking, the continental school supplies the necessary critique of foundational approaches, while the analytic school situates the argument in an overtly rigorous context. The necessity for a textualist view of reality is in part evidenced by the perception that analytic philosophy has no means whereby mathematical truth can be reconciled with truth in general. The thesis starts with an examination of number and the infinite (consideration of which is shown to be essential to a textualist view of reality) from an historical perspective, and then examines Cantor's theory of infinite sets. The four main philosophies of mathematics arising from the foundational problems associated with Cantor's ideas are then considered. It is maintained that Godel's Kantian platonism provides a means of reconciling mathematical truth with truth in general, and that Derrida's critique of Kant enables this platonism to be framed in more sophisticated. textualist terms. AS, however, a Kantian/Derridean model has implications for physics - in particular with regard to the physical infinite the thesis devotes two chapters to these implications. The final chapter shows how the thesis' textualist view of reality in many ways is most naturally expressed as a Cantorian "diagonal argument".

From Godel to Derrida: Undecidability, indeterminacy, and infinity

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