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date: 20 February 2020

Abstract and Keywords

This chapter explores some of the varieties of rigorous experience encountered in modern mathematical philosophy. It addresses the question ‘How rigorous?’ not along a single scale (‘How rigorous?’), but in terms of a complex, multi-faceted quality (‘How rigorous?’). It proposes a widened frame for the history of early analytic philosophy, following a trend in recent work on the history and philosophy of logic and mathematics that questions the oft-repeated assumption that early analytic philosophy began in 1879, with Friedrich Ludwig Gottlob Frege’s Begriffsschrift, and ended more or less in 1931, with Kurt Gödel’s incompleteness theorems. It uses Wilfried Sieg’s idea of the centuria mirabilis to generate a more purely philosophical interpretation of the period. It also discusses the link between rigour and residue, modernism, G. E. Moore’s arguments about rigour, Immanuel Kant’s claim that the power of reflective judgement is a fundamental cognitive capacity, and the views of Richard Dedekind and Alan Turing.

Keywords: rigorous experience, rigour, mathematical philosophy, analytic philosophy, Friedrich Ludwig Gottlob Frege, Wilfried Sieg, residue, modernism, G. E. Moore, Immanuel Kant, Alan Turing

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