The Riemannian Background to Frege's Philosophy

There was a methodological revolution in the mathematics of the nineteenth century, and philosophers have, for the most part, failed to notice.2 My objective in this chapter is to convince you of this, and further to convince you of the following points. The philosophy of mathematics has been informed by an inaccurately narrow picture of the emergence of rigour and logical foundations in the nineteenth century. This blinkered vision encourages a picture of philosophical and logical foundations as essentially disengaged from ongoing mathematical practice. Frege is a telling example: we have misunderstood much of what Frege was trying to do, and missed the intended significance of much of what he wrote, because our received stories underestimate the complexity of nineteenth-century mathematics and mislocate Frege’s work within that context. Given Frege’s perceived status as a paradigmatic analytic philosopher, this mislocation translates into an unduly narrow vision of the relation between mathematics and philosophy. This chapter surveys one part of a larger project that takes Frege as a benchmark to fix some of the broader interest and philosophical significance of nineteenth-century developments. To keep this contribution to a manageable..
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Otávio Bueno (2012). Styles of Reasoning: A Pluralist View. Studies in History and Philosophy of Science Part A 43 (4):657-665.

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Øystein Linnebo (2008). The Nature of Mathematical Objects. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America 205--219.
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