Chapter

<i>Das Überraschende:</i> Wittgenstein on the Surprising in Mathematics

Juliet Floyd

in Wittgenstein and the Philosophy of Mind

Published in print September 2012 | ISBN: 9780199737666
Published online January 2013 | e-ISBN: 9780199933372 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199737666.003.0010
Das Überraschende: Wittgenstein on the Surprising in Mathematics

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This chapter explores the epistemic role that surprise and other psychological reactions play in mathematics. The chapter pursues the issue for its own sake, but also for its usefulness in illuminating certain themes in Wittgenstein's philosophy of mathematics. In order to understand Wittgenstein's views in this area, we must acknowledge the significance of his “obsession” with the “patter” [Geschwätz] surrounding mathematical activity, e.g., expressions concerning heuristics, evaluations, diagrams, and other intuitive aids for understanding mathematical results. Due largely to the influence of Frege and Russell, it is widely held that the intuitive and the psychological are obstacles to proper understanding in mathematics and logic. Wittgenstein's middle and later work rejects this brand of anti-psychologism, or at least develops a complicated relationship to it. And, as the chapter's suggestive and mostly sympathetic treatment shows, there is a wealth of somewhat neglected material in Wittgenstein's writing on these issues, of importance especially for the question of what is involved in understanding a mathematical proof.

Keywords: Wittgenstein; philosophy of mathematics; surprise; intuitive; anti-psychologism; understanding; proof

Chapter.  16751 words.  Illustrated.

Subjects: Philosophy of Mind

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