Seeing-as and Mathematical Creativity

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

This chapter provides Ludwig Wittgenstein's remarks on seeing-as with another aspect of his investigations in the philosophy of mathematics. It considers two examples of mathematical creativity from the history of mathematics, one from geometry and one from arithmetic. The chapter also considers one of the most important sources—perhaps the most important source—of philosophical methodology in Plato's Meno. It looks at the emergence of non-Euclidean geometry. The 'discovery' of irrational numbers was a key stage in the development of the mathematical concept of a number, and lying at the core of this development was a move that essentially required a shift of conceptual aspect. The influence of Greek geometry on philosophy is first revealed in Plato's Meno, the dialogue in which Socrates cross-examines a slave boy in an attempt to get him to 'recollect' the answer to a geometrical problem.
Original languageEnglish
Title of host publicationAspect Perception after Wittgenstein
Subtitle of host publicationSeeing-As and Novelty
EditorsMichael Beaney, Brendan Harrison, Dominic Shaw
Place of PublicationNew York
PublisherRoutledge
Chapter6
Pages131–151
Number of pages21
ISBN (Electronic)9781315732855
DOIs
Publication statusPublished - 3 Jan 2018

Keywords

  • seeing-as
  • mathematical creativity
  • Wittgenstein
  • Meno's paradox
  • irrational numbers
  • non-Euclidean geometry
  • transfinite numbers
  • John Wallis
  • Georg Cantor

Fingerprint Dive into the research topics of 'Seeing-as and Mathematical Creativity'. Together they form a unique fingerprint.

  • Cite this

    Beaney, M. A., & Clark, R. (2018). Seeing-as and Mathematical Creativity. In M. Beaney, B. Harrison, & D. Shaw (Eds.), Aspect Perception after Wittgenstein: Seeing-As and Novelty (pp. 131–151). Routledge. https://doi.org/10.4324/9781315732855