Abstract
This chapter provides Ludwig Wittgenstein's remarks on seeingas 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 nonEuclidean 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 crossexamines a slave boy in an attempt to get him to 'recollect' the answer to a geometrical problem.
Original language  English 

Title of host publication  Aspect Perception after Wittgenstein 
Subtitle of host publication  SeeingAs and Novelty 
Editors  Michael Beaney, Brendan Harrison, Dominic Shaw 
Place of Publication  New York 
Publisher  Routledge 
Chapter  6 
Pages  131–151 
Number of pages  21 
ISBN (Electronic)  9781315732855 
DOIs  
Publication status  Published  3 Jan 2018 
Keywords
 seeingas
 mathematical creativity
 Wittgenstein
 Meno's paradox
 irrational numbers
 nonEuclidean geometry
 transfinite numbers
 John Wallis
 Georg Cantor
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Michael Beaney
 School of Divinity, History & Philosophy, Philosophy  Regius Chair of Logic
Person: Academic