Title

Loss of vision: How mathematics turned blind while it learned to see more clearly

Document Type

Book Chapter

Publication Date

Spring 3-1-2010

Publication Source

Philosophy of Mathematics: Sociological Aspects and Mathematical Practice

Inclusive pages

87–106

Publisher

College Publications

Place of Publication

London

ISBN/ISSN

978-1904987956

Peer Reviewed

yes

Abstract

To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a decrease of visualizations in mathematical practice.

Keywords

Philosophy of mathematics, structuralism, folk ontology, folk semantics, abstraction, visualization

Disciplines

Epistemology | Logic and Foundations | Logic and Foundations of Mathematics | Metaphysics | Philosophy

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