Loss of vision: How mathematics turned blind while it learned to see more clearly
Philosophy of Mathematics: Sociological Aspects and Mathematical Practice
Place of Publication
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.
Philosophy of mathematics, structuralism, folk ontology, folk semantics, abstraction, visualization
Epistemology | Logic and Foundations | Logic and Foundations of Mathematics | Metaphysics | Philosophy
Bernd Buldt and Dirk Schlimm (2010).
Loss of vision: How mathematics turned blind while it learned to see more clearly. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. 87–106. London: College Publications.
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