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Aspects of Mathematical Experience

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Philosophy of Mathematics Today

Part of the book series: Episteme ((EPIS,volume 22))

Abstract

In the current discussion on philosophy of mathematics some do as if systematic foundational work supported an exclusive alternative between Platonism and Constructivism; others do as if such mathematical and logical research were deeply misguided and had no bearing on our understanding of mathematics. Both attitudes prevent us from grasping insights that underlie such work and from appreciating significant results that have been obtained. In consequence, they keep us from turning attention to the task of understanding the role of accessible domains for foundational theories and that of abstract structures for mathematical practice.

My considerations are based on two papers of mine: the first, “Relative Consistency and Accessible Domains”, was published in Synthese 84, 1990, pp. 259–297; the second, “Mechanical Procedures and Mathematical Experience”, appeared in Mathematics and Mind, edited by A. George, Oxford University Press, 1994, pp. 71–117. Here, I focus squarely on broader strategic points and rely for details concerning the relevant (meta-)mathematical results, historical connections, and conceptual analyses on those earlier papers.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Wilfried Sieg

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  1. Wilfried Sieg
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Editor information

Editors and Affiliations

  1. University of Fribourg, Switzerland

    Evandro Agazzi (President of the Swiss Society of Logic and Philosophy of Science) (President of the Swiss Society of Logic and Philosophy of Science)

  2. University of Genova, Italy

    Evandro Agazzi (President of the Swiss Society of Logic and Philosophy of Science) (President of the Swiss Society of Logic and Philosophy of Science)

  3. Symmetrion — The Institute for Advanced Symmetry Studies, Budapest, Hungary

    György Darvas

  4. The Hungarian Academy of Sciences, Budapest, Hungary

    György Darvas

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© 1997 Springer Science+Business Media Dordrecht

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Sieg, W. (1997). Aspects of Mathematical Experience. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_11

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  • DOI: https://doi.org/10.1007/978-94-011-5690-5_11

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