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Cited by 35Epistemology, Ethics, and MetaphysicsHistory and Theory of MathematicsLogic and Philosophy of Science

The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.

Open texture clarified

Open access
Vecht, Joost Jacob·2023·Inquiry
DOI 10.1080/0020174x.2020.1787222
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Abstract

‘Open texture’ is the property of concepts or terms that they are not fully defined with regard to unexpected questions. Even though it is a ubiquitous phenomenon, there is no consensus on which concepts are subject to open texture. I present three equivalent definitions of open texture, connecting the concept to the notions of analyticity and algebraicity. I show that the claim that a concept is open-textured is equivalent to the claim that the class of analytic sentences using it can be changed, which in turn is equivalent to the claim that its definition is not algebraic. While this equivalence is interesting on its own, with it I can show the extent of open texture: all concepts that are not algebraically defined mathematical concepts are open textured. Finally, I show that this has unfortunate consequences for attempts to provide a foundation of mathematics.

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Research works printed but not linked: 3

  1. Husserl, Edmund. 2003. Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts from 1887–1901, edited by Rudolf Bernet. Translated by Dallas Willard. Dordrecht: Springer Science+Business Media.
  2. Waismann Friedrich., 1945, Proceedings of the Aristotelian Society, Supplementary Volumes, 19, 100
  3. Waismann Friedrich., 1949, Analysis, 10, 25

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Metadata

Authors
Vecht, J. J.
Affiliations
University of Oslo (NO)
Corresponding author
Vecht, Joost Jacob
ORCID
Vecht, Joost Jacob
Venue
Inquiry
Publisher
Informa UK Limited
Published
2020-07-07
Volume
66
Issue
6
Pages
1120-1140
ISSN
  • 0020-174X (ISSN-L)
  • 1502-3923
DOI
10.1080/0020174x.2020.1787222
OpenAlex
W3042055038
Cited by
35
References
24
Citations by year
2026: 5 · 2025: 17 · 2024: 8 · 2023: 2 · 2022: 2
FWCI
5.52
Type
journal article
Language
en
Open access
Licence
Locations
  • Inquiry (publishedVersion, cc-by)
  • NORA - Norwegian Open Research Archives (submittedVersion, cc-by)
Topics
  • Social Sciences › Arts and Humanities › Philosophy › Epistemology, Ethics, and Metaphysics
  • Social Sciences › Arts and Humanities › History and Philosophy of Science › History and Theory of Mathematics
  • Social Sciences › Arts and Humanities › History and Philosophy of Science › Logic and Philosophy of Science
Keywords
open texture, analyticity, algebraicity, definitions, mathematical concepts, foundations of mathematics, philosophy of mathematics

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