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 accessAbstract
‘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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From There is no such thing as conscious artificial intelligence (2025) · cites this paper as Vecht, 2023
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The Ethics of Conceptualization
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There is no such thing as conscious artificial intelligence
Porębski, A., & Figura, J. (2025) · Humanities and Social Sciences Communications · doi:10.1057/s41599-025-05868-8 · Cited by 20
Mathematical Rigour and Informal Proof
Tanswell, F. S. (2024) · Cambridge University Press eBooks · doi:10.1017/9781009325110 · Cited by 19
Open texture, rigor, and proof
Zayton, B. (2022) · Synthese · doi:10.1007/s11229-022-03842-4 · Cited by 17
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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
- 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
- hybrid
- doi.org
- 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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