Abstract
This article is a rejoinder to Hernández-Conde’s (Synthese 194(10):4011–4037, 2017) criticism of the convexity criterion in the theory of conceptual spaces. His arguments in general claim that the convexity criterion could be false and that it therefore is problematic for the theory. However, this is a misunderstanding since the convexity criterion is put forward as an empirically testable law for concepts. The long list of cases where the convexity criterion could be false that Hernández-Conde presents rather exhibits the rich empirical content of the criterion.
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References
Gärdenfors, P. (1990). Induction, conceptual spaces and AI. Philosophy of Science, 57, 78–95.
Gärdenfors, P. (2000). Conceptual spaces: The geometry of thought. Cambridge, MA: MIT Press.
Gärdenfors, P. (2014). The geometry of meaning: Semantics based on conceptual spaces. Cambridge, MA: MIT Press.
Hernández-Conde, J. V. (2017). A case against convexity in conceptual spaces. Synthese, 194(10), 4011–4037.
Jäger, G. (2010). Natural color categories are convex sets. Amsterdam Colloquium 2009, LNAI, 6042, 11–20.
Johannesson, M. (2002). Geometric models of similarity (Lund University Cognitive Studies 90). Lund: Lund University.
Acknowledgements
I thank the reviewers for valuable comments on an earlier version of the text. I also gratefully acknowledge support from the Swedish Research Council to the Linneaus environment Cognition, Communication and Learning.
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Gärdenfors, P. (2019). Convexity Is an Empirical Law in the Theory of Conceptual Spaces: Reply to Hernández-Conde. In: Kaipainen, M., Zenker, F., Hautamäki, A., Gärdenfors, P. (eds) Conceptual Spaces: Elaborations and Applications. Synthese Library, vol 405. Springer, Cham. https://doi.org/10.1007/978-3-030-12800-5_5
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DOI: https://doi.org/10.1007/978-3-030-12800-5_5
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