Abstract
Vagueness is often regarded as a kind of defect of our language or of our thinking. This paper portrays vagueness as the natural outcome of applying a number of rationality principles to the cognitive domain. Given our physical and cognitive makeup, and given the way the world is, applying those principles to conceptualization predicts not only the concepts that are actually in use, but also their vagueness, and how and when their vagueness manifests itself (insofar as the concepts are vague).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Different people will in general give somewhat different similarity judgments. For that reason, one might want to construct a similarity space for each person individually. However, that is often impractical, and non-individualized spaces—spaces typically constructed on the basis of similarity judgments coming from different people, and not pretending to represent anyone’s personal similarity space—tend to work well enough for many purposes; see Douven (2016).
- 2.
- 3.
Note that, to date, it is still largely unknown how broadly applicable the conceptual spaces framework really is. It has been successfully used to model perceptual concepts and to some extent also more abstract concepts (e.g., Gärdenfors and Zenker 2013). Whatever the framework’s limitations may be, it is clear that the current proposal, by relying so heavily on this framework, will face the same limitations.
- 4.
This result holds for Euclidean spaces, such as color space and many other similarity spaces, but not for all spaces. Again, these details are left aside here.
- 5.
To forestall misunderstanding, it is to be noted that RGB space and other color spaces frequently used in applications software are not similarity spaces; they are not intended to represent human similarity judgments concerning color, and they are also as a matter of fact known not to represent such judgments.
- 6.
Douven and Gärdenfors’ approach is somewhat akin to Anderson’s (1990, Chap. 3) rational analysis of categorization, which tries to understand categorization as the outcome of a procedure aimed at maximizing predictive success and in particular also invokes optimality considerations to identify what Anderson calls “basic level categories.” Apart from the fact that Anderson is not concerned with conceptual spaces, another important difference is that he takes the world to be carved up independently of any human mental activity. That objective structure is to be discovered by us, and that is where—on his account—optimality comes into play. In contrast, Douven and Gärdenfors are concerned with showing what the natural concepts are, not—in first instance—how we latch onto those concepts. It is in answering the first question that they appeal to optimality considerations. (Thanks to Daniel Lassiter for pressing me on this).
- 7.
Marzen and DeDeo (2017) formally show how cost considerations in organisms motivate parsimonious representational systems, even though this tends to come at the cost of greater inaccuracy.
- 8.
Or google images of CIELUV space, which is another, slightly different, perceptual color space; see Malacara (2002, pp. 86–90) for details and for a discussion of how CIELAB and CIELUV spaces differ.
- 9.
To be entirely precise, Douven et al. (2017) give a number of different estimates of the prototypical blue region in CIELUV space, but what is said above holds given any of those estimates.
- 10.
Douven et al. (2017) present the empirically determined locations of the blue and green prototypical regions in CIELUV space; the locations in that space of other prototypical regions are still unknown.
- 11.
I am greatly indebted to Richard Dietz, Daniel Lassiter, Christopher von Bülow, and an anonymous referee for very valuable comments on previous versions of this paper. I am also grateful to an audience at the Ruhr University Bochum for stimulating questions and remarks.
References
Anderson, J. R. (1990). The adaptive character of thought. New York: Psychology Press.
Berlin, B., & Kay, P. (1969). Basic color terms. Stanford, CA: CSLI Publications.
Borg, I., & Groenen, P. (2010). Modern multidimensional scaling (2nd ed.). New York: Springer.
Cook, R. S., Kay, P., & Regier, T. (2005). The world color survey database: istory and use. In H. Cohen & C. Lefebvre (Eds.), Handbook of categorization in cognitive science (pp. 223–242). Amsterdam: Elsevier.
Decock, L., & Douven, I. (2014). What is graded membership? Noûs, 48, 653–682.
Douven, I. (2016). Vagueness, graded membership, and conceptual spaces. Cognition, 151, 80–95.
Douven, I. (2017). Clustering colors. Cognitive Systems Research, 45, 70–81.
Douven, I., & Decock, L. (2017). What verities may be. Mind, 126, 385–428.
Douven, I., & Gärdenfors, P. (2018). What are natural concepts? A design perspective. Mind & Language (in press).
Douven, I., Decock, L., Dietz, R., & Égré, P. (2013). Vagueness: A conceptual spaces approach. Journal of Philosophical Logic, 42, 137–160.
Douven, I., Wenmackers, S., Jraissati, Y., & Decock, L. (2017). Measuring graded membership: The case of color. Cognitive Science, 41, 686–722.
Gärdenfors, P. (2000). Conceptual spaces: The geometry of thought. Cambridge MA: MIT Press.
Gärdenfors, P., & Zenker, F. (2013). Theory change as dimensional change: Conceptual spaces applied to the dynamics of empirical theories. Synthese, 190, 1039–1058.
Jäger, G. (2007). The evolution of convex categories. Linguistics and Philosophy, 30, 551–564.
Jraissati, Y., & Douven, I. (2017). Does optimal partitioning of color space account for universal color categorization? PLoS One, 12(6), e0178083. https://doi.org/10.1371/journal.pone.0178083.
Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data. Hoboken, NJ: Wiley.
Kemp, C., & Regier, T. (2012). Kinship categories across languages reflect general communicative principles. Science, 336, 1049–1054.
Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445–463.
Lewis, D. K. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.
Malacara, D. (2002). Color vision and colorimetry: Theory and applications. Bellingham, WA: SPIE Press.
Marzen, S. E., & DeDeo, S. (2017). The Evolution of Lossy Compression. Journal of the Royal Society, Interface, 14, 20170166. https://doi.org/10.1098/rsif.2017.0166.
Okabe, A., Boots, B., Sugihara, K., & Chiu, S. N. (2000). Spatial tessellations (2nd ed.). New York: Wiley.
Regier, T., Kay, P., & Khetarpal, N. (2007). Color naming reflects optimal partitions of color space. Proceedings of the National Academy of Sciences USA, 104, 1436–1441.
Rosch, E. (1973). Natural categories. Cognitive Psychology, 4, 328–350.
Rosch, E. (1975). Cognitive reference points. Cognitive Psychology, 7, 532–547.
Valentine, T., Lewis, M. B., & Hills, P. J. (2016). Face-space: A unifying concept in face recognition research. Quarterly Journal of Experimental Psychology, 69, 1996–2019.
van Rooij, R., & Jäger, G. (2007). Language structure: Psychological and social constraints. Synthese, 159, 99–130.
Verheyen, S., & Égré, P. (2018). Typicality and graded membership in dimensional adjectives. Cognitive Science (in press).
Xu, Y., & Regier, T. (2014). Numeral systems across languages support efficient communication: From approximate numerosity to recursion. In P. Bello, M. Guarini, M. McShane, & B. Scassellati (Eds.), Proceedings of the 36th Annual Meeting of the Cognitive Science Society. Austin, TX: Cognitive Science Society.
Xu, J., Dowman, M., & Griffiths, T. (2013). Cultural transmission results in convergence towards colour term universals. Proceedings of the Royal Society B, 280, 20123073.
Xu, Y., Regier, T., & Malt, B. C. (2016). Historical semantic chaining and efficient communication: The case of container names. Cognitive Science, 40, 2081–2094.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Douven, I. (2019). The Rationality of Vagueness. In: Dietz, R. (eds) Vagueness and Rationality in Language Use and Cognition. Language, Cognition, and Mind, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-15931-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-15931-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15930-6
Online ISBN: 978-3-030-15931-3
eBook Packages: Social SciencesSocial Sciences (R0)