Abstract
This paper proposes an experimental investigation of the use of vague predicates in dynamic sorites. We present the results of two studies in which subjects had to categorize colored squares at the borderline between two color categories (Green vs. Blue, Yellow vs. Orange). Our main aim was to probe for hysteresis in the ordered transitions between the respective colors, namely for the longer persistence of the initial category. Our main finding is a reverse phenomenon of enhanced contrast (i.e. negative hysteresis), present in two different tasks, a comparative task involving two color names, and a yes/no task involving a single color name, but not found in a corresponding color matching task. We propose an optimality-theoretic explanation of this effect in terms of the strict-tolerant framework of Cobreros et al. (J Philos Log 1–39, 2012), in which borderline cases are characterized in a dual manner in terms of overlap between tolerant extensions, and underlap between strict extensions.
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Notes
The expression ‘dynamic sorites’ is used to make a distinction with the ‘regular sorites argument’, viz. (Smith 2008), namely the abstract argument whereby a contradiction is drawn from the assumption that a soritical series is given, with the first individual being clearly \(P\), the last being clearly not \(P\), and one grants the tolerance principle that \(x_{n+1}\) is \(P\) in the series whenever \(x_{n}\) is \(P\).
We are indebted to Diana Raffman and to the referee of a previous paper for bringing Kalmus’ paper to our notice (see Egré 2011).
See Raffman (2005) and the description given by (Smith (2008), 118) of the response a contextualist might make to the finding of hysteresis:
“Suppose we are walked along our Sorites series for F, and asked of each object in the series whether it is F, and then walked back the other way, and asked the same question of each object again. It is very likely that the point at which we stopped saying ‘Yes’ on the way out would be further along the series than the point at which we started saying ‘Yes’ on the way back. This behavior might seem rather difficult to explain on the recursive truth gap view, but it is easily explained by the contextualist: as we classify an object as F, we thereby make it true that that object and all others very similar to it—including the next object in the series—are F. We thus push the boundary between the F’s and the borderline cases out before us as we go—and on the way back, we push the boundary back the other way”.
In a first pilot study, all participants were put in a dark environment over a black background: however, participants reported more visual fatigue, and this had the undesirable effect of creating too much contrast between the color and its background.
(Kamp 1981, 241) made a thought experiment in which he envisaged two situations of forced march from a clear green to a clear yellow: one in which all stimuli, including the ends of the color set, are always in view, and one in which color shades are only shown one by one. He predicted (with caution, see his fn. 7) that in the second situation, subjects might “carry on answering “green” for a longer time” than in the first. We do not have here a proper counterpart of his first scenario to really check the prediction. In the light of our data, this would imply that the enhanced contrast should be even more pronounced in the first setting than in the second, but this is not what Kamp intended. Rather, Kamp predicted that the lack of anchor points in the second case should favor hysteretical behavior past the middling shade. Judging from our findings, we see that the effect of anchoring points may indeed be to secure a critical boundary, as Kamp imagines for his first experiment, but their absence would have the counterhysteretical effect of subjects restricting the extension of the category they come from.
An alternative way of articulating informativeness would be to assume that informativeness requires accuracy; this would change some value assignments in the table, but make the same prediction of an enhanced constrast in the present setting.
For an atomic sentence relative to a three-valued logic, the negation of a sentence is strictly assertible iff the so-called ‘strong’ or Gödel negation (mapping False to True and the other values to False) is True; and the negation of a sentence is tolerantly assertible iff the corresponding ‘weak’ or ‘exclusion’ negation (mapping True to False and the other values to False) is True; for more complex sentences, however, the negations behave differently: the strict negation is in fact negation under a strong Kleene notion of designated value for assertion, and the tolerant negation negation under an LP notion: both negations are involutive (\(\lnot \lnot A\) and \(A\) are equivalent), unlike the Gödel and exclusion negations. We refer the reader to Alxatib and Pelletier (2011) for more details about Gödel and exclusion negation, and to Cobreros et al. (2012) and Cobreros et al. (2014) concerning negation in the strict-tolerant framework.
For a more detailed discussion of contrast versus assimilation in categorization (see Hampton et al. 2005).
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Acknowledgments
This work would not have been possible without institutional support, nor without the help and input of many people. First and foremost, we gratefully acknowledge the Agence Nationale de la Recherche, grant ANR-07-JCJC-0070, program “Cognitive Origins of Vagueness”, for funding. We thank Isabelle Brunet, Julien Boyer, Mélanie Brun, Claire Mégnin for their technical assistance, and the LSCP in Paris, where the experiments took place. Warm thanks go to Jean-Michel Hupé, Daniel Pressnitzer, Jean-Luc Schwartz for inspiring discussions and technical advice, as well as to participants in the ANR project MULTISTAP, where different stages of this paper were presented during meetings held in Grenoble, Lyon and Paris. Special thanks go to Diana Raffman for her pioneering work and input on this topic, and for numerous crucial exchanges over the years, as well as to Alan Hájek, Jakub Szymanik, and two anonymous reviewers of the journal for detailed comments and helpful criticisms. We also thank audiences at LSCP, at the Jean-Nicod Institute in Paris, and at ESSLLI 2012 in Opole, where this paper was presented. Further thanks go to various colleagues for related work, conversations and encouragements since 2008, in particular to Pablo Cobreros, Emmanuel Chemla, Igor Douven, James Hampton, Sid Kouider, Robert van Rooij and Jérôme Sackur. We also thank the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013) and the project ‘Borderlineness and Tolerance’ (FFI2010-16984), Ministerio de Economía y Competitividad, Government of Spain. Authorship is equally shared between the three authors of this work.
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Egré, P., de Gardelle, V. & Ripley, D. Vagueness and Order Effects in Color Categorization. J of Log Lang and Inf 22, 391–420 (2013). https://doi.org/10.1007/s10849-013-9183-7
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DOI: https://doi.org/10.1007/s10849-013-9183-7