Vagueness and hysteresis: a case study in color categorization
This paper presents the first results of an experimental study concerning the semantic status of borderline cases of vague predicates. Our focus is on the particular case of color predicates (such as “yellow’’, “orange’’, “blue’’, “green”), and on the influence of context in the categorization of color shades at the border between two color categories. In an unpublished study, D. Raffman and colleagues found that subjects have no difficulty in categorizing the same color shade as “blue” or “green” depending on the direction of the transition between the two categories, suggesting a phenomenon of hysteresis or persistence of the initial category. Hysteresis is a particularly intriguing phenomenon for vagueness for two reasons: i) it seems to comport with the tolerance principle, which says that once applied, a category can be extended to cases that differ very little ii) it seems to suggest that borderline cases are cases of overlap, rather than underlap between semantic categories (see Raffman 2009, Egré 2011, Ripley 2012). In our first study, we probed for hysteresis in two different tasks: in the first, subjects had to perform a task of color matching, namely to decide of each shade in a series between yellow and orange (respectively blue and green) whether it was more similar to the most yellow or to the most orange kept on the display. In the second task, subjects had to decide which of the two color labels “yellow” or “orange” was the most suitable. Shades were presented in three different orders, random, ascending from yellow to orange, and descending. While we found no order effect in the perceptual matching task, we found an effect of negative hysteresis in the linguistic task in each color set, namely subjects switched category at a smaller position rather than at a later position depending on the order. In a second study, we used the same design but asked subjects to report agreement or disagreement with various sentential descriptions of the shade (viz. “the shade is yellow/not yellow/yellow and not yellow”). No order effect was found in that task. These findings raise two particular issues concerning the boundaries of vague semantic categories, which we discuss in turn: the first concerns the interpretation of negative, as opposed to positive hysteresis. Another concerns the sensitivity of order effects to the task.
This is a joint work with Vincent de Gardelle and David Ripley.
Rationality, intractability and the prospects of “as if” explanations
Proponents of a probabilistic (Bayesian) turn in the study of human cognition have used the intractability of (non-monotonic) logics to argue against the feasibility of logicist characterizations of human rationality. It is known, however, that probabilistic computations are generally intractable as well. Bayesians have argued that, in their own case, this is merely as pseudoproblem. Their argument is that humans do not really perform the probabilistic calculations prescribed by probability theory, but only act as if they do—much like the planets do not calculate their own orbits, and birds fly without any knowledge of the theory of aerodynamics.
The prospects of such an “as if” explanation dissolving the intractability problem depends inter alia on what is meant by “as if”. I analyze some of the most plausible meanings that are compatible with various statements in the literature, and argue that none of them circumvents the problem of intractability.
The analysis will show that, even though the constraints imposed by tractability may prove pivotal for determining adequate characterizations of human rationality, these constraints do not directly favor one type of formalism over another. Cognitive science would be better off realizing this and putting efforts into dealing with the problem of intractability head-on, rather than playing a shell game.
This is joint work with:
Cory Wright (University of California, Long Beach, USA),
Johan Kwisthout (Radboud University Nijmegen, The Netherlands),
Todd Wareham (Memorial University of Newfoundland, Canada).