SORITICAL SERIES AND FISHER SERIES

Abstract

A general issue in the study of vagueness concerns whether vagueness can be reduced to a form of ambiguity (Fine 1975, Pinkal 1995, Williamson 1994). In this talk I propose to discuss the link between the notions of vagueness and ambiguity in the perceptual domain. Wellknown examples of ambiguous stimuli are so-called bistable figures, such as Necker's cube or Jastrow's duckrabbit, namely physically stable configurations that can be perceived in two different ways. A striking aspect of the perception of bistable stimuli is that even when one's attention is sustained, spontaneous transitions still happen from one percept to the other (Hupé and Rubin 2003). On the other hand, a concept or category is characterized as vague if it has borderline cases, namely cases for which the concept fails to apply clearly or to be excluded clearly. Typically, in a series of color hues ranging from a clear red to a clear yellow, some stimuli would count as borderline cases of either category when it is no longer clear to which category they should be assigned. While vagueness and ambiguity have often been opposed in the semantic domain (much as underdetermination vs. overdetermination of meaning, in K. Fine's words), D. Raffman has suggested that within soritical series, borderline cases pattern typically as ambiguous stimuli (Raffman 1994). Moreover, as discussed by Raffman, soritical transitions from one category to the other typically give rise to hysteresis effects, namely to the longer persistence of one percept over the other, depending on which category one is coming from (Lindsey, Brown and Raffman 2005 in progress, cited in Raffman 2005). As it turns out, this effect is also observed in the perception of bistable figures (see Hock, Kelso and Schöner 1993). In this talk, I wish to examine some philosophical consequences of the idea put forward by Raffman that borderline cases within soritical series might pattern as ambiguous stimuli. If the analogy is correct, one important such consequence seems to me to be that there should be no fact of the matter, in the relevant instances, as to whether patches of color in the borderline area can be classified as red or not. Indeed, bistable figures are such that there is no fact of the matter as to whether they should be perceived one way or the other, given that physically they are invariant. Rather, variations in judgments are to be traced solely to perceptual instability on the side of perceiving subjects. To that extent, the analogy appears to run against epistemic accounts of vagueness, which postulate the existence of an unknowable sharp cut-off within soritical series. A second aspect I shall examine concerns the characterization of the uncertainty specific to vagueness. Standardly, for bistable figures it is said that one percept excludes the other. A duck-rabbit is perceived as a duck or as a rabbit, but not as something in between. Prima facie therefore, the analogy between bistability and vagueness may seem inadequate. However, bistable figures themselves can be arranged in transition series consisting of slight alterations between adjacent members in the series (Fisher 1967, Gregson 2004). An interesting aspect of such configurations is the fact that although one percept becomes less probable than the other as one moves along the series, both percepts can still be applied all along in principle for such stimuli, even for the end stimuli. One issue is whether the uncertainty which is often used to characterize vagueness can be explained in a similar way 9 on the basis of a competition between overlapping categories.