graded membership and fuzzy truth

The interpretation of Armstrong, Gleitman, and Gleitman’s (1983) results regarding well-defined concepts such as ‘odd number’ illustrates the debate over typicality effects well. Their participants make conscious verbal report of whether a concept has a clear definition, and show the typical kinds of typicality effects that arise (gradient ratings, reaction times) even for well-defined concepts. Based on these results, the authors argue for graded typicality as a peripheral property rather than a constitutive aspect of a concept, whereas other researchers have argued these results show precisely the pervasiveness of gradient conceptual structure. Gleitman, Connolly, and Armstrong (2012) still argue that it is laughable to deny the clear-cut nature of arithmetic concepts.

Why should one, however, give privileged status to the participants’ conscious verbal report and the authors’ intuition regarding the ‘classical’ status of these concepts, while dismissing the typicality effects as merely incidental properties? After all, the problem goes back to how one defines a concept, but to those psychologists who don’t assume an absolute status of definitions external to our gradient mental representations, Armstrong and colleagues’ study reveals an assumption, rather than a demonstration, of classical concepts.

Osherson and Smith (1981; also Smith & Osherson, 1984) considered the feasibility of Zadeh’s (1965) fuzzy set theory and suggested that its limitations might generalize to all versions of prototype theory. After a brief mention of alternative versions of fuzzy logic and subsequent developments in the field, Osherson and Smith simply concluded that fuzzy logic is implausible because fuzzy truth is against our strong intuitions of truth. Again, this is no argument, but only an assumption. After all, I don’t think many people find quantum physics any more intuitive than Newtonian physics, but paradigm shifts occur regardless of our intuitions (and sometimes even reshape our intuitions – e.g., Copernican heliocentrism).

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