i admit it; i've had vagueness on the brain these last few weeks. to be honest, it's a pretty frustrating condition. Suddenly, everything seems vague - objects, verbs, adjectives, Kilimanjaro, heaps, baldness, redness. and there is, as yet, no theoretical or philosophical explanation. how do any of us ever know what we're talking about?
fuzzy logic seems promising - especially from a computational view - but it still supposes certain unfuzzy boundaries. if we assign a value of "1" to all atoms that are definently a part of Kilimanjaro, and a range of values between "1" and "0" to those that may or may not be, we still beg the question: how do we know where the boundary of "definently" vs. "potentially" part of Kilimanjaro is?
According to McGee & McLaughlin, who have funny names, supervaluation theory attempts to lay out a set of acceptable models "such that a sentence is determinately true if and only if it is true in each member of the collection." (I don't know what, exactly, a model is, either, but bear with me...) They cite Kit Fine (1975), who came up with constraints that a model has to meet to count as acceptable: these include classificatory and penumbral constraints. (i can't say i know exactly what these are, either.)
one thing i do know is that these constraints are dumb. "classificatory constraints are external: they require a correct classification of extralinguistic objects." how conveeeenient. for a model to evaluate whether "that object is red" is true, it has to first correctly identify whether the object is red. OUTSIDE of language.
and how is that accomplished? i'm glad you asked: "Roughly (the details are elusive), our usage of 'red' will... [consist] of things linguistically competent and visually acute speakers, observing the things under good viewing conditions, would classify as 'red'..." so... uh.... whether something is 'red' extralinguistically is based on how SPEAKERS would CLASSIFY an object. in language.
i'm starting to formulate my own theory, because i've been reading Convention with vagueness on the brain as well, but this post is too long already. stay tuned!