Chad Hall
University of Connecticut
Ideal language philosophy’s solution to the problem of vagueness calls for the elimination of vague expressions. This is set forth by constructing a formal language that is precise and logically perfect (i.e., it is an ideal language). While this solution adequately handles first-order vagueness, it faces a new challenge from higher-order vagueness, that is, the vagueness associated with predicates such as borderline',clear’, and even `vague’. In this paper, I argue that higher-order vagueness can be deflated through a strategy of modal nesting, wherein apparent higher-order vagueness is analyzed as modal uncertainty layered over vague first-order predicates. The ideal language philosopher can run this sort of analysis in their ideal object language. However, this comes at a cost, for it requires the reintroduction of vague first-order predicates into the ideal object language. The result is a dilemma for ideal language philosophy: namely, either (i) reject vague predicates and fail to account for higher-order vagueness, or (ii) admit them and forfeit the ideal of complete precision. I conclude that vagueness cannot be eliminated, even from ideal languages that are designed to escape it.
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SOPhiA 2026 