Implicit comparatives and the Sorites

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an IQ of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided.
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DOI 10.1080/01445340500232401
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PhilPapers Archive John-Michael Kuczynski, Implicit comparatives and the Sorites
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Roy A. Sorensen (1988). Blindspots. Oxford University Press.
Timothy Williamson (2010). Vagueness and Ignorance. In Darragh Byrne & Max Kölbel (eds.), Aristotelian Society Supplementary Volume. Routledge 145 - 177.

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