Implicit comparatives and the Sorites

Abstract
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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References found in this work BETA
Vagueness.Timothy Williamson - 1994 - Routledge.
Truth and Other Enigmas.Michael A. E. Dummett - 1978 - Harvard University Press.
Blindspots.Roy A. Sorensen - 1988 - Oxford University Press.
Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.
Vagueness and Ignorance.Timothy Williamson - 2010 - In Darragh Byrne & Max Kölbel (eds.), Aristotelian Society Supplementary Volume. Routledge. pp. 145 - 177.

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