David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 27 (1):1-8 (2006)
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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References found in this work BETA
Timothy Williamson (1994). Vagueness. Routledge.
Michael A. E. Dummett (1978). Truth and Other Enigmas. Harvard University Press.
Roy A. Sorensen (1988). Blindspots. Oxford University Press.
Kit Fine (1975). Vagueness, Truth and Logic. Synthese 30 (3-4):265-300.
Timothy Williamson (2010). Vagueness and Ignorance. In Darragh Byrne & Max Kölbel (eds.), Aristotelian Society Supplementary Volume. Routledge 145 - 177.
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