Implicit comparatives and the Sorites
History and Philosophy of Logic 27 (1):1-8 (2006)
| 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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Similar books and articlesC. L. Hardin (1988). Phenomenal Colors and Sorites. Noûs 22 (June):213-34.
Rosanna Keefe (2011). Phenomenal Sorites Paradoxes and Looking the Same. Dialectica 65 (3):327-344.
Wai-hung Wong (2008). What Williamson's Anti-Luminosity Argument Really Is. Pacific Philosophical Quarterly 89 (4):536-543.
Mark Colyvan (2010). A Topological Sorites. Journal of Philosophy 107 (6):311-325.
Ofra Magidor (2012). Strict Finitism and the Happy Sorites. Journal of Philosophical Logic 41 (2):471-491.
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