A paraconsistent-preservationist approach to a common confusion concerning predicate extensions

Martin Allen

Abstract

The existence of multiple criteria for the introduction of a predicate may lead to confusion when the criteria diverge as to whether or not some object falls under the predicate. It can be difficult to represent the semantics of sentences featuring such a predicate-term, and it is not obvious how a person is supposed to employ such confused terms in the business of language and reasoning. I consider two approaches to the problem: dialethism, which allows both a sentence and its negation to be true at once; and disambiguation, which represents any such confused predicate in terms of other, distinct predicates. I show the equivalency of plausible formal treatments of these approaches, discuss reasons for this equivalency, and present an alternative approach---a preservationist one, which does not interpret the confused predicates but rather seeks to contain the confusion present. I argue that a meaningful, and useful, concept of inference is available, even where the semantics of certain predicate-terms remain confusing. 

@InCollection{Allen01a,
  author = 	 {Martin Allen},
  title = 	 {A Paraconsistent-Preservationist Approach to a 
                  Common Confusion concerning Predicate Extensions},
  booktitle = 	 {Logical Consequence: Rival Approaches 
                  (Proceedings of 1999 Conference of the Society for Exact Philosophy ({SEP}-99))},
  pages = 	 {181--252},
  publisher =    {Hermes Science},
  year = 	 2001,
  editor = 	 {John Woods and Bryson Brown},
  address = 	 {Middlesex, England}
}

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