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1 - Introduction

Published online by Cambridge University Press:  05 June 2012

Merrie Bergmann
Affiliation:
Smith College, Massachusetts
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Summary

Issues of vagueness

Some people, like 6′ 7″ Gina Biggerly, are just plain tall. Other people, like 4′ 7″ Tina Littleton, are just as plainly not tall. But now consider Mary Middleford, who is 5′ 7″. Is she tall? Well, kind of, but not really – certainly not as clearly as Gina is tall. If Mary Middleford is kind of but not really tall, is the sentence Mary Middleford is tall true? No. Nor is the sentence false. The sentence Mary Middleford is tall is neither true nor false. This is a counterexample to the Principle of Bivalence, which states that every declarative sentence is either true, like the sentence Gina Biggerly is tall, or false, like the sentence Tina Littleton is tall (bivalence means having two values). The counterexample arises because the predicate tall is vague: in addition to the people to whom the predicate (clearly) applies or (clearly) fails to apply, there are people like Mary Middleford to whom the predicate neither clearly applies nor clearly fails to apply. Thus the predicate is true of some people, false of some other people, and neither true nor false of yet others. We call the latter people (or, perhaps more strictly, their heights) borderline or fringe cases of tallness.

Vague predicates contrast with precise ones, which admit of no borderline cases in their domain of application. The predicates that mathematicians typically use to classify numbers are precise.

Type
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An Introduction to Many-Valued and Fuzzy Logic
Semantics, Algebras, and Derivation Systems
, pp. 1 - 11
Publisher: Cambridge University Press
Print publication year: 2008

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  • Introduction
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.002
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  • Introduction
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.002
Available formats
×

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

  • Introduction
  • Merrie Bergmann, Smith College, Massachusetts
  • Book: An Introduction to Many-Valued and Fuzzy Logic
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801129.002
Available formats
×