Fuzzy Logic and Restricted Quantifiers

  • James D. McCawley
Part of the Synthese Library book series (SYLI, volume 143)


This paper is part of an ongoing attempt to do justice to both a linguist’s concerns and a logician’s within a single consistent system. The principal respect in which a linguist’s concerns will affect what follows here is the matter of coverage: I will assume Lakoff’s (1972) conclusion that a multi-valued logic is essential for an adequate treatment of the semantics of a large amount of natural language vocabulary, particularly adjectives such as fat, obnoxious, and pleasant, which do not make a clear division between things of which they are true and things of which they are false, nouns such as vermin, vegetable, and toy, which denote categories with imprecise boundaries, and many ‘hedge’ words such as somewhat, quite, pretty much, and par excellence. I will take truth values to be real numbers on the interval from 0 to 1, with 0 corresponding to unqualified falsehood, 1 to unqualified truth, and intermediate numbers to intermediate degrees of truth to which such terms as ‘fairly true’, ‘pretty well false’, and the like could be applied1.


Fuzzy Logic Truth Condition Modal Logic Natural Deduction Tall Person 
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  1. Anderson, A. R. and N. Belnap: 1975, Entailment, Vol. 1 ( Princeton University Press, Princeton ).Google Scholar
  2. Haack, Susan: 1975, Deviant Logics ( Cambridge University Press, London).Google Scholar
  3. Herzberger, Hans: 1973, ‘Dimensions of Truth’, Journal of Philosophical Logic 2,429–435 Also in Hockney et al (1975), 71–92.Google Scholar
  4. Herzberger, Hans: 1975, ‘Supervaluations in Two Dimensions’, Proceedings of the 1975 International Symposium on Multiple-Valued Logic ( IEEE, Long Beach ), 429–435.Google Scholar
  5. Hockney, D., W. Harper, and B. Freed: 1975, Contemporary Research in Philosophical Logic and Linguistic Semantics ( Reidel, Dordrecht).Google Scholar
  6. Kripke, Saul: 1959, ‘A Completeness Theorem in Modal Logic’, Journal of Symbolic Logic 24, 1–15.CrossRefGoogle Scholar
  7. Kripke, Saul: 1963, ‘Semantical Considerations on Modal Logic’, Acta Philosophica Fennica 16, 83–94.Google Scholar
  8. Lakoff, George: 1972, ‘Hedges: A study in Meaning Criteria and the Logic of Fuzzy Concepts’, Paper from the 8th Regional Meeting, Chicago Linguistic Society, 183–228. Corrected version appears in the Journal of Philosophical Logic (1973), 2, 458–508 and in Hockney et al. (1975) 221–271.Google Scholar
  9. Lewis, David: 1974, Counterfactuals (Harvard University Press, Cambridge, Mass.).Google Scholar
  10. McCawley, James D.: 1972, ‘A Program for Logic’, in D. Davidson and G. Harman (eds.), Semantics of Natural Language ( Reidel, Dordrecht ), 498–544.CrossRefGoogle Scholar
  11. McCawley, James D.: 1975, ‘Truth Functionality and Natural Deduction’, Proceedings of the 1975 International Symposium on Multiple-Valued Logic ( IEEE, Long Beach ), 412–418.Google Scholar
  12. Rescher, Nicholas: 1969, Many-Valued Logics (McGraw Hill, New York).Google Scholar

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • James D. McCawley

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