Skip to main content

Part of the book series: Synthese Library ((SYLI,volume 248))

  • 178 Accesses

Abstract

The word quantifier comes from the latin quantitas (quantity) as contrasted with qualitas (quality). This intuition does not mean that the notion of quantifier is understood as an arithmetical concept. We understand quantifiers rather as qualifiers for distributive concepts (such as countable nouns) unlike those applicable to nondistributive concepts.

This work has been supported by Polish Government Grant Projekt Badawczy “KWANTYFIKATORY”.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. T.Baldwinand S.Shelah,Second-orderquantifiers and the complexity of theories,Notre Dame Journal of Formal Logic26 (1985), pp. 229–303.

    Article  Google Scholar 

  2. J.Barwise,Axioms for abstract model theory,Annals of Mathematical Logicvol. 7 (1974), pp. 221–265.

    Article  Google Scholar 

  3. J. Barwise, On branching quantifiers in English, Journal of Philosophical Logic 8 (1979), pp. 47–80.

    Article  Google Scholar 

  4. J.Barwiseand R.Cooper, Generalized quantifiers and natural language,Linguistics and Philosophy 4 (1981), pp. 159–219.

    Article  Google Scholar 

  5. J.Barwiseand S.Feferman(eds.),Model-Theoretic Logics, Springer-Verlag 1985.

    Google Scholar 

  6. I. Bellert, Feature System for Quantification Structures in Natural Language, Foris Publications Dordrecht/Providence 1989.

    Google Scholar 

  7. J. Van Benthem, Questions about quantifiers, The Journal of Symbolic Logic 49 (1984), pp. 443–466.

    Article  Google Scholar 

  8. J.VanBenthem,Towards a Computational Semantics,in[GĂ€rdenfors 1987], pp. 31–71.

    Google Scholar 

  9. S. Feferman, Two notes on abstract model theory, I: Properties invariant on the range of definable relations between structures, Fundamenta Mathematicae 82 (1974), pp. 153–165.

    Google Scholar 

  10. S. Feferman, Two notes on abstract model theory, II: Languages for which the set of valid sentences is s.i.i.d., Fundamenta Mathematicae 89 (1975), pp. 111–130.

    Google Scholar 

  11. P.Gardenfors(ed.),Generalized QuantifiersReidel Publish. Company 1987.

    Google Scholar 

  12. Y.Gurevich, Towards logic tailored for computational complexity,Computation and Proof TheoryRichter, M. M. and others (eds.), Springer, Lecture Notes in Mathematics 1104 (1984), pp. 175–216.

    Google Scholar 

  13. P. Hájek, Generalized quantifiers and finite sets, in Set Theory and Hierarchy Theory, J. Waszkiewicz, A. Wojciechowska and A. Zarach (eds.) Prace Naukowe Instytutu Matematyki Politechniki Wroclawskiej, Wroclaw 1977, pp. 91–104.

    Google Scholar 

  14. K. J. J.Hintikkaand V.Rantala,Anew approach toinfinitary languagesAnnals of Mathematical Logic10 (1976), pp. 95–115.

    Article  Google Scholar 

  15. H. J. Keisler, Logic with the quantifier “there exist uncountably many”, Annals of Mathematical Logic 1 (1970), pp. 1–93.

    Article  Google Scholar 

  16. M. Krynicki, M. Mostowski, and L. W. Szczerba,Quantifiers II, Kluwer Academic Publishers 1995.

    Google Scholar 

  17. P. Lindström, First order predicate logic with generalized quantifiers, Theoria 32 (1966), pp. 165–171.

    Article  Google Scholar 

  18. P. Lindström P, On extensions of elementary logic, Theoria 35 (1969), pp. 1–11.

    Article  Google Scholar 

  19. P.Lipparini, Duality for compact logics and substitution in abstract model theory, Zeitschrift fur Mathematische Logik and Grundlagen der Mathematik 31 (1985), pp. 517–532.

    Article  Google Scholar 

  20. A. J.Macintyre,Ramseyquantifiers inarithmetic,in:Model Theory of Algebra and ArithmeticL. Pacholski, J. Wierzejewski and A. Wilkie (eds.), serieLecture Notes in Mathematics834 (1980), pp. 186–210.

    Google Scholar 

  21. MakowskyJ. A.,Shelah, S. andStaviJ., A-logics and generalized quantifiers. Annals of Mathematical Logic10 (1976), pp. 155–192.

    Article  Google Scholar 

  22. A. Mostowski, On a generalization of quantifiers, Fundamenta Mathematicae 44 (1957), pp. 12–36.

    Google Scholar 

  23. W. V. Quine, Philosophy of Logic, Prentice-Hall, Inc., New Jersey 1970.

    Google Scholar 

  24. B. A. Trakhtenbrot, The impossibility of an algorithm for the decision problem for finite domains (Russian), Doklady Akademii Nauk SSSR, 70 (1950), pp. 569–572

    Google Scholar 

  25. R. L. Vaught, The completeness of logic with the added quantifier “there are uncountably many”, Fundamenta Mathematicae 54 (1964) pp. 303–304.

    Google Scholar 

  26. J.VÀÀnĂ€nen, Remarks on generalized quantifiers and second-order logic, in Set Theory and Hierarchy Theory J. Waszkiewicz, A. Wojciechowska and A. Zarach (eds.) Prace Naukowe Instytutu Matematyki Politechniki Wroclawskiej, Wroclaw 1977, pp. 117–123.

    Google Scholar 

  27. D. WesterstĂ„hl, Quantifiers in formal and natural languages, Handbook of Philosophical Logic D. Gabbay and F. Guenthner (eds.) vol. IV, Reidel, Dordrecht (1989), pp. 1–131.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Krynicki, M., Mostowski, M. (1995). Quantifiers, Some Problems and Ideas. In: Krynicki, M., Mostowski, M., Szczerba, L.W. (eds) Quantifiers: Logics, Models and Computation. Synthese Library, vol 248. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0522-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0522-6_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4539-3

  • Online ISBN: 978-94-017-0522-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics