Skip to main content

Part of the book series: Studies in Linguistics and Philosophy ((SLAP,volume 33))

Abstract

How, one may reasonably wonder, could mathematics be applied to anything so unquantifiable as language? An analogy with, say, mathematical physics raises the puzzling question of how one could write equations which might be solved for the meaning of some French word or the correct case in German for the object of glauben. The source of such confusion is the common but incorrect idea that all mathematics deals with numbers. Virtually any paper in generative linguistics illustrate how one can make precise statements of a nonquantitative nature about language. Mathematical linguistics involves studying this sort of statement by applying mathematics. In this chapter we will see how some such applications have yielded interesting results about language.

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

  • Bever, T., Fodor, J., and Garrett, M., (1968) A Formal Limitation of Associationism, In T. Dixon and D. Horton (Eds.) Verbal Behavior and General Behavior Theory, Englewood Cliffs, N. J., Prentice-Hall.

    Google Scholar 

  • Chomsky, N. (1956). Three Models for the Description of Language, IRE Transactions on Information Theory, IT-2, 113–124.

    Article  Google Scholar 

  • Chomsky, N., (1957b) Review of a Manual of Phonology, IJAL, 23, 223–234.

    Google Scholar 

  • Chomsky, N., (1963) Formal Properties of Grammars, In R. Luce, R. Bush and E. Galanter (Eds.), Handbook of Mathematical Psychology, New York, Wiley.

    Google Scholar 

  • Chomsky, N., and Miller, G., (1963) Introduction to the Formal Analysis of Language, In R. Luce, R. Bush and E. Galanter (Eds.), Handbook of Mathematical Psychology, New York, Wiley.

    Google Scholar 

  • Hockett, Charles A. (1955) A Manual of Phonology, Bloomington, Ind., Indiana University Press.

    Google Scholar 

  • Lancelot, C., and Arnauld, A., (1660) Grammaire Générale et Raisonée, Reprinted (1967), Menston, England, Scolar Press.

    Google Scholar 

  • Peters, S., and Ritchie, R., (1969a) A Note on the Universal Base Hypothesis, JL, 5, 150–152.

    Article  Google Scholar 

  • Peters, S., and Ritchie, R., (1969b) Context—Sensitive Immediate Constituent Analysis -Context-free Languages Revisited.

    Google Scholar 

  • Peters, S., and Ritchie, R., (1969c) On the Generative Power of Transformational Grammars.

    Google Scholar 

  • Peters, S., and Ritchie, R., (1971) On Restricting the Base Component of Transformational Grammars, Information and Control 18, 493–501.

    MathSciNet  Google Scholar 

  • Postal, P., (1964) Limitations of Phrase Structure Grammars, In J. Fodor and J. Katz (Eds.), The Structure of Language, Englewood Cliffs, N.J., Prentice-Hall.

    Google Scholar 

  • Rabin, M., and Scott, D., (1959) Finite Automata and Their Decision Problems, IBM Journal of Research and Development, 3, 114–125.

    Article  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 D. Reidel Publishing Company

About this chapter

Cite this chapter

Peters, S. (1987). What is Mathematical Linguistics?. In: Savitch, W.J., Bach, E., Marsh, W., Safran-Naveh, G. (eds) The Formal Complexity of Natural Language. Studies in Linguistics and Philosophy, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3401-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3401-6_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-55608-047-0

  • Online ISBN: 978-94-009-3401-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics