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3 - Mathematical linguistics

Published online by Cambridge University Press:  22 September 2009

Marcus Tomalin
Affiliation:
University of Cambridge
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Summary

Chapter overview

The purpose of this chapter is to summarise some of the developments, associated with the formal sciences, that grew out of the foundations debates of the early decades of the twentieth century, and to examine the way in which they exerted an influence upon the formulation of linguistic theory. The basic strategy is to focus upon particular techniques or theories that were ultimately to be involved in the creation of TGG. Consequently, it should be remembered throughout that this chapter is necessarily selective, and that it does not attempt to provide an exhaustive coverage of all the associations between mathematics and linguistics that were mooted during the first half of the twentieth century. The first subject, discussed in section 3.2, is the use of the axiomatic-deductive method, and detailed attention is given to the work of Bloomfield, Bloch, and Harwood. Recursive function theory is considered next, in section 3.3, with specific reference to the work of Gödel, Kleene, Post, and Bar-Hillel. In section 3.4 the work of the Lvov-Warsaw school of logicians is assessed, and particular emphasis is placed upon the way in which some of Ajdukiewicz's research into logical systems was revived by Bar-Hillel in the early 1950s. The evolution of constructional system theory is considered in section 3.5, and the associations between Carnap and Goodman are explored, while, in section 3.6, the extreme philosophical stance that came to be known as constructive nominalism is presented.

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Linguistics and the Formal Sciences
The Origins of Generative Grammar
, pp. 54 - 107
Publisher: Cambridge University Press
Print publication year: 2006

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  • Mathematical linguistics
  • Marcus Tomalin, University of Cambridge
  • Book: Linguistics and the Formal Sciences
  • Online publication: 22 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511486340.003
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  • Mathematical linguistics
  • Marcus Tomalin, University of Cambridge
  • Book: Linguistics and the Formal Sciences
  • Online publication: 22 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511486340.003
Available formats
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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.

  • Mathematical linguistics
  • Marcus Tomalin, University of Cambridge
  • Book: Linguistics and the Formal Sciences
  • Online publication: 22 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511486340.003
Available formats
×