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Positional Value and Linguistic Recursion

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References

  • Aitchison Jean (2001). Language change: Progress or decay? (3rd ed.). New York, Cambridge University Press

    Google Scholar 

  • Bag A.K. (1975). al-Biruni on Indian Arithmetic. Indian Journal for the History of Science 10: 174–184

    Google Scholar 

  • Barber Charles (2000). The English language revised edition. New York, Cambridge University Press

    Google Scholar 

  • Baron-Cohen Simon (1997). Mindblindness: An essay on autism and theory of mind. New York, Cambridge University Press

    Google Scholar 

  • Boolos George (1979). The unprovability of consistency. New York, Cambridge University Press

    Google Scholar 

  • Brinton Laurel, Traugott Elizabeth (2005). Lexicalization and language change. New York, Cambridge University Press

    Google Scholar 

  • Brough John (1951). Theories of general linguistics in the Sanskrit grammarians. In Staal 1972: 402–413

    Google Scholar 

  • Chomsky, Noam (1963). Formal properties of grammars. In Luce et al. 323–418.

  • Chomsky Noam (1980). Rules and representations. New York, Columbia University Press

    Google Scholar 

  • Chomsky, Noam, & Miller, George (1963). Introduction to the formal analysis of natural languages. In Luce et al. 269–322.

  • Clark Herbert (1996). Using language. New York, Cambridge University Press

    Google Scholar 

  • Datta, Bibhutibhushan, & Singh, Avadesh Narayan (1935). History of Hindu mathematics I, II. Delhi: Bharatiya Kala Prakashan. (Reprinted (2001)).

  • Davis Martin Davis (Ed.) (1965). The undecidable: Basic papers on undecidable propositions, unsolvable problems and computable functions. Hewlett, New York, Raven Press

    Google Scholar 

  • Davis, Martin Davis, Sigal, Ron, & Weyuker, Elaine (1994). Computability, complexity, and langauges: Fundamentals of theoretical computer science (2nd ed.), New York: Academic Press.

  • Deutscher Guy (2005). The unfolding of language. New York, Metropolitan Books

    Google Scholar 

  • Emch, Gerard, Sridharan, R., & Srinivas, M. D. (Eds.) (2005). Contributions to the history of Indian mathematics. New Delhi: Hindustan Book Agency.

  • Enderton Herbert (1972). A mathematical introduction to logic. New York, Academic Press

    Google Scholar 

  • Fischer, Michael, & Rabin, Michael (1974). Super-exponential complexity of Presburger arithmetic. SIAM-AMS Proceedings, No. 7, American Mathematics Society, Providence, R.I., 27–41.

  • Gandy, Robin (1995). The confluence of ideas in 1936. In Rolf Herken (Ed.), The universal turing machine: A half-century survey (2nd ed.). New York: Springer-Verlag.

  • Gardner Howard (1987). The mind’s new science: A history of the cognitive revolution. New York, Basic Books

    Google Scholar 

  • Gentner Dedre, Goldin-Meadow Susan (eds). (2003). Language in mind: Advances in the study of langauge and thought. Cambridge, MIT Press

    Google Scholar 

  • Goody Jack (1987). The interface between the written and the oral. New York, Cambridge University Press

    Google Scholar 

  • Ifrah, Georges (2000). The universal history of numbers: From prehistory to the invention of the computer. (David Bellos et al. trans.). New York: John Wiley & Sons.

  • Karmiloff-Smith Annette (1992). Beyond modularity: A developmental approach to cognitive science. Cambridge, MIT Press

    Google Scholar 

  • Keller, Agathe (2006). Expounding the mathematical seed: A translation of Bhāskara I on the mathematical chapter of the Āryabhatīya I, II. Boston: Birkhäuser.

  • Klein, Jacob (1936). Greek mathematical thought and the origin of algebra. (Eva Brann trans. 1968). New York: Dover (Reprint (1992)).

  • Luce R. Duncan, Bush R., Galanter E. (eds). (1963). Handbook of mathematical psychology (Vol. II). New York, John Wiley & Sons

    Google Scholar 

  • Minsky Marvin (1967). Computation: Finite and infinite machines. New York, Prentice-Hall

    Google Scholar 

  • Nayar B.K. (1975) al-Biruni and science communication in Sanskrit. Indian Journal for the History of Science 10, 249–252

    Google Scholar 

  • Pullum Geoffrey, Scholz Barbara (2005). Contrasting applications of logic in natural language syntactic description. In Petr Hájek, et al. (eds). Logic, methodology and philosophy of science: Proceedings of the twelfth international congress. London, King’s College Publications, pp. 481–503

    Google Scholar 

  • Renou Louis (1941). Les connexions entre le rituel et la grammaire en Sanskrit. In Staal 1972: 435–469

    Google Scholar 

  • de Saussure, Ferdinand (1915/1959). Course in general linguistics. (Wade Baskin trans. C. Bally et al. (Eds.)). New York: McGraw-Hill.

  • Sharma, Rama Nath (1987). The Aṣṭādhyāyī of Pāṇini I: Introduction to the Aṣṭādhyāyī as a grammatical device. New Delhi: Munshiram Manoharlal.

  • Staal Frits (Ed.) (1972). Reader on the Sanskrit grammarians. Cambridge, MIT Press

    Google Scholar 

  • Staal, Frits (1983). Agni: The Vedic fire ritual I, II. Delhi: Motilal Banarsidass (Reprint (2001)).

  • Staal Frits (1988). Universals: Studies in Indian logic and linguistics. Chicago, University of Chicago Press

    Google Scholar 

  • Staal Frits (1990). Ritual and mantras: Rules without meaning. Delhi, Motilal Banarsidass

    Google Scholar 

  • Staal Frits (2006). Artificial languages across sciences and civilizations. Journal of Indian Philosophy 34, 87–139

    Article  Google Scholar 

  • Tomasello Michael (1999). The social origins of human cognition. Cambridge, Harvard University Press

    Google Scholar 

  • Tomasello Michael (2003). Constructing a language: A usage-based theory of language acquistion. Cambridge, Harvard University Press

    Google Scholar 

  • Turing, Alan (1936). On computable numbers with an application to the Entscheidungsproblem. In Davis 115–153.

  • Woepcke, Franz (1863). Mémoire sur la Propagation des Chiffres Indiens. Journal Asiatique, Sixth Series, 1, 442–529. In Fuat Sezgin (Ed.), Franz Woepcke, Études sur les Mathématiques Arabo-Islamiques (Vol. 2). Frankfurt: Institute for the History of Arabic-Islamic Science and the Goethe University, 1986.

  • Young, Paul (1985). Gödel theorems, exponential difficulty and undecidability of arithmetic theories: An exposition. In Anil Nerode, & Richard Shore (Eds.), Recursion theory: Proceedings of symposia in pure mathematics (Vol. 42). Providence: American Mathematical Society.

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Kadvany, J. Positional Value and Linguistic Recursion. J Indian Philos 35, 487–520 (2007). https://doi.org/10.1007/s10781-007-9025-5

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