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Can Natural Language Be Captured in a Formal System?

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Abstract

The question whether natural language can be captured in a formal system has been argued at length, and both a positive and a negative answer has been defended. The paper investigates the main lines of argument for both, and argues that the stalemate that appears to have been reached is an indication that the question itself rests on a wrong conception of the relation between natural languages and formal languages, and hence of the methodological status of formal modelling of natural language.

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Notes

  1. 1.

    Cf., Hauser et al. [11]. The position that semantics is not part of grammar is one that Chomsky has defended throughout, cf., e.g., [4], Chapter 2.

  2. 2.

    The most prominent example perhaps being Hans Reichenbach, whose Elements of symbolic logic, which dates from 1947, contained a substantial part devoted to systematic treatment of, among other things, tenses and other temporal expressions in natural language, which became known and very influential only much later.

  3. 3.

    Which is what happened to Yehoshua Bar-Hillel, who, inspired by Carnap’s work in intensional logic, in the early fifties suggested that the formal methods of logic could be applied to the results of Chomsky’s early work in generative syntax so as to provide a formal semantics for natural language (cf., [1]). The proposal met with a brusque and negative response from Chomsky (cf., [3]), and it took another decade for other people to take up on this idea.

  4. 4.

    Cf., e.g., Davidson: ‘Recent work by Chomsky and others is doing much to bring the complexities of natural languages within the scope of serious theory.’ [7], and Montague: ‘On this point [viz., that natural languages can be treated formally, MS] I differ from a number of philosophers, but agree, I believe, with Chomsky and his associates.’ [21].

  5. 5.

    Cf., Moerdijk and Landman [20]. Cf., also Cresswell’s defence of his use of set theory as his metalanguage in his Logics and languages [5].

  6. 6.

    Thus, in that respect aligning formal semantics with the generative tradition. Cf., Stokhof [30] for a diagnosis of how that came about.

  7. 7.

    Cf., Kamp and Stokhof [16] for extensive discussion of this development.

  8. 8.

    Cf., above on Chomsky’s distinction between the computational and the conceptual system. Cf., Higginbotham 1997 for extensive discussion of the implications of such a move for formal semantics.

  9. 9.

    Cf., Maat [19].

  10. 10.

    Page references are to the English translation in Van Heijenoort.

  11. 11.

    The locus classicus is Tarski’s 1944 paper on the semantic conception of truth, where he writes: “The problem of the definition of truth obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified. For other languages – thus, for all natural, ‘spoken’ languages – the meaning of the problem is more or less vague, and its solution can have only an approximate character.”

  12. 12.

    Cf., Pagin and Westerståhl [23, 24] for a comprehensive overview.

  13. 13.

    Cf., Pullum and Scholz [27].

  14. 14.

    In view of the fact that for example model-theoretic approaches to syntax (cf., [26]), though definite alternatives to generative ones, are committed to the formal specifiability of syntax just as well.

  15. 15.

    Cf. Perry [25].

  16. 16.

    The most well-known instance of such an approach is that of Kaplan, cf., [17].

  17. 17.

    Cf., Stokhof and Van Lambalgen [32, 33] for further discussion.

  18. 18.

    Cf., Wittgenstein [37], section 122.

  19. 19.

    Asterisks (*) indicate recommended readings.

References

Asterisks (*) indicate recommended readings.

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Authors and Affiliations

  1. ILLC/Department of Philosophy, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Martin Stokhof

  2. Department of Philosophy, Tsinghua University, Beijing, China

    Martin Stokhof

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Editors and Affiliations

  1. Division of Philosophy, Royal Institute of Technology (KTH), Stockholm, Sweden

    Sven Ove Hansson

  2. Center for Information and Bubble Studies, University of Copenhagen, Copenhagen, Denmark

    Vincent F. Hendricks

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Stokhof, M. (2018). Can Natural Language Be Captured in a Formal System?. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_12

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