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A Logic Inspired by Natural Language: Quantifiers As Subnectors

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Abstract

Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors (operators forming terms from formulas). A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard first-order logic, and shows that the proof-theoretic meanings of both logics coincide. The paper criticizes Frege’s original regimentation of quantified sentences of natural language, and argues for advantages of the proposed variant.

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Notes

  1. All NL example expressions are depicted in san-serif font and are mentioned, not used.

  2. The vp-implication has no natural counterpart in NL.

  3. Under current theories, the task of excluding such expressions is relayed to syntax.

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Acknowledgments

I thank Hartley Slater, who, in spite of objecting to my whole approach, helped by lengthy discussions of the issues involved. I also thank Hanoch Ben-Yami for discussions of the issues involved and for updating me regarding his recent work. I thank Bartosz Wieckowski for his help in cleaning up a previous draft. An anonymous referee for JPL helped a lot in improving the presentation.

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  1. Department of Computer Science, Technion-IIT, Haifa, Israel

    Nissim Francez

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  1. Nissim Francez
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Francez, N. A Logic Inspired by Natural Language: Quantifiers As Subnectors. J Philos Logic 43, 1153–1172 (2014). https://doi.org/10.1007/s10992-014-9312-z

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