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Quantifiers. Hintikka and Frege on Quantification Concepts

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Jaakko Hintikka on Knowledge and Game-Theoretical Semantics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 12))

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Abstract

Hintikka’s semantic approach to meaning, a development of Wittgenstein’s view of meaning as use, is the general theme of this chapter. We will focus on the analysis of quantified sentences and on the scope of the principle of compositionality and compare Hintikka’s take on these issues with that of Frege. The aim of this paper is to show that Hintikka’s analysis of quantified expressions as choice functions, in spite of its obvious dissimilarities with respect to the higher-order approach, is actually very close to the Fregean stance on compositionality and context dependence. In particular, we will defend that the Fregean approach to quantifiers is unavoidably linked to the idea that quantified expressions are context-dependent, and therefore should not be conceived under the traditional inside-out model for analysis.

This Project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 653056. It has also been supported by the Spanish Ministerio de Economía y Competitividad, Proyecto FFI2013-44836-P, Expresivismo, Naturalismo y Normatividad, and by the Plan Propio, University of Granada, Proyecto Expresivismo Doxástico.

We are deeply indebted to Gabriel Sandu and Hans van Ditmarchs for the invitation to contribute to this volume.

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Notes

  1. 1.

    The expression “inter-linguistic” is due to Sellars, who uses it to explain the status of propositions. Propositions are not linguistic but cannot live outside some linguistic system or other. See, for instance, ([42], 100).

  2. 2.

    Although ([15], 49) explicitly place Russell in line with Montague, and Quine in line with Lakoff.

  3. 3.

    As we have stressed elsewhere ([5], 5), Frege’s take on content is also alien to those views that make use of a different principle of compositionality—reverse Compositionality ([4], cfr. [44]). Of course, only if this principle receives a strict—and meaningful—interpretation, as a semantic version of “reverse engineering.” It is indeed incompatible with the Fregean stance regarding the fact that multiple logical forms can result from the analysis of a single judgment. If the principle is only meant as ‘a statistical psychological generalization that holds with great regularity’ ([27], p. 52), then Reverse Compositionality is indeed compatible with Frege’s positions, but of no particular use in semantics.

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Author information

Authors and Affiliations

  1. University College London, London, UK

    María J. Frápolli

  2. University of Granada, Granada, UK

    Neftalí Villanueva

Authors
  1. María J. Frápolli
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  2. Neftalí Villanueva
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Correspondence to María J. Frápolli .

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Editors and Affiliations

  1. LORIA, CNRS, Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Hans van Ditmarsch

  2. Department of Philosophy, University of Helsinki, Helsinki, Finland

    Gabriel Sandu

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Frápolli, M.J., Villanueva, N. (2018). Quantifiers. Hintikka and Frege on Quantification Concepts. In: van Ditmarsch, H., Sandu, G. (eds) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-62864-6_11

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