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On Hierarchical Propositions

  • Giorgio SbardoliniEmail author
Open Access
Article

Abstract

There is an apparent dilemma for hierarchical accounts of propositions, raised by Bruno Whittle (Journal of Philosophical Logic, 46, 215–231, 2017): either such accounts do not offer adequate treatment of connectives and quantifiers, or they eviscerate the logic. I discuss what a plausible hierarchical conception of propositions might amount to, and show that on that conception, Whittle’s dilemma is not compelling. Thus, there are good reasons why proponents of hierarchical accounts of propositions (such as Russell, Church, or Kaplan) did not see the difficulty Whittle raises.

Keywords

Paradoxes Propositions Type theory Simple and ramified hierarchy 

Notes

Funding Information

This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 758540) within the project From the Expression of Disagreement to New Foundations for Expressivist Semantics.

References

  1. 1.
    Church, A. (1976). Comparison of Russell’s Resolution of the semantical Antinomies with that of Tarski. Journal of Symbolic Logic, 41(4), 747–760.CrossRefGoogle Scholar
  2. 2.
    Giaquinto, M. (2002). The search for certainty. Oxford: Clarendon Press.Google Scholar
  3. 3.
    Gödel, K. (1944). Russell’s mathematical logic. In Schlipp, P.A. (Ed.) The philosophy of Bertrand Russell (pp. 125–153). New York: Tudor Publishing Company.Google Scholar
  4. 4.
    Goldfarb, W. (1989). Russell’s reasons for ramification. In Savage, C.W., & Anderson, C.A. (Eds.) Rereading Russell: essays on Bertrand Russell’s metaphysics and epistemology (pp. 24–40). Minneapolis: University of Minnesota Press.Google Scholar
  5. 5.
    Hodes, H. (2015). Why Ramify? Notre Dame Journal of Formal Logic, 56(2), 379–415.CrossRefGoogle Scholar
  6. 6.
    Jung, D. (1999). Russell, presupposition, and the vicious circle principle. Notre Dame Journal of Formal Logic, 40(1), 55–80.CrossRefGoogle Scholar
  7. 7.
    Kaplan, D. (1995). A problem in possible world semantics. In Raffman, D., Sinnott-Armstrong, W., Asher, N. (Eds.) Modality, morality and belief: essays in honor of Ruth Barcan Marcus (pp. 41–52). Cambridge: Cambridge University Press.Google Scholar
  8. 8.
    Myhill, J. (1958). Problems arising in the formalization of intensional logic. Logique et Analyse, 1, 78–83.Google Scholar
  9. 9.
    Prior, A. (1961). On a family of paradoxes. Notre Dame Journal of Formal Logic, 2, 16–32.CrossRefGoogle Scholar
  10. 10.
    Quine, W.V.O. (1969). Set Theory and Its Logic. Cambridge: Belknap Press.Google Scholar
  11. 11.
    Ramsey, F.P. (1926). The foundations of mathematics. Proceedings of the London Mathematical Society, 2(25), 338–384. Reprinted in F. P. Ramsey, Foundations, London: Routledge and Kegan Paul, 152212, 1978.CrossRefGoogle Scholar
  12. 12.
    Russell, B. (1903). The Principles of Mathematics. Cambridge: Cambridge University Press.Google Scholar
  13. 13.
    Russell, B. (1908). Mathematical logic as based on a theory of types. American Journal of Mathematics, 30, 222–262.CrossRefGoogle Scholar
  14. 14.
    Russell, B. (1971). Introduction to mathematical philosophy. Simon and Schuster: New York.Google Scholar
  15. 15.
    Whittle, B. (2017). Hierarchical propositions. Journal of Philosophical Logic, 46, 215–231.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.ILLC, University of AmsterdamAmsterdamThe Netherlands

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