Skip to main content

Modal Expansionism

Abstract

There are various well-known paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion.

References

  1. Correia, F. (2007). Modality, quantification, and many Vlach-operators. Journal of Philosophical Logic, 36, 473–488.

    Article  Google Scholar 

  2. Divers, J. (2014). Modal reality and (modal) logical space. Philosophy and Phenomenological Research, 88, 726–733.

    Article  Google Scholar 

  3. Fine, K. (1977). Prior on the construction of possible worlds and instants, reprinted in K. Fine (Ed.) (2005) Modality and tense. Oxford: Clarendon Press.

  4. Fine, K. (2002). Problem of Possibilia, reprinted in K. Fine (Ed.) (2005) Modality and tense. Oxford: Clarendon Press.

  5. Fine, K. (2006). Relatively unrestricted quantification. In A. Rayo, & G. Uzquiano (Eds.) , Absolute generality. Oxford: Clarendon Press.

  6. Forbes, G. (1992). Melia on modalism. Philosophical Studies, 68, 57–63.

    Article  Google Scholar 

  7. Forster, T.E. (1995). Set theory with a universal set: exploring an untyped universe, 2nd edn. Oxford: Clarendon Press.

    Google Scholar 

  8. Fritz, P. (2016). A purely recombinatorial puzzle, forthcoming in Noûs.

    Article  Google Scholar 

  9. Hawthorne, J. (2006). Quantity in Lewisian metaphysics. In J. Hawthorne (Ed.) , Metaphysical essays. Oxford: Clarendon Press.

  10. Hawthorne, J., & Uzquiano, G. (2011). How many angels can dance on the point of a needle? Transcendental theology meets modal metaphysics. Mind, 123, 317–337.

    Google Scholar 

  11. Kaplan, D. (1995). A problem in possible-world semantics. In W. Sinnot-Armstrong (Ed.) , Modality, morality, and belief: essays in honour of Ruth Barcan Marcus. Cambridge: Cambridge University Press.

  12. Kratzer, A. (2012). Modals and conditionals. Oxford: Oxford University Press.

    Google Scholar 

  13. Lewis, D. (1986). On the plurality of worlds. Oxford: Basil Blackwell.

    Google Scholar 

  14. Linnebo, Ø. (2010). Pluralities and sets. Journal of Philosophy, 107, 144–164.

    Article  Google Scholar 

  15. Melia, J. (1992). Against modalism. Philosophical Studies, 68, 35–56.

    Article  Google Scholar 

  16. Nolan, D. (1996). Recombination unbound. Philosophical Studies, 84, 239–262.

    Article  Google Scholar 

  17. Rayo, A. & (MS) On the Open-Endedness of Logical Space, unpublished manuscript.

  18. Rayo, A., & Uzquiano, G. (Eds.). (2006). Absolute generality. Oxford: Clarendon Press.

  19. Russell, B. (1906). On some difficulties in the theory of transfinite numbers and order types. Proceedings of The London Mathematics Society, 4, 29–53.

    Google Scholar 

  20. Salmon, N. (1989). The logic of what might have been. The Philosophical Review, 98, 3–34.

    Article  Google Scholar 

  21. Sider, T. (2009). Williamson’s many necessary existents. Analysis, 69, 50–58.

    Article  Google Scholar 

  22. Studd, J. (2013). The iterative conception of set: a (bi-)modal axiomatisation. The Journal of Philosophical Logic, 42, 697–725.

    Article  Google Scholar 

  23. Studd, J. (forthcoming). Everything, more or less: a defence of generality relativism, forthcoming with Oxford University Press.

  24. Uzquiano, G. (2003). Plural quantification and classes. Philosophia Mathematica, 11, 67–81.

    Article  Google Scholar 

  25. Uzquiano, G. (2015). Varieties of indefinite extensibility. Notre Dame Journal of Formal Logic, 56, 147–166.

    Article  Google Scholar 

  26. Warren, J. (2017). Quantifier variance and indefinite extensibility. Philosophical Review, 126, 81–122.

    Article  Google Scholar 

  27. Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press.

    Book  Google Scholar 

  28. Williamson, T. (2016). Modal science. Canadian Journal of Philosophy, 46, 453–492.

    Article  Google Scholar 

  29. Yablo, S. (2006). Circularity and paradox. In T. Bolander, V.F. Hendricks, S.A. Pedersen (Eds.) , Self-reference. CSLI Publications.

  30. Yu, A. (2017). A modal account of propositions. Dialectica, 71, 463–488.

    Article  Google Scholar 

Download references

Acknowledgments

Thanks to Ben Brast-Mckie, Adrian Moore, and Ted Sider for discussions about earlier versions of this paper, and to Peter Fritz and an anonymous referee for this journal for their helpful and perceptive comments. Special thanks to James Studd and Timothy Williamson for their encouragement and comments on several drafts of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Roberts.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Roberts, A. Modal Expansionism. J Philos Logic 48, 1145–1170 (2019). https://doi.org/10.1007/s10992-019-09515-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-019-09515-x

Keywords

  • Metaphysical necessity
  • Indefinite extensibility
  • Bimodal logic