, Volume 82, Issue 4, pp 929–946 | Cite as

Against Naturalized Cognitive Propositions

  • Lorraine Juliano KellerEmail author
Original Research


In this paper, I argue that Scott Soames’ theory of naturalized cognitive propositions (hereafter, ‘NCP’) faces a serious objection: there are true propositions for which NCP cannot account. More carefully, NCP cannot account for certain truths of mathematics unless it is possible for there to be an infinite intellect. For those who reject the possibility of an infinite intellect, this constitutes a reductio of NCP.


Singular Proposition Linguistic Community Liberal Conception Singular Thought Representational Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I’m indebted to many philosophers for helpful feedback on ancestors and relatives of this paper—I’ve tried to acknowledge their contributions in the relevant parts of the paper. In particular, I’d like to thank those who read and commented on earlier drafts or proper parts thereof: Paddy Blanchette, Laura Crosilla, Chris Menzel, Paul Nedelisky, Josh Rasmussen, and Jeff Speaks. Thanks also to participants at the Propositions Workshop at the University of Leeds (Spring 2014), and to those who attended my talks at the University at Buffalo and the 2015 Central APA for helpful comments on earlier drafts of this paper. Special thanks to John Keller for extremely helpful and detailed comments at all stages of progress.


  1. Arrigoni, T. (2011). V = L and intuitive plausibility in set theory: A case study. Bulletin of Symbolic Logic, 17(3), 337–360.CrossRefGoogle Scholar
  2. Bell, J. L. (2011). The axiom of choice in the foundations of mathematics. In G. Sommaruga (Ed.), Foundational theories of classical and constructive mathematics. Berlin: Springer.Google Scholar
  3. Benacerraf, P., & Putnam, H. (1983). Philosophy of mathematics: Selected readings (2nd ed.). Cambridge: Cambridge UP.Google Scholar
  4. Bernays, P. (1935). Sur le platonisme dans les mathématiques. L’Enseignement Mathématique, 34, 52–69.Google Scholar
  5. Crane, T. (2011). The singularity of singular thought. In Proceedings of the aristotelian society supplementary volume (Vol. LXXXV).Google Scholar
  6. Crosilla, L. (2014). Set theory: Constructive and intuitionistic ZF. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. (Summer 2015 Edition)
  7. Davis, W. (2002). Meaning, expression, and thought. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  8. Feferman, S. (2000). Mathematical intuition versus mathematical monsters. Synthese, 125, 317–332.CrossRefGoogle Scholar
  9. Ferreirós, J. (2011). On arbitrary sets and ZFC. The Bulletin of Symbolic Logic, 17(3), 361–393.CrossRefGoogle Scholar
  10. Gödel, K. (1944). Russell’s mathematical logic. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics: Selected readings, 1983.Google Scholar
  11. Hanks, P. (2007). The content-force distinction. Philosophical Studies, 134(2), 141–164.CrossRefGoogle Scholar
  12. Hanks, P. (2011). Structured propositions as types. Mind, 120, 477.CrossRefGoogle Scholar
  13. Hawthorne, J., & Manley, D. (2012). The reference book. Oxford: Oxford University Press.CrossRefGoogle Scholar
  14. Jeshion, R. (2010). New essays on singular thought. Oxford: Oxford University Press.CrossRefGoogle Scholar
  15. Kaplan, D. (1978). Dthat. In P. Cole (Ed.), Syntax and semantics (Vol. 9, pp. 221–243). New York: Academic Press.Google Scholar
  16. Keller, L. J. Forthcoming. Propositions supernaturalized. In T. Dougherty & J. Walls (eds.), Two dozen (or so) arguments for God. Oxford University Press.Google Scholar
  17. King, J. (2007). The nature and structure of content. Oxford: Oxford University Press.CrossRefGoogle Scholar
  18. King, J. (2013). Propositional unity: What’s the problem, who has it, and who solves it? Philosophical Studies, 165(1), 71–93.CrossRefGoogle Scholar
  19. Kripke, S. (1980). Naming and necessity. Cambridge: Harvard University Press.Google Scholar
  20. Lewis, D. (1986). A comment on armstrong and forrest. Australasian Journal of Philosophy, 64(1986), 92–93.CrossRefGoogle Scholar
  21. Maddy, P. (1997). Naturalism in mathematics. Oxford: Clarendon Press.Google Scholar
  22. Plantinga, A. (1961). A valid ontological argument? Philosophical Review, 70, 93–101.CrossRefGoogle Scholar
  23. Richard, M. (2013). What are propositions? Canadian Journal of Philosophy, 43, 702–719.CrossRefGoogle Scholar
  24. Russell, B. (1903). Principles of mathematics. Cambridge: Cambridge University Press.Google Scholar
  25. Smolin, L. (2014). Atoms of space and time. Scientific American, 23, 94–103.Google Scholar
  26. Soames, S. (1989). Semantics and semantic competence. Philosophical Perspectives, 3, 575–596.CrossRefGoogle Scholar
  27. Soames, S. (1995). Beyond singular propositions? Canadian Journal of Philosophy, 25(4), 514–549.CrossRefGoogle Scholar
  28. Soames, S. (2010). What is meaning?. Princeton: Princeton University Press.CrossRefGoogle Scholar
  29. Soames, S. (2013). Cognitive propositions. Philosophical Perspectives: Philosophy of Language, 27, 1–23.CrossRefGoogle Scholar
  30. Soames, S. (2015). Rethinking language, mind, and meaning. Princeton: Princeton University Press.CrossRefGoogle Scholar
  31. Soames, S., King, J., & Speaks, J. (2014). New thinking about propositions. Oxford: OUP.Google Scholar
  32. Solovay, R. (1970). A model of set theory in which every set of reals is lebesgue measurable. Annals of Mathematics, Second Series, 92(1), 1–56.CrossRefGoogle Scholar
  33. Stalnaker, R. (2012). Mere possibilities: Metaphysical foundations of modal semantics. Princeton: Princeton University Press.Google Scholar
  34. van Inwagen, P. (2012). Three versions of the ontological argument. In M. Szatkowki (Ed.), Ontological proofs today. Berlin: DeGruyter.Google Scholar
  35. Vitali, G. (1905). Sul problema della misura dei gruppi di punti di una retta. Bologna: Tip. Gamberini e Parmeggiani.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Philosophy DepartmentNiagara UniversityLewistonUSA
  2. 2.Department of PhilosophyUniversity of Notre DameNotre DameUSA

Personalised recommendations