# Against Naturalized Cognitive Propositions

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## Abstract

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.

## Notes

### Acknowledgments

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.

### References

- Arrigoni, T. (2011).
*V*=*L*and intuitive plausibility in set theory: A case study.*Bulletin of Symbolic Logic,**17*(3), 337–360.CrossRefGoogle Scholar - 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 - Benacerraf, P., & Putnam, H. (1983).
*Philosophy of mathematics: Selected readings*(2nd ed.). Cambridge: Cambridge UP.Google Scholar - Bernays, P. (1935). Sur le platonisme dans les mathématiques.
*L’Enseignement Mathématique,**34*, 52–69.Google Scholar - Crane, T. (2011). The singularity of singular thought. In
*Proceedings of the aristotelian society supplementary volume*(Vol. LXXXV).Google Scholar - Crosilla, L. (2014). Set theory: Constructive and intuitionistic ZF. In E. N. Zalta (Ed.),
*The stanford encyclopedia of philosophy*. http://plato.stanford.edu/archives/sum2015/entries/set-theory-constructive/. (Summer 2015 Edition) - Davis, W. (2002).
*Meaning, expression, and thought*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Feferman, S. (2000). Mathematical intuition versus mathematical monsters.
*Synthese,**125*, 317–332.CrossRefGoogle Scholar - Ferreirós, J. (2011). On arbitrary sets and ZFC.
*The Bulletin of Symbolic Logic,**17*(3), 361–393.CrossRefGoogle Scholar - Gödel, K. (1944). Russell’s mathematical logic. In P. Benacerraf & H. Putnam (Eds.),
*Philosophy of mathematics: Selected readings*, 1983.Google Scholar - Hanks, P. (2007). The content-force distinction.
*Philosophical Studies,**134*(2), 141–164.CrossRefGoogle Scholar - Hawthorne, J., & Manley, D. (2012).
*The reference book*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Jeshion, R. (2010).
*New essays on singular thought*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Kaplan, D. (1978). Dthat. In P. Cole (Ed.),
*Syntax and semantics*(Vol. 9, pp. 221–243). New York: Academic Press.Google Scholar - Keller, L. J. Forthcoming. Propositions supernaturalized. In T. Dougherty & J. Walls (eds.),
*Two dozen (or so) arguments for God*. Oxford University Press.Google Scholar - King, J. (2007).
*The nature and structure of content*. Oxford: Oxford University Press.CrossRefGoogle Scholar - King, J. (2013). Propositional unity: What’s the problem, who has it, and who solves it?
*Philosophical Studies,**165*(1), 71–93.CrossRefGoogle Scholar - Kripke, S. (1980).
*Naming and necessity*. Cambridge: Harvard University Press.Google Scholar - Lewis, D. (1986). A comment on armstrong and forrest.
*Australasian Journal of Philosophy,**64*(1986), 92–93.CrossRefGoogle Scholar - Maddy, P. (1997).
*Naturalism in mathematics*. Oxford: Clarendon Press.Google Scholar - Plantinga, A. (1961). A valid ontological argument?
*Philosophical Review, 70*, 93–101.CrossRefGoogle Scholar - Richard, M. (2013). What are propositions?
*Canadian Journal of Philosophy,**43*, 702–719.CrossRefGoogle Scholar - Russell, B. (1903).
*Principles of mathematics*. Cambridge: Cambridge University Press.Google Scholar - Smolin, L. (2014). Atoms of space and time.
*Scientific American, 23*, 94–103.Google Scholar - Soames, S. (1989). Semantics and semantic competence.
*Philosophical Perspectives,**3*, 575–596.CrossRefGoogle Scholar - Soames, S. (1995). Beyond singular propositions?
*Canadian Journal of Philosophy,**25*(4), 514–549.CrossRefGoogle Scholar - Soames, S. (2010).
*What is meaning?*. Princeton: Princeton University Press.CrossRefGoogle Scholar - Soames, S. (2013). Cognitive propositions.
*Philosophical Perspectives: Philosophy of Language,**27*, 1–23.CrossRefGoogle Scholar - Soames, S. (2015).
*Rethinking language, mind, and meaning*. Princeton: Princeton University Press.CrossRefGoogle Scholar - Soames, S., King, J., & Speaks, J. (2014).
*New thinking about propositions*. Oxford: OUP.Google Scholar - 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 - Stalnaker, R. (2012).
*Mere possibilities: Metaphysical foundations of modal semantics*. Princeton: Princeton University Press.Google Scholar - van Inwagen, P. (2012). Three versions of the ontological argument. In M. Szatkowki (Ed.),
*Ontological proofs today*. Berlin: DeGruyter.Google Scholar - Vitali, G. (1905).
*Sul problema della misura dei gruppi di punti di una retta*. Bologna: Tip. Gamberini e Parmeggiani.Google Scholar