Are there ‘self-referential’ propositions? That is, propositions that say of themselves that they have a certain property, such as that of being false. There can seem reason to doubt that there are. At the same time, there are a number of reasons why it matters. For suppose that there are indeed no such propositions. One might then hope that while paradoxes such as the Liar show that many plausible principles about sentences must be given up, no such fate will befall principles about propositions. But the existence of self-referential propositions would dash such hopes. Further, the existence of such propositions would also seem to challenge the widespread claim that Liar sentences fail to express propositions. The aim of this paper is thus to settle the question–at least given an assumption. In particular, I argue that if propositions are structured, then self-referential propositions exist.
KeywordsSelf-referential propositions Paradoxes for propositions Truth The liar paradox
For comments and discussion, I am grateful to Andrew Bacon, Agustín Rayo, Ian Rumfitt, Zoltán Szabó, an audience at the 2014 Eastern APA, and two referees for this journal.
- Aczel, P. (1988). Non-well-founded sets. Stanford: CSLI Publications.Google Scholar
- Barwise, J., & Etchemendy, J. (1987). The liar: An essay on truth and circularity. New York: Oxford University Press.Google Scholar
- Gaifman, H. (2000). Pointers to propositions. In A. Chapuis & A. Gupta (Eds.), Circularity, definition, and truth (pp. 79–121). New Delhi: Indian Council of Philosophical Research.Google Scholar
- Gupta, A., & Belnap, N. (1993). The revision theory of truth. Cambridge, MA: MIT Press.Google Scholar
- Kaplan, D. (1989). Demonstratives: An essay on the semantics, logic, metaphysics, and epistemology of demonstratives and other indexicals. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan (pp. 481–563). New York: Oxford University Press.Google Scholar
- McGee, V. (1991). Truth, vagueness, and paradox: An essay on the logic of truth. Indianapolis: Hackett.Google Scholar
- Priest, G. (1987/2006). In Contradiction (2nd ed.). Oxford: Clarendon Press.Google Scholar
- Salmon, N. (1986). Frege’s puzzle. Cambridge, MA: MIT Press.Google Scholar
- Skyrms, B. (1984). Intensional aspects of self-reference. In R. L. Martin (Ed.), Recent essays on truth and the liar paradox (pp. 119–131). Oxford: Clarendon Press.Google Scholar
- Soames, S. (2010). What is meaning? Princeton: Princeton University Press.Google Scholar
- Tarski, A. (1935). The concept of truth in formalized languages In his J. Corcoran (Ed.) Logic, semantics, metamathematics: Papers from 1923 to 1938, 1983. 2nd edn. (pp. 152–267) (J. H. Woodger trans.). Indianapolis: Hackett.Google Scholar