Assertoric Semantics and the Computational Power of Self-Referential Truth
There is no consensus as to whether a Liar sentence is meaningful or not. Still, a widespread conviction with respect to Liar sentences (and other ungrounded sentences) is that, whether or not they are meaningful, they are useless. The philosophical contribution of this paper is to put this conviction into question. Using the framework of assertoric semantics, which is a semantic valuation method for languages of self-referential truth that has been developed by the author, we show that certain computational problems, called query structures, can be solved more efficiently by an agent who has self-referential resources (amongst which are Liar sentences) than by an agent who has only classical resources; we establish the computational power of self-referential truth. The paper concludes with some thoughts on the implications of the established result for deflationary accounts of truth.
KeywordsSelf-referential truth Liar paradox Inferential semantics Information retrieval
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- 1.Belnap, N. (1977). A useful four-valued logic. In J. Dunn & G. Epstein (Eds.), Modern uses of multiple-valued logic.Google Scholar
- 2.de Wolf, R. (2001). Quantum computing and communication complexity. PhD thesis, ILLC dissertation series.Google Scholar
- 3.Grover, D. (2005). How significant is the liar. In J. Beall & B. Armour-Garb (Eds.), Deflationsim and paradox.Google Scholar
- 4.Grover, L. (1996). A fast quantum mechanical algorithm for database search. In Proceedings, 28th annual ACM symposium on the theory of computing.Google Scholar
- 6.Horwich, P. (1999). Truth (2nd ed.). Oxford University Press.Google Scholar
- 8.Nielsen, M., & Chang, I. (2000). Quantum computation and quantum information. Cambridge University Press.Google Scholar
- 9.Rabern, B., & Rabern, L. (2008). A simple solution to the hardest logic puzzle ever. Analysis, 68, 105–112.Google Scholar
- 10.Smullyan, R. (1995). First-order Logic. Dover, New York.Google Scholar
- 11.Wittgenstein, L. (1939). In C. Diamond (Ed.), Lectures on the foundations of mathematics, Cambridge 1939. Hassocks: Harvestor.Google Scholar