Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T19:35:30.639Z Has data issue: false hasContentIssue false

TRUTH AND SPEED-UP

Published online by Cambridge University Press:  16 April 2014

MARTIN FISCHER*
Affiliation:
Mathematical Center for Mathematical Philosophy, Ludwig-Maximilians-University Munich
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITY 80539 MUNICH, GERMANY E-mail: [email protected]

Abstract

In this paper, we investigate the phenomenon of speed-up in the context of theories of truth. We focus on axiomatic theories of truth extending Peano arithmetic. We are particularly interested on whether conservative extensions of PA have speed-up and on how this relates to a deflationist account. We show that disquotational theories have no significant speed-up, in contrast to some compositional theories, and we briefly assess the philosophical implications of these results.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Boolos, G. S. (1984). Don’t eliminate cut. Journal of Philosophical Logic, 13, 373378.Google Scholar
Burgess, J. P. (2005). Fixing Frege. Princeton, NJ: Princeton University Press.Google Scholar
Buss, S. R. (1994). On Gödel’s theorems on length of proofs I: Number of lines and speedup for arithmetics. The Journal of Symbolic Logic, 59(3), 737756.CrossRefGoogle Scholar
Caldon, P., & Ignjatović, A. (2005). On mathematical instrumentalism. Journal of Symbolic Logic, 70(3), 778794.Google Scholar
Cantini, A. (1989). Notes on formal theories of truth. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 35, 97130.Google Scholar
Enayat, A., & Visser, A. (2014). New constructions of satisfaction classes. In Achourioti, T.,Galinon, H., Fujimoto, K., and Martínez-Fernández, J., editors. Unifying the Philosophy of Truth. Berlin: Springer.Google Scholar
Fujimoto, K. (2010). Relative truth definability of axiomatic truth theories. Bulletin of Symbolic Logic, 16(3), 305344.Google Scholar
Gödel, K. (1936). Über die Länge von Beweisen. In Ergebnisse eines mathematischen Kolloquiums, pp. 2324. Reprinted in Feferman, Dawson, S., Kleene, J., Moore, S., Solovay, G., R., and Heijenoort, J., editors. Kurt Gödel: Collected Works, Vol. I. Publications 1929–1936. Oxford: Oxford University Press.Google Scholar
Gupta, A. (1993). A critique of deflationism. Philosophical Topics, 21(1), 5781.Google Scholar
Hájek, P., & Pudlák, P. (1993). Metamathematics of First-Order Arithmetic. Berlin: Springer Verlag.Google Scholar
Halbach, V. (1999). Disquotationalism and infinite conjunctions. Mind, 108, 122.Google Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge, UK: Cambridge University Press.Google Scholar
Heck, R. G. (2009). The strength of truth-theories. draft.Google Scholar
Horsten, L. (1995). The semantical paradoxes, the neutrality of truth, and the neutrality of the minimalist theory of truth. In Cortois, P., editor. The Many Problems of Realism, Tilburg: Tilburg University Press, pp. 173187.Google Scholar
Horsten, L. (2011). The Tarskian Turn. Deflationism and Axiomatic Truth. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Horwich, P. (1998). Truth (second edition). Oxford, UK: Clarendon Press.Google Scholar
Ketland, J. (1999). Deflationism and Tarski’s paradise. Mind, 108, 6994.Google Scholar
Kotlarski, H., Krajewski, S., & Lachlan, A. (1981). Construction of satisfaction classes for non-standard models. Canadian Mathematical Bulletin, 24, 283293.Google Scholar
Leigh, G. E. (2013). Conservativity for theories of compositional truth via cut elimination. arXiv:1308.0168 [math.LO].Google Scholar
Leitgeb, H. (2007). What theories of truth should be like (but cannot be). Philosophy Compass, 2(2), 276290.Google Scholar
McGee, V. (1992). Maximal consistent sets of instances of Tarski’s schema (T). The Journal of Philosophical Logic, 21, 235241.Google Scholar
Paris, J., & Dimitracopoulos, C. (1983). A note on the undefinability of cuts. The Journal of Symbolic Logic, 48(3), 564569.Google Scholar
Pudlák, P. (1985). Cuts, consistency statements and interpretations. The Journal of Symbolic Logic, 50, 423441.CrossRefGoogle Scholar
Pudlák, P. (1998). The lengths of proofs. In Buss, S. R., editor. Handbook of Proof Theory, Chapter VIII, Amsterdam, Netherlands: Elsevier Science Publisher. pp. 547637.CrossRefGoogle Scholar
Pudlák, P. (2013). Logical Foundations of Mathematics and Computational Complexity. London: Springer.Google Scholar
Quine, W. V. O. (1970). Philosophy of Logic. Cambridge, MA: Harvard University Press.Google Scholar
Shapiro, S. (1998). Proof and truth: Through thick and thin. The Journal of Philosophy, 95, 493521.Google Scholar
Tarski, A., Mostowski, A., & Robinson, R. (1953). Undecidable Theories. Amsterdam, Netherlands: North-Holland Publishing Company.Google Scholar