Skip to main content
×
Home

EQUIVALENCES FOR TRUTH PREDICATES

  • CARLO NICOLAI (a1)
Abstract
Abstract

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension.

Copyright
Corresponding author
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL PLATZ 1, MUNICH GERMANY E-mail: Carlo.Nicolai@lrz.uni-muenchen.de
References
Hide All
Cantini A. (1989). Notes on formal theories of truth. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 35, 97130.
Cieśliński C. (2010). Truth, conservativeness, and provability. Mind, 474, 409422.
Davidson D. (1984). Inquiries into Truth and Interpretation. Oxford: Oxford University Press.
Enayat A. & Visser A. (2015). New constructions of satisfaction classes. In Achourioti D., Fernández J. M., Galinon H., and Fujimoto K., editors. Unifying the Philosophy of Truth. Netherlands: Springer, pp. 321335.
Enayat A., Schmerl J. H., & Visser A. (2010). ω-models of finite set theory. In Kennedy J. and Kossak R., editors. Set theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Lecture Notes in Logic, Vol. 36. La Jolla, CA: Association for Symbolic Logic, 2010, pp. 4365.
Feferman S. (1960). Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae, 49(1), 3592.
Feferman S. (1964). Systems of predicative analysis. The Journal of Symbolic Logic, 29(1), 130.
Feferman S. (1991). Reflecting on incompleteness. The Journal of Symbolic Logic, 56, 149.
Feferman S. (1998). What rests on what? The proof-theoretic analysis of mathematics. In Feferman S., editor. In the Light of Logic. Oxford: Oxford University Press, pp. 187208.
Field H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.
Fischer M. (2009). Minimal truth and interpretability. The Review of Symbolic Logic, 2(4), 799815.
Fischer M., Halbach V., Kriener J. & Stern J. (2015). Axiomatizing semantic theories of truth? The Review of Symbolic Logic, 8(2), 257278.
Friedman H. & Sheard M. (1987). An axiomatic approach to self-referential truth. Annals of Pure and Applied Logic, 33, 121.
Friedman H. & Visser A. (2014). When Bi-Interpretability Implies Synonymy. Logic Group Preprint Series. University of Utrecht.
Fujimoto K. (2010). Relative truth definability of axiomatic truth theories. The Bulletin of Symbolic Logic, 16(3), 305344.
Hájek P. & Pudlák P. (1998). Metamathematics of First-Order Arithmetic. Berlin: Springer.
Halbach V. (1999). Disquotationalism and infinite conjunctions. Mind, 108, 122.
Halbach V. (2009). Reducing compositional to disquotational truth. The Review of Symbolic Logic, 2, 786798.
Halbach L. (2014). Axiomatic Theories of Truth (revised edition). Cambridge: Cambridge University Press.
Halbach V. & Horsten L. (2015). Norms for theories of reflexive truth. In Achourioti D., Fernández J. M., Galinon H. and Fujimoto K., editors. Unifying the Philosophy of Truth. Netherlands: Springer, pp. 263280.
Heck R. (2015). Consistency and the theory of truth. The Review of Symbolic Logic, 8(3), 424466.
Horsten L. (2011). The Tarskian Turn: Deflationism and Axiomatic Truth. Cambridge, MA: MIT Press.
Kaye R. & Wong T. L. (2007). On interpretations of arithmetic and set theory. Notre Dame Journal of Formal Logic, 48(4), 497510.
Kripke S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690712.
Laurence S. & Margolis E. (1999). Concepts: Core Readings. Cambridge, MA: MIT Press.
Leigh G. E. (2015). Conservativity for theories of compositional truth via cut elimination. The Journal of Symbolic Logic, 80(3), 825865.
Leigh G. & Nicolai C. (2013). Axiomatic truth, syntax, metatheoretic reasoning. The Review of Symbolic Logic, 6(4), 613636.
Leitgeb H. (2007). What theories of truth should be like (but cannot be). Blackwell Philosophy Compass 2. Blackwell, pp. 276290.
Lutz S. (2016). What was the syntax-semantics debate in the philosophy of science about? Philosophy and Phenomenological Research, forthcoming, doi: 10.1111/phpr.12221.
Nicolai C. (2016a). A note on typed truth and consistency assertions. Journal of Philosophical Logic, 45(1), 89119.
Nicolai C. (2016b). More on systems of truth and predicative comprehension. In Boccuni F. and Sereni A., editors. Philosophy of Mathematics: Objectivity, Cognition and Proof. Boston Studies in the History and Philosophy of Science, Netherlands: Springer.
Rogers H. (1987). Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press.
Schwichtenberg H. & Wainer S. (2011). Proofs and Computations. ASL Lecture Notes Series. Cambridge: Cambridge University Press.
Simpson S. G. (2009). Subsystems of Second-Order Arithmetic. Cambridge: Cambridge University Press.
Smorynski C. (1977). The incompleteness theorems. In Barwise J., editor. Handbook of Mathematical Logic. Amsterdam: North Holland, pp. 821865.
Takeuti G. (1987). Proof Theory (second edition). Amsterdam: North-Holland.
Visser A. (1991). The formalization of interpretability. Studia Logica, 50(1), 81105.
Visser A. (1992). An inside view of Exp. The Journal of Symbolic Logic, 57(1), 131165.
Visser A. (1997). An overview of interpretability logic. In Kracht M., de Rijke M., and Wansing H. editors. Advances in Modal Logic ’96. Stanford, CA: CSLI Publications, pp. 307359.
Visser A. (2006). Categories of theories and interpretations. In Enayat A., Kalantari I., and Moniri M., editors. Logic in Tehran, Vol. 26. Lecture Notes in Logic, La Jolla, CA: Association for Symbolic Logic, pp. 284341.
Visser A. (2015). The interpretability of inconsistency: Feferman’s theorem and related results. Forthcoming in the Bulletin of Symbolic Logic.
Woodfield A. (1991). Conceptions Mind , 100(4), 547572.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 43 *
Loading metrics...

Abstract views

Total abstract views: 277 *
Loading metrics...

* Views captured on Cambridge Core between 19th January 2017 - 22nd November 2017. This data will be updated every 24 hours.