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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.

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A Cantini . (1989). Notes on formal theories of truth. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 35, 97130.

A. Enayat & A Visser . (2015). New constructions of satisfaction classes. In D. Achourioti , J. M. Fernández , H. Galinon , and K. Fujimoto , editors. Unifying the Philosophy of Truth. Netherlands: Springer, pp. 321335.

S Feferman . (1964). Systems of predicative analysis. The Journal of Symbolic Logic, 29(1), 130.

S Feferman . (1991). Reflecting on incompleteness. The Journal of Symbolic Logic, 56, 149.

H Field . (2008). Saving Truth from Paradox. Oxford: Oxford University Press.

M Fischer . (2009). Minimal truth and interpretability. The Review of Symbolic Logic, 2(4), 799815.

M. Fischer , V. Halbach , J. Kriener & J Stern . (2015). Axiomatizing semantic theories of truth? The Review of Symbolic Logic, 8(2), 257278.

H. Friedman & M Sheard . (1987). An axiomatic approach to self-referential truth. Annals of Pure and Applied Logic, 33, 121.

K Fujimoto . (2010). Relative truth definability of axiomatic truth theories. The Bulletin of Symbolic Logic, 16(3), 305344.

V Halbach . (1999). Disquotationalism and infinite conjunctions. Mind, 108, 122.

V Halbach . (2009). Reducing compositional to disquotational truth. The Review of Symbolic Logic, 2, 786798.

L Halbach . (2014). Axiomatic Theories of Truth (revised edition). Cambridge: Cambridge University Press.

V. Halbach & L Horsten . (2015). Norms for theories of reflexive truth. In D. Achourioti , J. M. Fernández , H. Galinon and K. Fujimoto , editors. Unifying the Philosophy of Truth. Netherlands: Springer, pp. 263280.

R Heck . (2015). Consistency and the theory of truth. The Review of Symbolic Logic, 8(3), 424466.

L Horsten . (2011). The Tarskian Turn: Deflationism and Axiomatic Truth. Cambridge, MA: MIT Press.

R. Kaye & T. L Wong . (2007). On interpretations of arithmetic and set theory. Notre Dame Journal of Formal Logic, 48(4), 497510.

S Kripke . (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690712.

G. E Leigh . (2015). Conservativity for theories of compositional truth via cut elimination. The Journal of Symbolic Logic, 80(3), 825865.

G. Leigh & C Nicolai . (2013). Axiomatic truth, syntax, metatheoretic reasoning. The Review of Symbolic Logic, 6(4), 613636.

H Leitgeb . (2007). What theories of truth should be like (but cannot be). Blackwell Philosophy Compass 2. Blackwell, pp. 276290.

C Nicolai . (2016a). A note on typed truth and consistency assertions. Journal of Philosophical Logic, 45(1), 89119.

H. Schwichtenberg & S Wainer . (2011). Proofs and Computations. ASL Lecture Notes Series. Cambridge: Cambridge University Press.

S. G Simpson . (2009). Subsystems of Second-Order Arithmetic. Cambridge: Cambridge University Press.

C Smorynski . (1977). The incompleteness theorems. In J. Barwise , editor. Handbook of Mathematical Logic. Amsterdam: North Holland, pp. 821865.

A Visser . (1991). The formalization of interpretability. Studia Logica, 50(1), 81105.

A Visser . (1992). An inside view of Exp. The Journal of Symbolic Logic, 57(1), 131165.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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