Abstract
In Hannes Leitgeb’s article What truth depends on (Leitgeb in J Philos Logic 34:155–192, 2005) the author provides a formally correct and materially adequate truth definition for the set of all grounded sentences, defined as the least fixed point of a monotone operator of semantic dependence. In this paper we will focus on the mathematical aspects of Leitgeb’s notions of dependence, grounding and truth, recasting Leitgeb’s construction in a functional setting in which we establish some new facts about these notions.
Similar content being viewed by others
References
Aczel, P., An introduction to inductive definitions, in J. Barwise, (ed.), Handbook of Mathematical Logic, North Holland, 1977, pp. 739–782.
Beringer, T., and T. Schindler, Reference graphs and semantic paradox, in P. Arazim, and M. Dancak, (eds.), The Logica Yearbook 2015, College Publications, London, 2016, pp. 1–15.
Beringer, T., and T. Schindler, A graph-theoretic analysis of the semantic paradoxes, Bulletin of Symbolic Logic 23(4): 442–492, 2017.
Bolander, T., Restricted truth predicates in first-order logic, in T. Childers, and O. Mayer, (eds.), The Logica Yearbook 2002, Philosophia Press, Prague, 2002, pp. 41–55.
Bonnay, D., and F. T. van Vugt, Groundedness, truth and dependence, in T. Achourioti, et al., (eds.), Unifying the Philosophy of Truth, Springer, 2015, pp. 355–368.
Cantini, A., A theory of formal truth arithmetically equivalent to ID\(_{1}\), Journal of Symbolic Logic 55: 244–259, 1990.
Gupta, A., Truth and paradox, Journal of Philosophical Logic 11(1): 1–60, 1982.
Hsiung, M., What paradoxes depend on, Synthese, https://doi.org/10.1007/s11229-018-1748-1 (2018). In print.
Kripke, S., Outline of a theory of truth, Journal of Philosophy 72: 690–716, 1975.
Leitgeb, H., What truth depends on, Journal of Philosophical Logic 34: 155–192, 2005.
Leitgeb, H., On the probabilistic convention T, Review of Symbolic Logic 1: 218–224, 2008.
Lévy, A., Basic Set Theory, Springer-Verlag, Berlin, 1979.
Meadows, T., Truth, dependence and supervaluation: Living with the ghost, Journal of Philosophical Logic 42(2): 221–240, 2013.
Rivello, E., Formal representations of dependence and groundedness, The Review of Symbolic Logic, https://doi.org/10.1017/S1755020319000315 (2019). In print.
Rivello, E., Generalising Montague’s theorem on recursive definitions, (n.d.). Submitted.
Schindler, T., Axioms for grounded truth, Review of Symbolic Logic 7(1): 73–83, 2014.
Speranski, S. O., Notes on the computational aspects of Kripke’s theory of truth, Studia Logica 105(2): 407–429, 2017.
Väänänen, J., Grelling on dependence, in S. Abramsky, J. Kontinen, J. Väänänen, and H. Vollmer, (eds.), Dependence Logic: Theory and Applications, Birkhäuser, 2016, pp. 33–52.
Visser, A., Semantics and the Liar paradox, in D. Gabbay, and F. Guenthner, (eds.), Handbook of Philosophical Logic, vol. 10, Kluwer Academic Publishers, The Netherlands, 2002, pp. 159–245.
Welch, P. D., The complexity of the dependence operator, The Journal of Philosophical Logic 44: 337–340, 2015.
Yablo, S., Grounding, dependence and paradox, Journal of Philosophical Logic 11: 117–137, 1982.
Acknowledgements
Parts of this article were presented at the workshop on “Formal truth theories” held in Warsaw in September 2017: I wish to thank both the organisers and the audience of this event. I am also indebted to Martin Fischer for suggesting me a refinement of an older version of Theorem 4.11.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rivello, E. Notes on Leitgeb’s What Truth Depends on. Stud Logica 108, 1235–1262 (2020). https://doi.org/10.1007/s11225-019-09895-w
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-019-09895-w