Hostname: page-component-7f64f4797f-pffzl Total loading time: 0 Render date: 2025-11-04T08:23:11.714Z Has data issue: false hasContentIssue false
  • English
  • Français

FORMAL REPRESENTATIONS OF DEPENDENCE AND GROUNDEDNESS

Published online by Cambridge University Press:  16 July 2019

EDOARDO RIVELLO
EDOARDO RIVELLO*
Affiliation:
Department of Philosophy and Educational Sciences, Università degli Studi di Torino
*
†DEPARTMENT OF PHILOSOPHY AND EDUCATIONAL SCIENCES UNIVERSITÀ DEGLI STUDI DI TORINO VIA SANT’OTTAVIO, 20 10124, TORINO, ITALY E-mail: edoardo.rivello@unito.it
Get access Rights & Permissions [Opens in a new window]

Abstract

We study, in an abstract and general framework, formal representations of dependence and groundedness which occur in semantic theories of truth. Our goals are (a) to relate the different ways in which groundedness is defined according to the way dependence is represented and (b) to represent different notions of dependence as instances of a suitable generalisation of the mathematical notion of functional dependence.

Keywords

Primary 03E20Secondary 03E75dependencegroundingmonotone operator

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 1 , March 2020 , pp. 105 - 140
Copyright
Copyright © Association for Symbolic Logic 2019 

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.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Aczel, P. (1977). An introduction to inductive definitions. In Barwise, J., editor. Handbook of Mathematical Logic. Amsterdam: North Holland, pp. 739–782.CrossRefGoogle Scholar
Beringer, T. & Schindler, T. (2016). Reference graphs and semantic paradox. In Arazim, P. and Dancak, M., editors. The Logica Yearbook 2015. London: College Publications, pp. 1–15.Google Scholar
Beringer, T. & Schindler, T. (2017). A graph-theoretic analysis of the semantic paradoxes. Bulletin of Symbolic Logic, 23 (4), 442–492.CrossRefGoogle Scholar
Bolander, T. (2002). Restricted truth predicates in first-order logic. In Childers, T. and Mayer, O., editors. The Logica Yearbook 2002. Prague: Philosophia Press, pp. 41–55.Google Scholar
Grelling, K. (1939). A logical theory of dependence. In 5th International Congress for the Unity of Science. Reprinted in: Smith, B., editor. Foundations of Gestalt Theory. Munich and Vienna: Philosophia, 1988.Google Scholar
Herzberger, H. (1970a). Paradoxes of grounding in semantics. The Journal of Philosophy, XVII, 145–167.CrossRefGoogle Scholar
Herzberger, H. G. (1970b). Erratum to: Paradoxes of grounding in semantics. The Journal of Philosophy, XVII, 317.Google Scholar
Kremer, P. (2009). Comparing fixed-point and revision theories of truth. Journal of Philosophical Logic, 38, 363–403.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.CrossRefGoogle Scholar
Leitgeb, H. (2005). What truth depends on. Journal of Philosophical Logic, 34, 155–192.CrossRefGoogle Scholar
Lévy, A. (1979). Basic Set Theory. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Rivello, E. (Forthcoming). Notes on the mathematical aspects of Leitgeb’s “What truth depends on”, submitted.Google Scholar
Väänänen, J. (2016). Grelling on dependence. In Abramsky, S., Kontinen, J., Väänänen, J., and Vollmer, H., editors. Dependence Logic: Theory and Applications. Cham: Birkhäuser, pp. 33–52.CrossRefGoogle Scholar
Yablo, S. (1982). Grounding, dependence and paradox. Journal of Philosophical Logic, 11, 117–137.CrossRefGoogle Scholar