Periodicity and Reflexivity in Revision Sequences

Studia Logica 103 (6):1279-1302 (2015)
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Abstract

Revision sequences were introduced in 1982 by Herzberger and Gupta as a mathematical tool in formalising their respective theories of truth. Since then, revision has developed in a method of analysis of theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so-called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurring hypothesis and draw from this fact some observations about the problem of choosing the “right” limit rule when performing a revision-theoretic analysis.

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Edoardo Rivello
Università di Torino

Citations of this work

Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
Designing Paradoxes: A Revision-theoretic Approach.Ming Hsiung - 2022 - Journal of Philosophical Logic 51 (4):739-789.

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References found in this work

Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Notes on Naive Semantics.Hans Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
Gupta's Rule of Revision Theory of Truth.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (1):103-116.
Naive Semantics and the Liar Paradox.Hans G. Herzberger - 1982 - Journal of Philosophy 79 (9):479-497.
Ultimate Truth Vis- À- Vis Stable Truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.

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