The Elimination of Direct Self-reference

Studia Logica 111 (6):1037-1055 (2023)
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Abstract

This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘_m_-cycle unwinding’ of the original Boolean system for any positive integer _m_. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the _m_-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of a Boolean paradox, this paradox and its _m_-cycle unwinding have the same primary periods. In this way, we can produce an indirectly self-referential Boolean paradox with the same periodic characteristics as a known Boolean paradox.

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2023-08-03

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Author Profiles

Ming Hsiung
Zhongshan University
Qianli Zeng
LMU Munich

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References found in this work

Truth and paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Vagueness and Contradiction.Roy Sorensen - 2005 - Philosophy and Phenomenological Research 71 (3):695-703.
Notes on naive semantics.Hans Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
What Truth Depends on.Hannes Leitgeb - 2005 - Journal of Philosophical Logic 34 (2):155-192.
Patterns of paradox.Roy T. Cook - 2004 - Journal of Symbolic Logic 69 (3):767-774.

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