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The Elimination of Direct Self-reference

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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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Authors and Affiliations

  1. School of Philosophy and Social Development, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Qianli Zeng & Ming Hsiung

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  1. Qianli Zeng
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  2. Ming Hsiung
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Correspondence to Ming Hsiung.

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Zeng, Q., Hsiung, M. The Elimination of Direct Self-reference. Stud Logica 111, 1037–1055 (2023). https://doi.org/10.1007/s11225-023-10060-7

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