Korean Journal of Logic 1 (24):1-30 (2021)

Abstract
In his paper, “On paradox without self-reference”, Neil Tennant proposed the conjecture for self-referential paradoxes that any derivation formalizing self-referential paradoxes only generates a looping reduction sequence. According to him, the derivation of the Liar paradox in natural deduction initiates a looping reduction sequence and the derivation of the Yablo's paradox generates a spiral reduction. The present paper proposes the counterexample to Tennant's conjecture for self-referential paradoxes. We shall show that there is a derivation of the Liar paradox which generates a spiraling reduction procedure. Since the Liar paradox is a self-referential paradox, the result is a counterexample to his conjecture. Tennant has believed that classical reductio has no essential role to formalize paradoxes. As our counterexample applies the rule of classical reductio, he may reject the counterexample. In this sense, it will be briefly argued that classical reductio and his rules for the liar sentence share some inferential role. If classical reductio should not be used in paradoxical reasoning, neither should be his rules for the liar sentence.
Keywords The liar paradox  yablo's paradox  neil tennant   Gunnar Stålmarck   Classical reductio  Self-reference
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
Logic and Structure.D. van Dalen - 1980 - Springer Verlag.
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1975 - Journal of Symbolic Logic 40 (2):232-234.
Core Logic.Neil Tennant - 2017 - Oxford, England: Oxford University Press.

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