We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or (equivalently) initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi : we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.
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We wish to thank an anonymous reviewer for helpful comments on a previous draft as well as the FWF (project number 29716-G24) for generous financial support.
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Murzi, J., Rossi, L. Non-reflexivity and Revenge. J Philos Logic 51, 201–218 (2022). https://doi.org/10.1007/s10992-021-09625-5
- Liar paradox
- Curry’s Paradox
- Validity Curry
- Non-reflexive logics