Porter (2023) [Three essays on substructural approaches to semantic paradoxes [PhD thesis]. City University of New York, New York, USA. https://academicworks.cuny.edu/gc_etds/5144/] has presented higher-level metainferential versions of the validity Curry argument introduced by Beall and Murzi (2013) [Two flavours of curry paradox. Journal of Philosophy, 110(3), 143–65]. What is peculiar of these paradoxes is that no operational rule nor any structural rule play any role in the derivation of the unpleasant result. Thus, to block them and have a uniform solution to, at least, every validity Curry paradox, something else needs to be done. We introduce, as an answer to Porter's challenge, validity theories that are substructural at every metainferential level. In this sense, they are free from Porter's criticism. These theories count as both theories of naïve validity (because they do not give up V P or V D, nor any higher-level version of them) and as offering a uniform solution to validity curries, in the more traditional and intuitive sense: either they give up every higher-level version of Cut – as well as every higher-level version of it – or they give up Contraction – as well as every higher-level version of it. Finally, we provide philosophical justifications for each of these options.
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