Capturing naive validity in the Cut-free approach

@article{Barrio2016CapturingNV,
  title={Capturing naive validity in the Cut-free approach},
  author={Eduardo Barrio and Lucas Rosenblatt and Diego Tajer},
  journal={Synthese},
  year={2016},
  pages={1-17}
}
Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized… CONTINUE READING

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