Conservatively Extending Classical Logic with Transparent Truth

@article{Ripley2012ConservativelyEC,
  title={Conservatively Extending Classical Logic with Transparent Truth},
  author={David Ripley},
  journal={Rew. Symb. Logic},
  year={2012},
  volume={5},
  pages={354-378}
}
This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth-involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and… CONTINUE READING

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