Proof theory in the abstract

@article{Hyland2002ProofTI,
  title={Proof theory in the abstract},
  author={Martin Hyland},
  journal={Ann. Pure Appl. Logic},
  year={2002},
  volume={114},
  pages={43-78}
}
We are left in no doubt that proof theory as currently practised is essentially syntactic in nature. Indeed proof theory has been the poor relation of logic, at least partly for this very reason. So the reference to semantic motivation is tantalising and should give one pause. Reflecting on the notion of semantic motivation, one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one… CONTINUE READING

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