proof theory and meaning : on second order logic

  title={proof theory and meaning : on second order logic},
  author={Greg Restall},
Second order quantification is puzzling. The second order quantifiers have natural and compelling inference rules, and they also have natural models. These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real problem, since they take “second order logic” to be a misnomer. It is not logic but set theory in sheep’s clothing [7, page 66–68], so one would not… CONTINUE READING
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