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- W2185996974 abstract "Second order quantification is puzzling. The 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 com- plete, 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 to be a misnomer. It is not logic but set theory in sheep's clothing (7, page 66-68), so one would not expect to have a sound and complete axiomatisa- tion of the theory. I think that this judgement is incorrect, and in this paper I attempt to explain why. I show how on Nuel Belnap's criterion for logicality, order quan- tification can count as properly logic so-called, since the quantifiers are properly defined by their inference rules, and the addition of order quantification to a basic language is conservative. With this notion of logicality in hand I then diagnose the incompleteness of the proof theory of order logic in what seems to be a novel way." @default.
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- W2185996974 date "2008-01-01" @default.
- W2185996974 modified "2023-09-27" @default.
- W2185996974 title "Proof Theory and Meaning: on second order logic" @default.
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