Synthese:1-15 (forthcoming)

Zach Weber
University of Otago
Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive theory is to be genuinely closed, then it must be free of all contraction, even in the metatheory.
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DOI 10.1007/s11229-016-1226-6
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