David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Notre Dame Journal of Formal Logic 30 (3):459-484 (1989)
Kalrnaric. We set out a system T, consisting of normal proofs constructed by means of elegantly symmetrical introduction and elimination rules. In the system T there are two requirements, called ( ) and ()), on applications of discharge rules. T is sound and complete for Kalmaric arguments. ( ) requires nonvacuous discharge of assumptions; ()) requires that the assumption discharged be the sole one available of highest degree. We then consider a 'Duhemian' extension T*, obtained simply by dropping the requirement ()). T* is a proper subsystem of intuitionistic relevant logic. Our main result is that T* is a double negation consistency companion to classical logic. Thus all one needs to add to T* to obtain classical logic is the (intuitionistic) absurdity rule, and the (classical) rule of double nega-
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By Neil Tennant (2005). Rule-Circularity and the Justification of Deduction. Philosophical Quarterly 55 (221):625–648.
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