|Bilateralism based on corrective denial|
Assertion and Proof special issue
The standard notion of denial in the bilateralism literature is based on exclusion, in some sense, of the denied φ. I present a new variant of bilateralism based on a different, stronger notion of denial, not being excluding only, but also corrective. A corrective denial, while also excluding, points to an atomic incompatible alternative to the denied φ, the latter serving as the ground for the denial. An atomic incompatibility class is a finite set of atomic sentences with at least two elements, with the following intended interpretation: exactly one of its members can be asserted, provided all others are denied. The paper presents a bilateral natural-deduction proof-system for corrective denial, with connective-independent introduction and elimination rules. Rumfitt’s connective-dependent rules are derivable in my system.