NEGATION IN PHILOSOPHICAL LOGIC

In this talk I will survey various conceptions of negation as a unary sentential operator that have been discussed in philosophical logic. The main focus will be on negation as a modal operator, with a special emphasis on work by Michael Dunn. The central idea is to analyze negation in terms of a notion of incompatibility or orthogonality, leading to the notions of negation as impossibility and negation as unnecessity. Other conceptions to be presented are negation as the Routley star, negation as inconsistency, negation as contradictoriness, negation as falsity, negation as cancellation, and ?perfect negation?

Finally, I will make some comments on negation, rejection, and denial.

FALSIFICATION, NATURAL DEDUCTION, AND BI-INTUITIONISTIC LOGIC

A kind of a bi-intuitionistic propositional logic is introduced that combines verification and its dual. This logic, 2Int, is motivated by a certain dualization of the natural deduction rules for intuitionistic propositional logic, Int. It is shown that 2Int can be faithfully embedded into Int with respect to validity.

Moreover, 2Int can be faithfully embedded into dual intuitionistic logic, DualInt, with respect to a notion of dual validity. In 2Int, from a falsificationist perspective, intuitionistic negation internalizes support of truth, whereas from the verificationist perspective, co-negation internalizes support of falsity.