There is a Logical Negation

"Yes," "No," Both, and Neither

Abstract

Jc Beall agues that if FDE is logic proper, then there is no logical negation. This claim is largely based on the fact that, in standard proof systems for FDE, there are no stand-alone negation rules that suffice to capture the behavior of negation. In this paper, I show that by adopting a bilateral proof system for FDE, one can maintain that there is a logical negation, it is the very same logical negation that belongs to classical logic, and its basic function is to flip-flop between assertion and denial. I conclude by responding to the objection that it can never be coherent to both assert and deny the very same thing.