Depicting Negation in Diagrammatic Logic: Legacy and Prospects

Abstract

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: to review the basic concepts involved in the definition of logical negation; to account for a variety of epistemological obstacles against the introduction of non-classical negations within diagrammatic logic. It will be mainly argued that non-classical logics don’t challenge dichotomy as such but merely show that a logical operator may be a negation without operating as a dichotomy.