Neoclassical logic, cloisonnist vagueness, nonobjectual truth

Abstract

In a series of works, Alan Weir has suggested that the paradoxes are due not so much to the operational principles of classical logic, but to some of its structural principles. Weir’s insightful suggestion has opened up the programme of developing a system that, while validating the principles of naive truth (or of naive vagueness), preserves the classical essence of the logical operations and remains coherent by denying instead, in a philosophically motivated way, some of the classical structural principles. This paper first presents Weir’s logical system and argues that it does not adequately preserve operational classicism. The paper then presents Weir’s nontransitive system of vagueness and argues that it does not adequately preserve naive vagueness. The paper finally presents Weir’s nontransitive system of truth and argues that it does not adequately preserve naive truth. As a contrast, the paper mentions how these shortcomings are overcome by my favoured nontransitive system of vagueness and by my favoured noncontractive system of truth.