‘Neither–Nor’ Statements and ‘Neither–Nor’ States

Abstract

Most claims for the falsification of the Law of the Excluded Middle (LEM) rest on confusion or can be circumvented. A few of them, however, cannot. I concentrate on two of those, (a) cases involving conflicting criteria(border line cases) and (b) cases imposed by quantum discontinuity(no real state admitted between any two consecutive states). Nevertheless, despite the authenticity of both, closer analysis reveals these two modes of violating LEM to be direct opposites In (a) LEM fails in the relation between language and the world, and not in the world when viewed independently of this relation; in (b) LEM fails in the world itself, if at all. In (a) LEM fails because the Law of Non-Contradiction fails first (mutually exclusive classifications are equally warranted). But in (b) LEM fails because The Law of Non-Contradiction holds and not otherwise Finally, ‘a statement is neither true nor false’ and ‘two contradictory assertions are both false’ should be equivalent ways of expressing LEM’s failure. Howev...