  Sylvan’s instrumental need for inconsistent worlds in order to account for implication led to tentative endorsement of the possibility of true contradictions (dialetheism). Most relevant logicians thought of these “worlds” merely as artefacts of the semantics, not as legitimate possibilities (indeed—they’re impossible!); but there the idea was, of “dialectical” or contradictory worlds. By (1976), he and Meyer consider a rather literal interpretation of Hegelian dialectic, and openly question the “Consistency Hypothesis” that the world is consistent. They urge instead a “dialectical” possibility. They present the (relevant) logic DL (for dialectical logic), and give it an axiomatization that explicitly includes an outright contradiction \(p \amp \twiddle p\) as an axiom. (Smiley calls this “Routley and Meyer’s war work” (Smiley and Priest 1993, 17). See also van Benthem 1979, Havas 1981.)