The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon

1 Aristotelian versus Duality Square (1) Piaget (1949) inversion réciprocation corrélation Gottschalk (1953) complement contradual dual Löbner (1990) negation (NEG) subnegation (SNEG) dual (DUAL) Westerstahl (2010) outer negation inner negation dual Quantifier (domain/restrictor, predicate/nuclear scope) 2-place second-order predicates All (children , be asleep) <,,t> (3) All children are asleep = No children are awake/are not asleep. No children are asleep = All children are awake/are not asleep. Some children are asleep = Not all children are awake/are not asleep. Not all children are asleep = Some children are awake/are not asleep. (4) All children are asleep = It is not the case that some children are awake/are not asleep. Some children are asleep = It is not the case that all children are awake/are not asleep. Not all children are asleep = It is not the case that no children are awake/are not asleep. No children are asleep = It is not the case that not all children are awake/are not asleep.