While the traditional Square of Opposition was based on Aristotle’s logic, its first appearance postdates the Stagyrite by five centuries. In the Prior Analytics I, Aristotle himself lays out a somewhat different square, which I dub the Singular Square, to formalize his treatment of the interrelation of singular statements (it’s good, it isn’t good, it’s not-good, it isn’t not-good). Like the more familiar square, the Singular Square is based on the distinction between contradictory and contrary opposition. This paper focuses on the role of the Singular Square as a device for unmasking the conspiracy of MaxContrary, the natural language tendency for a formal contradictory (apparent wide-scope) negation ¬p to strengthen to a contrary of p in a variety of syntactic and lexical contexts. This conspiracy extends from the non-compositional narrow-scope readings of negation interacting with bare plurals, definite plurals, conjunctions, and neg-raising predicates to the prevalence of prohibitives and litotes, the contrary interpretations of affixal negation, and the seemingly illogical behavior of “logical” double negation.