  Not all systems of propositional logic accept a biconditional law of double negation (LDN), ¬(¬Φ) ≡ Φ. In particular, LDN, along with LEM, is not valid for the Intuitionists, who reject ¬(¬Φ) → Φ while accepting its converse, Φ → ¬(¬Φ). But the very possibility of applying negation to a negated statement presupposes the analysis of contradictory negation as an iterative operator (one capable of applying to its own output), or as a function whose range is identical to (or a subset of) its domain. Within the categorical term-based logic of Aristotle and his Peripatetic successors, every statement—whether singular or general—is of subject-predicate form. Contradictory negation is not a one-place operator taking propositions into propositions, but rather a mode of predication, a way of combining subjects with predicates: a given predicate can be either affirmed or denied of a given subject. Unlike the apophatikon or propositional negation connective introduced by the Stoics and formalized in Fregean and Russellian logic, Aristotelian predicate denial, while toggling truth and falsity and yielding the semantics of contradictory opposition, does not apply to its own output and hence does not syntactically iterate. In this respect, predicate denial both anticipates the form of negation in Montague Grammar (see the entry on  Montague semantics) and provides a more plausible representation of contradictory negation in natural language, whether Ancient Greek or English, where reflexes of the iterating one-place connective of the Stoics and Fregeans (“Not: not: the sun is shining”) are hard to find outside of artificial constructs like the “it is not the case” construction (Horn 1989, §7.2). In a given natural language, contradictory negation may be expressed as a particle associated with a copula or a verb, as an inflected auxiliary verb, as a verb of negation, or as a negative suffix or prefix. 