  It will be noted that this statement of the LNC is an explicitly modal claim about the incompatibility of opposed properties applying to the same object (with the appropriate provisos). Since Łukasiewicz (1910), this ontological version of the principle has been recognized as distinct from, and for Aristotle arguably prior to, the logical formulation (“The opinion that opposite assertions are not simultaneously true is the firmest of all”—Met. 1011b13–14) and the psychological formulation (“It is impossible for anyone to believe that the same thing is and is not, as some consider Heraclitus said”—Met. 1005b23–25) offered elsewhere in Book Γ; we return to Heraclitus below. Wedin (2004a), who argues for the primacy of the ontological version (see also Meyer 2008, Other Internet Resources), formalizes it as ¬◊(∃x)(Fx ∧ ¬Fx). These three formulations of LNC differ in important respects, in particular as to whether the law is explicitly modal in character, whether it applies to propositions or to properties and objects, and whether it requires the invocation of a metalinguistic truth predicate. (See also the entry   Aristotle on non-contradiction.) 