Hegel seems to overcome the ontological principle of contradiction Aristotle referred to as "the most certain of all principles." According to Aristotle, "everything must be either affirmed or denied;" "is" has all the strength of a statement and "is not" is its negation. Our mind compares affirmation with its proper negation to see which corresponds to reality. Therefore contradiction, strictly speaking, does not exist in reality but only in diction. Modern philosophy changes this formulation. Leibniz starts from the identity: "everything is what it is" ("every A is A") and his principle of contradiction is articulated as follows: "a statement is either true or false." His contradiction is conceptual ("A no-A"). Aristotle opposes "it is not" to "it is" whereas Leibniz opposes "it is true (T)" to "it is no-T (F)." Hegel follows Leibniz's line of thought placing contradiction between "S" and "P" so in "S is P" there is contradiction. For Hegel identity contains its own negation: "S is S" because "S is not P," or even "S is no-P." For Hegel, contradiction is also at a conceptual level-"is not" is "is no-." Hegel's theory of negation neglects ontological negation.
With the juxtaposition of Augustine’s interpretation of Christian orthodoxy and Manichaean dualism we see how much it matters, both metaphysically and ethically, whether reality is conceived as carrying negation within itself. If it does, then reality is strife; we are dealing with “ontological violence,” to use John Milbank’s expression. Violence becomes “the engine of history,” as Carlos McCadden and José Manuel Orozco write in the present book.