Modern binary informatics with its so-called “classical” two-valued logic admits to create an artificial intellect and suppresses the natural intellect of students and other thinking people. Logic that based on dogmatic law of the excluded middle is incompatible with dialectical principle of opposition coexistence. Such logic is deprived of fundamental logical relation – the content consequence, and then cannot reach a conclusion. Aristotle’s syllogistics includes the content consequence as common affirmative premise “All x are y”. However, binarity misinterprets it as a paradoxical material implication that is not a relation at all. Lewis Carroll’s “Symbolic logic” correctly represented syllogistics, but it is not intelligible for modern binary logic. Our paper reveals the essence of content consequence; it explains Carroll’s intentional judgments and syllogistic relations submitted to opposite coexistence.