 The basic paraconsistent logic FDE of first-degree entailment lacks a primitive implication connective and lends itself to adding an implication connective that validates Aristotle’s and Boethius’ theses by using the falsity conditions of implications as expressed by BTe′. This is possible because negation is treated according to “the American Plan,” i.e., by making use of four semantical values: T (“told true only”), F (“told false only”), N (“neither told true nor told false”), and B (“both told true and told false”), so that support of truth and support of falsity emerge as two independent semantical dimensions: