“Rephrasing the amendment as a conditional (hypothetical) syllogism, its first premise would state: If a well regulated militia is necessary to the security of a free state (p), then the right of the people to keep and bear arms shall not be infringed (q); that is, p implies q. If one then asserts p as a second premise, then the conclusion q would follow. Logicians speak of this syllogism as being valid by reason of modus ponens.39 Yet the denial of the antecedent, should it be expressed in the second premise, fails to imply the denial of the consequent in the conclusion; that is, even if a militia is not necessary for the existence of a free state, the people still have the right to keep and bear arms. To say that “not p” implies “not q” is to commit the logical fallacy of denying the antecedent.40 These rules concerning syllogisms derive from classic Aristotelian logic and have not changed since ancient Greece. The Founders were familiar with logic.”