 He also notes that his preferred counterfactual logic invalidates several familiar implications involving conditionals. We already mentioned that strengthening the antecedent, the implication of (p ∧ r) □→ q by p □→ q, is invalid on Lewis’s theory, and gave some natural language examples that suggest that it should be invalid. Lewis also shows that contraposition, the implication of ~q □→ ~p by p □→ q, and conditional syllogism, the implication of p □→ r by p □→ q and q □→ r, are invalid on his model, and gives arguments that they should be considered invalid.