 As Pizzi and Williamson (1997, p. 571) point out, their investigation is a “contribution to the modal treatment of logics intermediate between logics of consequential implication and connexive logics.” They emphasize a difficulty of regarding consequential implication as a genuine implication connective by showing that in any normal system of consequential logic that admits modus ponens for consequential implication and contains BT, the following formulas are provable: