 Where we need to distinguish between different interpretations, we write “\(A \supset B\)” for the truth-functional conditional, “\(A \rightarrow B\)” for a non-truth-functional conditional and “\(A \Rightarrow B\)” for the conditional as interpreted by the suppositional theory; and for brevity we call protagonists of the three theories Hook, Arrow and Supp, respectively. We use “\({\sim}\)” for negation.