Embedded Conditionals and Modus Ponens
Abstract
It is commonly accepted that those embedded conditionals of the type "if A, then if B, then C" we do understand, we understand as equivalent to sentences without embedded conditionals. This reduction is in classical logic achieved with the use of laws of exportation and importation. V. McGee even presents counterexamples to modus ponens which are based on the classical treatment of embedded conditionals and proposes to trade the validity of modus ponens for the validity of laws of importation and exportation. It is argued that for a large class of indicative conditionals the laws of exportation and importation are invalid. With the help of Stalnaker's selection function theory of conditionals and the distinction between valid and reasonable inferences it is shown that modus ponens is valid but can be unreasonable, whereas laws of importation and exportation are invalid, but still reasonable.