The paradox ceases to exist the moment we replace informal logic with propositional logic. The Tortoise and Achilles don’t agree on any definition of logical implication. In propositional logic the logical implication is defined as follows:

P ⇒ Q if and only if the proposition P → Q is a tautology

[H]ence de modus ponens [P ∧ (P → Q)] ⇒ Q is a valid logical implication according to the definition of logical implication just stated. There is no need to recurse since the logical implication can be translated into symbols and propositional operators such as →. Demonstrating the logical implication simply translates into verifying that the compound truth table is producing a tautology.

— Wikipedia on *What the Tortoise Said to Achilles*

2013.09.25 Wednesday ACHK