Die Logik indikativischer wenn-Sätze.

Abstract

Abstract Philosophers such as Bertrand Russell, Ludwig Wittgenstein, Alfred Tarski and Paul Grice have taken the position that wenn-dann (Engl. if-then) constitutes a truth-value function. They identify the subjunction wenn-dann (if-then) with the conditional of classical bivalent logic, or at least regard it as equivalent. Our article objects to the assumption that the truth value of a conditional sentence depends exclusively on the truth values of its sub-sentences. While it is far from clear whether the inference rules of classical logic, such as contraposition, are universally valid, application of classical logic may nevertheless have some advantages. In the context of natural and ordinary language varieties the inference rules appear both elegant and easy to use. Our article takes a pragmatic approach which is based on classical logic, but without equalizing wenn-dann (if-then) with the classical conditional. It is essential to draw a linguistic distinction between real conditional sentences, which are based on a ground-consequence-relation, and concessive if-clauses. In English it may sometimes be difficult to distinguish between real conditionals and concessive if-clauses: there is no grammatical need to mark concessive if-clauses with expressions like even or still. German, by contrast, has a stronger iconic potential: it clearly marks most concessive if-clauses with selbst wenn, auch wenn, or with concessive terms like trotzdem and dennoch. Our article shows that it is always possible to apply contraposition to real conditional sentences, while it is impossible to apply it to concessive if-clauses.