Counterpossibles and normal defaults in the filioque controversy (Q2297957)

The paradoxes of strict implication, in particular that from the impossible any arbitrary proposition follows (\textit{ex impossibili quodlibet}), threaten the use of reductio arguments. A \textit{default} logic is a non-monotonic logic in which as well as ordinary deduction, certain consequences follow provided there is nothing to prevent them: in particular, a \textit{normal default} is of the form that given $\gamma$, $\theta$ may be assumed provided there is nothing to prevent it. In his \textit{Procession of the Holy Spirit}, Anselm used reasoning of this kind in his defence of the Western Church's claim that the Holy Spirit proceeds not only from the Father (as in the earliest creeds and in the teaching of the Eastern Churches), but from the Father \textit{and from the Son} (in Latin, \textit{filioque}), and also in his response to anticipated replies from the Eastern position. The theological dispute, which had far-reaching consequences, may thus be regarded as due not to a change in doctrine, but to a change in the kind of logic employed.