 First of all, it is well known that using \(\infty\) would give wrong predictions for the cases with more than two disjuncts. For example, \(\alpha \infty (\beta \infty \gamma)\) is true, if all disjuncts are true, but Marie ira au cinéma soit lundi soit mardi soit mercredi is not (see Reichenbach 1947; Simons 2000). Secondly, the use of exclusive disjunction would also fail to explain certain embedded uses of soit-soit constructions. While these constructions are ungrammatical under negation, making therefore hard to apply the Gricean argument of the previous section to these cases, they are licensed in the scope of a universal quantifier, but the inferences corresponding with the exclusive reading are no longer present in such cases: