On the Paradox of entailment

http://en.wikipedia.org/wiki/Paradox_of_entailment

I think the intuition behind the existence of this paradox is following. The premises are contradictory. This is only possible in the 'mother-universe' which is not consistent, in which all self consistent but mutually exclusive logical systems can persist. Thus the premises take us into that mother world where everything is vacuously true. So the conclusion achieved is actually, after all, a meaningful one.