If a person accepts (or doesn’t even note) an inconsistency (such as the conjunction P & ¬P), then he or she may as well accept any statement!

That sounds right. Two colloquial versions come to mind. "If you believe that, I have a bridge you might be interested in." and "We already know what kind of girl you are; now. we're just talking price."

There is an interesting two-step process here.

(1) If a person's logic enables him to believe one contradiction, then it will enable him to believe any contradiction (assuming no domain knowledge a priori).

AND

(2) For every proposition A, there is a P which, if both it and its negation are true, implies A.

How does one proves (2)? To be useful, must "explosive" entail all propositions, or just an infinite number of false propositions?