Nice example. To follow up:

Next, Omega places two boxes in front of you. One carries the label "The label on the other box contains a true sentence". The label on the other box reads "The label on the other box contains a false sentence". You are told that the box(es) without false labels contain $1,000,000, whereas the box(es) with false labels are boobytrapped. It is conceivable that the labels are meaningless - therefore not false. It is also conceivable that the labels are both true and false - contradictory, but paraconsistent.

Do you open the boxes?

Quadratic equations are relatively clear-cut.