Indeed, the pair show that any set of self-referential sentences that assert complete truth or falsity about one another are exactly half-true. (Though other solutions are possible as well.) Other fractional truth-values arise when the sentences themselves make fuzzy assertions.

ECONOMIST: Fuzzy logic

Mr. ADAIR: Well, we ended up giving it a barely true on the Truth-o-Meter.

NPR: Fact-Checking the Campaign Ads

So, this one ended up a half true on the Truth-o-Meter.

NPR: Fact-Checking the Campaign Ads

Mr. ADAIR: We gave this a barely true on our Truth-O-Meter, and this is typical of the kind of cherry picking that we're seeing from both campaigns.

NPR: Political Ads May Not Tell Whole Story

So, that one earned a barely true on our Truth-O-Meter.

NPR: Political Ads May Not Tell Whole Story

Team's first album made the silly myth about lo-fi sound conveying truth and beauty come true, only now he's made a very similar album in the studio.

NPR: The Go! Team Is Still Having Fun

They are true patriots, truth tellers and unabashedly post-partisan.

FORBES: Simpson-Bowles Unplugged: Time's Running Out

Finally, there is the overarching truth (indeed, requirement) that in a system of true free-market capitalism, two parties enter into a transaction only when they are both made better off, while at the same time not trampling the rights of a third party.

FORBES