Lies, falsehoods and "vacuous truths": GOP explores a new realm of absolute emptiness

As the midterm elections bear down on us like a falling piano, I've been reflecting on the current information environment. Republican nominees in about half the country's gubernatorial races continue to dismiss the results of the 2020 election, and in at least four key swing states there's a good chance the next vote count will be overseen by an election denier.

Two years after Trump's unceremonious exit, with his infamous 30,573 lies in the rearview mirror, might seem a little late to sound the alarm on the post-truth era. It can be tempting to assume there's simply nothing new to say about this moment. Politicians always lie and always will. I'll admit that the endless hand-wringing in op-eds like this one about the value of the words "lie" vs. "falsehood" often leave me feeling depleted and apathetic.

It took a logic puzzle on a math test, of all things, to get me thinking about this problem in a different way.

The puzzle first appeared in the 17th annual Brazilian Mathematics Olympiad, and has since become the subject of fierce debate online. Don't worry, I won't bore you by transcribing the whole thing here. What you need to know are two starting propositions:

1. Pinocchio always lies.
2. Pinocchio says, "All my hats are green."

There's nothing special about the color green in this case, or the fact that the liar is a wooden puppet. He could just as well be, say, the former president of the United States, and he could just as well be wearing a red MAGA hat. The crux of the puzzle is in deciding which of the following statements must be true, given what we know about Pinocchio's track record:

1. Pinocchio has no hats.
2. Pinocchio has at least one hat.

In pure mathematics, the definition of a falsehood is surprisingly narrow, and an important exception exists for what are called "vacuous truths." These are essentially statements about the world which are predicated on false or nonsensical antecedents. Vacuous truths are seen as more absurd than false, since they are often unfalsifiable and may not even make contact with reality. In other words, it is not exactly a lie for Pinocchio to say, "All my hats are green," if he has no hats at all.

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Of course, in the real world, we treat both A and B as lies. There is a point at which formal logic and conversational implicature diverge, and a claim such as "all the stolen ballots were for Trump," does not, by some bizarre application of the horseshoe theory, become more true if there were no stolen ballots in the first place.

Yet the distinction between conventional lies and vacuous truths articulates an important problem, even if the logician's answer to it is ill-suited to daily life. Call it the absurdity problem. We tend to think of truth and lies as opposite points on a spectrum, but what if the spectrum kept going well past lying and into some uncharted territory of invention?

If you've been following the Republican primaries lately, you'd be forgiven for thinking there's no more spectrum left to travel. With the ouster of Liz Cheney in Wyoming and the ascendancy of a new species of conspiracy theorist in Congress, it's as if the consensus on the right is that an unequivocal break with the truth actually goes full circle.

In the media, the absurdity problem helps explain the asymmetry that keeps reputable journalists forever playing defense. The slightest error in an otherwise scrupulous article is touted as proof of bias, while a full-fledged disinformation campaign is almost too big of a target to hit.

At a certain distance from reality, our intuitions tend to fall apart. As Jonathan Rauch once put it, "This is not about persuasion: This is about disorientation." Laughter, puzzlement, dismissal — our usual reactions to absurdity — are worse than impotent, in that they offer cover for bad actors to push us further and further away from the truth. We need to stop treating the current information crisis as a carnival sideshow and start seeing it for the headliner it has become. Importantly, the mathematical concept of vacuity ignores the way that truly cynical people have always lied: not in separate units but as an accretion, a slow buildup of falsehood on falsehood, so that we bury ourselves looking for the bottom.