Gödel, Escher, Brock

David Brock’s escalating confessions of right-wing treachery, already the stuff of parody three years ago, seem to have hit a new, pornographic plateau. In a book excerpt in the August issue of Talk, Brock lets us know that he’s an even bigger creep than we (or, perhaps, he) thought when we read his two earlier confessions in Esquire. Brock now says that “conservative rhetoric, including my own … sought to conceal 10 years ago” what a “mean-spirited, rabid ideologue” Clarence Thomas was. Brock writes that,

[D]oing everything I could to ruin [Thomas sexual-harrassment accuser Anita] Hill’s credibility, I took a scattershot approach, dumping virtually every derogatory–and often contradictory–allegation I had collected on Hill into the vituperative mix.

Brock writes that when one of his key sources told him, after publication of Strange Justice, a book about the Hill-Thomas imbroglio by Jane Mayer and Jill Abramson, that Thomas must have committed sexual harassment after all, he tried to talk her out of it, then proceeded to write a book review of Strange Justice making assertions that he knew to be false. Most amazingly, Brock admits to having been loathsome enough to blackmail one of Mayer’s and Abramson’s sources into retracting a particularly damning Thomas anecdote, supposedly with some assistance–via an intermediary–from Thomas himself. (Click here  to read Dahlia Lithwick’s Explainer on whether this may have been illegal.) Only years later would Brock begin

[T]o face, in half steps, what I was, and what I had become. I could see that my reportorial method in [his book] The Real Anita Hill could be attributed to journalistic carelessness, ideological bias, and my misdirected quest for acceptance by a political movement.

You see the problem. Chatterbox yields to no one in his eagerness to believe the awful things Brock is now saying about himself and the conservative movement in America. But the more Brock insists that he has lied, and lied, and then lied again, the more one begins to suspect Brock of being, well, a liar. Which poses a familiar philosophical riddle. How do we interpret the assertion, “Everything I say is a lie”?

“Everything I say is a lie” is a standby of late-night bull sessions in college dormitories, sometimes attributed to Episode 41 of Star Trek, titled “I, Mudd.”  In fact, the true provenance of such riddles is Kurt Gödel’s Incompleteness Theorem, as elucidated in his 1930 paper, “On Formally Undecideable Propositions of Principa Mathematica and Related Systems.” Possibly because Gödel’s essay loses something in the translation from German, Chatterbox can’t make head or tail of it. Its essence, though, is intriguingly summarized by Douglas Hofstadter in his Pulitzer Prize-winning book, Gödel, Escher, Bach: “[P]rovability is a weaker notion than truth, no matter what axiom system is involved.” Seeking a deeper understanding, Chatterbox phoned Hofstadter. “Gödel’s theorem is based on taking that kind of twisty, self-undermining structure and importing it into a more formal mathematical context,” he explained patiently. The sentence, “Everything I say is a lie” (actually, Hofstadter prefers the simpler and more elegant,”This sentence is a lie”) “flips back and forth. If it’s a lie, it’s false, and if it’s false, it isn’t a lie.” And Gödel was able to reduce this to a mathematical formula? Hofstadter, bristling at Chatterbox’s implication that it’s reductionist to state principals in terms of mathematical formulae, corrected him: Gödel “translated it into a mathematical statement.” (Perhaps more familiarly, M.C. Escher translated it into art.) So: If you want to know whether David Brock is lying when he says he’s a liar, here’s your answer:

 (x) [Fn(x) = 0] or (x) [F(x) = 0]

[Update, 6:30 p.m.: “Alas, wrong,” writes Barry Simon, IBM professor of mathematics and theoretical physics at Caltech. “These kinds of riddles go back to the Greeks in a version that accuses Cretans of being liars. It is apparently called Epimenides’ Paradox.” In a separate e-mail, Vance Maverick offers up this link, attributing to Eubulides of Miletus the question, “A man says that he is lying. Is what he says true or false?” Evidently the notion also comes up in one of Paul’s Epistles.]

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