Why not rather untruth?
Nietzsche went mad, but those who ignore what he wrote before his madness do so at their peril. (Ian Hacking, The Social Construction of What?)
The caption, taken from a Facebook post in April 2022 by Peter Zalmayev, reads “Sergei Markov: a shining example of how Russian propagandists are trying to disclaim responsibility for Bucha.” Zalmayev and Markov were invited to debate the events of Bucha on the Turkish station TRT World. Markov repeated here what he had reported to the Russian press, namely that accusations of Russian atrocities in Bucha are “100% fake”; he attributed the murders in Bucha to Ukrainian forces under United States control. In Markov’s Russian interviews he actually uses the word фейк, pronounced “fake,” and you can also read about фе́йковые новости [fake-ovie novosti], but the standard Russian term is подделка.
Concerned some years ago after reading Hacking’s comment that I might be in peril I turned to Nietzsche’s Beyond Good and Evil and paused upon reading the following passage:
Suppose we want truth: why not rather untruth? and uncertainty? even ignorance?1
The example of Markov, as a demonstration of what happens when we prefer untruth or ignorance, looks like a satisfactory retort to Nietzsche’s question.2 This is not to say that generalized untruth is to no one’s benefit:
If you have no facts, you can’t have truth. If you don’t have truth, you don’t have trust. If you don’t have any of these things … we have no shared reality. Without that, there’s no rule of law and no democracy. (Maria Ressa, Democracy Now, May 11, 2022)
According to Steven Shapin’s A Social History of Truth, Ressa has it backwards: trust — specifically trust in the word of gentlemen — is one of the foundations of the success of the scientific revolution’s codification of truth in 17th century England. Contemporary mathematics, the practice of which seems to require accepting more statements as true than any one of us has the time to verify, also
currently relies on a complex system of mutual trust based on reputations.
(Vladimir Voevodsky, 2014)
The word “currently” expressed Voevodsky’s hope that the future of research would dispense with trust and reputations in favor of mechanical formal verification.
Guest post by Michael Thaddeus
My Columbia colleague Michael Thaddeus has been thinking about truth lately, though not (as far as I know) the formalized kind. He has generously allowed me to quote from his (as yet) unpublished essay about the distortions that politicians and the media have been circulating with regard to the current wave of protests on the Columbia campus.
Politicians are lying about the protests
By Michael Thaddeus
May 1, 2024
Columbians have a wide range of views about the pro-Palestinian student protests and their suppression by our administration. Still, I hope we would all agree that the political debate about the protests should be based on reality, not fiction.
Sadly, this is far from true. Leading politicians have lost no time in spreading outright lies about the protests to a vast audience. Here are two cases in point.
Israeli Prime Minister Binyamin Netanyahu addressed the American university protests in a video released early last week. It has had 18.6 million views on X (formerly Twitter).
In the video, Netanyahu describes the protesters as "antisemitic mobs" and alleges: "They attack Jewish students. They attack Jewish faculty."
In reality, violent assaults on Jewish students, or anyone else, were vanishingly rare during the protests, both at Columbia and elsewhere. There were no black eyes, no broken bones. And, to the best of my knowledge, there were no assaults on Jewish faculty at any pro-Palestinian protest nationwide. Absolutely none. This is an audacious lie on Netanyahu's part.
Netanyahu went on to claim that the protesters "say not only 'Death to Israel, death to the Jews,' but 'Death to America.'"
Yet a Fox News story, devoted to making the same insinuation, was unable to document a single instance of campus protesters chanting "Death to America." This represents another bare-faced lie from the prime minister.
[Thaddeus quotes a segment with Fox News correspondent Lawrence Jones and a call by Donald Trump to Sean Hannity’s program, then continues:]
The lies serve, of course, to conceal the extreme one-sidedness of the positions these gentlemen adopt. Hannity and Trump speak at length about October 7th but never mention the atrocities visited on the people of Gaza since then. Netanyahu goes so far as to say, "It is Israel...that is falsely accused of starvation and all sundry war crimes. It's all one big libel."
[Editor’s note: Or as Markov might say, “It’s all 100% фейк.” Has Netanyahu been studying Markov or is it the other way around?]
Is it false to accuse Netanyahu's government of starving the people of Gaza? Heartrending photographs of emaciated children are appearing in the Western press, illustrating stories like the one in the Financial Times headed "Starvation stalks children of northern Gaza: Families resort to eating weeds, cactus and livestock fodder in struggle to survive war."
Thaddeus wisely stuck to Trump’s and Netanyahu’s well-established reputations as liars3 and chose not to address the question, much debated among Columbia faculty these days, whether our administration has been entirely truthful in its account of its negotiations with students and its decision to call in the police. Nor did Thaddeus allude to Columbia Law Professor Katherine Franke’s assertion that President Shafik “knows I didn’t say those things” that Representative Elise Stefanik attributed to her during Shafik’s problematic Congressional hearing.
Has there ever been fake news in mathematics?
Quora, you’ll be relieved to know, has not neglected that question. The instance that came to Scott Brickner’s mind is the one that came to many other minds, including mine, namely Shinichi Mochizuki’s claim to have proved the ABC conjecture.4 Mathematicians now mainly break down into two camps: those who are convinced that Mochizuki’s claim is fake news, in large part because of the questions about the purported proof raised by Peter Scholze and Jacob Stix, and the rather smaller camp of those who are convinced that the Scholze-Stix objections are fake news. The failure of the mathematical community to reach consensus on such an important as well as elementary5 question about numbers is so anomalous that Anthony Bordg sees it as a shining symptom of a Replication Crisis in Mathematics — more precisely, of a crisis in the existing peer review system, whose resolution may ultimately lead to a replacement of the existing system by one based on formal verification (though he acknowledges that this would still be inconclusive).
But what is truth?
A couple of years ago, [Kevin] Buzzard saw talks by the senior mathematicians Thomas Hales and Vladimir Voevodsky that introduced him to proof verification software that was becoming quite good. With this software, proofs can be systematically verified by computer, taking it out of the hands of the elders and democratizing the status of truth.
That’s from an article in Vice about Buzzard’s Lean project, entitled “Number Theorist Fears All Published Math Is Wrong,” where “wrong” means the opposite of “true.” By “democratizing” the article refers to the tendency, dangerous in Buzzard’s view, to rely on the judgment of experts (“elders”), who have been known to be “wrong before.”
We can agree that “true” is preferable to “wrong,” in mathematics as in the fog of war or the administration of Ivy League universities, but before we draw any conclusions from that preference we should agree on the meaning of “truth.” I didn’t expect the dictionary to be of much use, and I was right. The Oxford English Dictionary online entry on “true” stretches over 33 pages.6 After the initial (primary?) definition in terms of loyalty we reach the first possibly relevant definition on p. 6:
In accordance with fact or reality.
This is helpful in dealing with what happened in Bucha or at the Columbia Encampment but trying to apply it to mathematics immediately spirals into a bottomless pit of philosophical controversies, over the factual as opposed to consensually hallucinatory nature of mathematical propositions, or the real as opposed to nominal character of mathematical objects, that you fail to ignore at your peril.
Clutching at reassuring platitudes
Before he evolved into one of Putin’s most shameless parrots, Markov had acquired a certain reputation as a political analyst willing to cater to the international press’s insatiable appetite for vacuous remarks affirmed with authority.
a politician can survive only one heart attack, says Sergei Markov of the Carnegie Endowment for International Peace. "Who will vote for a sick man?" he asked. "Once, maybe, it could be explained away, but not twice." (NY Times, October 19, 1995)
''People are angry, yes; but people are also tired,'' said Sergei Markov, a well-known political analyst here. ''And people are afraid of bad government much less than they're afraid of chaos. They're prepared to have any kind of bad government more than instability.” (NY Times, October 10, 1998)7
Below a certain degree of lethargy any competent journalist should have been capable of justifying or rejecting such declarations without needing to rely on the authority of any old “well-known political analyst.” But in the confusion of 1990s Russia, shaken by shock therapy, ruled by a sick man, and prey to the first wave of oligarchs as well as to the illusions of the “End of History,” who can blame journalists for clutching at the reassuring platitudes of a “political analyst” with formal credentials conferred by the Carnegie Endowment?
More than 25 years later mainstream journalists are still prey to confusion. I eavesdropped on efforts of journalists on Columbia’s campus to trick students who were participating in the Gaza Solidarity Encampment — if you had been there you would have agreed it was an unimaginably serene oasis in the middle of the turbulent city — into confessing in any of a dozen languages that they were no more than the “antisemitic mobs” of Netanyahu’s feverish imagination. Like multiple copies of the same software, they asked the same questions and insisted on addressing the same isolated incidents that opponents of the Encampment had highlighted on social media; in their published articles they (or their editors) typically disregarded answers that didn’t conform to the editorial line, in the same way that Lean will return a “Sorry” if a formalized proof doesn’t meet its norms.
Faced with uncertainty, or with information that they can’t fit into their narrative, the journalists’ impulse is to follow a trajectory that reminds me of the image of
proofs that are not beyond reasonable doubt, either due to the sheer scale of the reviewing task or due to gaps that cannot be easily filled, [that] will remain in Purgatory even when the methods involved in the attempt are strong enough to lead later to a mechanized proof written with a proof assistant. After all, the authors of those methods remain human, hence fallible, even if their methods are not. Thus, only formal proofs seem to be destined for Paradise, while some proofs may remain in Purgatory before sometimes being condemned to Hell when mistakes are uncovered or gaps are deemed impossible to fill. Thus, contrasting with the platonism often assumed by mathematicians with respect to mathematical objects, mathematical proofs seem to have a temporal component displayed in a dramatic remake of the Divine Comedy.
(Bordg, “A Replication Crisis in Mathematics?”)
Maybe you see where I’m heading with this?
Two years have gone by…
… since I wrote “Maybe you see where I’m heading with this?” and nearly all the text above. And maybe you do and you can tell me. Maybe, for example, I meant this:
The Gartner Hype Cycle argues that all new technologies start with an “innovation trigger”, or a new breakthrough that gets everyone excited, and eventually reaches a “peak of inflated expectations” before falling into a “trough of disillusionment”, where all the life-changing promises made about the new technology fails to deliver. I have a sinking feeling that we’re close to the “peak of inflated expectations” when it comes to generative AI.8
(substitute “Lean” for “generative AI” and “democratizing the status of truth” for “life-changing promises.)
So much truth has been packed into the events of the last two weeks, especially but not only at my campus, and so much more has been struggling to escape the distortions imposed by the media, the politicians, and, most shamefully of all, by university administrators, that I have been unable to remember how I was planning to tie the loose ends of the Markov and formal proof stories into an aesthetically satisfying conclusion.
Was the conclusion going to be that the real value of mathematics as a human practice is the possibility of establishing trust among its practitioners? But then why did I choose the quotation about Purgatory from Bordg’s article about the “replication crisis,” rather than this one:
a mathematical proof can be thought of as a set of instructions that allow readers to replicate the proof, hence convincing themselves of its correctness.
Two years ago Russia’s invasion of Ukraine was fresh news. Even though it had no obvious connection to the mechanization of mathematics I felt the need to register my horror, especially after the Bucha atrocities. Markov came to mind, as an illustration of the consequences of becoming untethered from truth, because an obsession with a certain view of truth is one of the motivations of formalized mathematics, and because I actually knew Markov many years ago, before he became, in Peter Zalmayev’s words, “Putin’s former trusted face, deputy, demagogue, and liar”; and because I guessed, correctly, that he would have found a way to exile the Bucha story to the universe of alternative facts.
Atrocities are now being visited upon Gaza with a terrifying rhythm and intensity. But now the truth is being undermined by the same politicians who presumably would not tolerate such attacks on the part of a Markov.
When I met Markov in Moscow, some now-forgotten political operatives of the perestroika period appreciated his skill in extracting the truth concealed between the unpromising lines of the official Soviet press. What he has since become is a nagging riddle for me, and a source of distress and Nietzschean dread, because I have to assume that he chooses to lie although he still knows the difference between what is and isn’t true. The same can’t be said of the industrial-grade prevaricators who held a press conference on my campus two weeks ago. Which of the two has strayed the farthest beyond good and evil?9
In the original German: Gesetzt, wir wollen Wahrheit: warum nicht lieber Unwahrheit? Und Ungewissheit? Selbst Unwissenheit?
While what Nietzsche meant by such provocative questions is still a matter of controversy among philosophers, it’s fairly safe to assume he wasn’t thinking of the modern concept of fake news, as practiced by the likes of Markov, or (as we see below) Israeli Prime Minister Netanyahu, as a desirable alternative to truth.
French President Nicolas Sarkozy — hardly a stranger to mendacity himself — was overheard saying “I cannot bear Netanyahu, he's a liar” to US President Barack Obama,
I will let readers discover the page that declares “All Math is Fake News.”
Readers who are not mathematicians will not find a statement of the conjecture in the article in Nature and therefore may not believe that it is genuinely elementary. There is a reasonably elementary explanation of the meaning of the conjecture, though not a precise statement, in the Quanta article on the controversy.
Since the OED (and the Oxford American Dictionary) define “truth” in terms of “true,” we may as well skip immediately to the latter.
It’s easy to find examples in Le Monde, La Repubblica, and other European newspapers. For example:
A 2006 interview — alongside Michael McFaul, Ambassador to Russia under President Obama — describes him as “Sergei ‘Kremlin Insiderovich’ Markov”. Markov and McFaul coauthored The Troubled Birth of Russian Democracy in 1993.
Peter Spiegel, https://www.ft.com/content/aa191322-13b1-4468-ab7b-431dfee2cc07
There’s another link between the invasion of Ukraine and mathematics: Yuri Milner, creator of the Breakthrough Prizes, “started his venture capital career with help from Alisher Usmanov, an Uzbek-born metals magnate close to … Putin”; Usmanov is now on the EU Sanctions list because (according to the European Court of Justice) he “actively supported the Russian government's policies of destabilisation of Ukraine.” Milner himself says he no longer has Kremlin connections.