There’s a new bogeyman gaining traction in the world of left-wing academic and online discourse around current events, and it goes by the name “stochastic terrorism.”

Loosely defined, it is the notion that demonization or criticism of an individual or group in society on mass media and social media inevitably leads to acts of violence against that individual or group. The word stochastic, from the Greek stokhastikos — meaning to aim at or guess — refers to outcomes that may appear random but are actually probable, just not predictable.

Stochastic terrorism, in the discourse of today’s commentariat, is the end result of unchecked hate speech. Because the left believes hate speech only comes from one direction on the political spectrum — the right — then the purveyors of that speech must be called to account for the real-world violence that results from their opinions or commentary. “Free speech is killing us,” the New York Times declared in 2019.

The phrase first gained widespread usage in certain circles when an assistant secretary in President Obama’s Department of Homeland Security, Juliette Kayyem, now teaching at Harvard’s Kennedy School, used the phrase in reference to a mass shooting in 2019 at a Walmart at El Paso. Ahead of the attack, the white perpetrator had posted a racist, anti-immigrant screed on 8chan. Most of his victims were Latino.

In a piece in the Washington Post, Ms. Kayyem placed blame for the El Paso shooting at the feet of President Trump. Mr. Trump’s rhetorical winks and nods, his language about Hispanics and immigrants, and his failure to shame his fringiest supporters created an atmosphere in which attacks like El Paso, while not predictable, are probable, she claimed.

“Public speech that may incite violence, even without that specific intent, has been given a name: stochastic terrorism, for a pattern that can’t be predicted precisely but can be analyzed statistically,” Mr. Kayyem wrote. “It is the demonization of groups through mass media and other propaganda that can result in a violent act because listeners interpret it as promoting targeted violence — terrorism.”

More recently, the phrase has been trotted out to describe a shooting during a drag show at a gay nightclub at Colorado Springs last weekend, when five people were murdered. Voices on the left had been warning for weeks that something like it was going to happen and had already found a culprit for any violence — conservatives who have been campaigning against the hyper-sexualization of children in schools and the larger society.

In recent months, those conservatives have been railing against drag shows advertised as “family friendly.” Online activists have posted a steady stream of videos depicting children participating in such events, along with diatribes against “gender-affirming” medical care for confused adolescents and videos of public school teachers bragging about the myriad ways they attempt to persuade schoolchildren that gender is fluid and biological sex a fallacy. None of the videos are fake. They are merely broadcast to an audience that otherwise might not have seen them.

Writing in the Advocate, an LGBT magazine, Christopher Wiggins blamed these activists and their counterparts in conservative media for fomenting an atmosphere in which an attack like that at Colorado Springs was inevitable.

“Far-right influencers have set their sights on the LGBTQ+ community, specifically the transgender community and drag queens, to generate a divisive culture war issue in the run-up to the recent midterm election,” Mr. Wiggins wrote. “For months, experts have warned that the attacks targeting the LGBTQ+ community were not only bigoted but also dangerous.”

The attack, Mr. Wiggins continued, is prima facie evidence that the stochastic terrorism described by Ms. Kayyem is alive and well in America. There is, he said, a “direct correlation” between online criticism of radical gender theory and “angry and potentially violent extremists.” That the shooter’s lawyers said Tuesday he is “non-binary” and prefers “they/them” pronouns — the imprimatur of an enlightened progressive as opposed to a knuckle-dragging conservative — is apparently irrelevant.

The ultimate aim of these attempts to rebrand hate speech as terrorism is to silence the voices that the left finds offensive or disagreeable — mission creep for the speech police. Writing in Scientific American earlier this month, author Bryn Nelson of Seattle suggested that the key to combatting stochastic terrorism is “turning off the source of fuel.” Americans must, he said, strengthen and enforce laws against hate speech and incitement to violence.

There are those who believe, however, that the pendulum has already swung too far in favor of suppressing speech. Speaking to the Sun in March, one of America’s most esteemed judges, Laurence Silberman, who passed away on October 2, warned that the current climate surrounding the First Amendment is “worse than McCarthyism.” He called freedom of speech “the most fundamental American value” and repression of it “un-American.”

If the increasingly shrill voices on the left succeed in equating with terrorism criticism of drag queen story hours and medical intervention to prevent adolescents from going through puberty, then Silberman could turn out to have been, if anything, understating the danger to American values.