In an essay last week in the online journal Aeon, the journalist Mark Hay lays out how the industry uses data collection to discover and satisfy the most outré desires. “You can boot up Pornhub, xHamster or any other popular porn tube site that collects videos from around the web, and there’s a decent chance that you’ll see a moving thumbnail of a topless girl in a diaper,” writes Mr. Hay, or “some other fetish you used to have to scour to the dark edges of the net to find.” The fetish that’s trending right now, Mr. Hay told me when I called him, is necrophilia — “artificial snuff films.”

I’m not against the proliferation of internet sexualities (nor is Mr. Hay — he wanted to be very clear about that). I just don’t want my preteens watching actors having sex with corpses, even fake corpses, before they’ve begun to date.

“It’s a really hard problem,” says Clay Shirky, an associate arts professor at New York University’s Interactive Telecommunications Program, and the author of eloquent defenses of social media. Mr. Shirky thinks it’s futile for now to try to control what his children do on the web. He serves as “IT support” for his family, including his 12-year-old daughter and 15-year-old son, so he sees their phones and computers, and is pretty sure he doesn’t “have anything to worry about.” He says that’s just lucky, and “when luck is your only back-up strategy, it’s really troubling.” Mr. Shirky believes that it’s possible to come up with a constitutional way to curtail children’s access to pornography; there just hasn’t been the political will to work on the problem.

Most other experts, however, say that there is no solution that wouldn’t backfire or flunk the free-speech test. The best parents can do is teach children to put disturbing material in context. “The key to parenting children around pornography is not to start an arms race with them by trying to block their access,” Danah Boyd, the author of “It’s Complicated: The Social Lives of Networked Teens,” wrote in an email. “It’s about equipping them with the critical sensibilities to interrogate the kinds of sexualized content that is presented to them regularly,” whether by “Game of Thrones” or pornography aggregators.

Contextualizing is a good idea, but we have to do more, because Justice Kennedy was wrong. Filtering software is not up to the job. Left-leaning parents shy away from a cause they identify with right-wing culture warriors, but I challenge any parent to affirm that it’s O.K. for her kids to become digital porn consumers at 11, the average age of a child’s first encounter.

My generation made fun of Tipper Gore in the 1980s, when she urged music companies to label record covers when the lyrics were obscene. I apologize to Mrs. Gore. She wasn’t stopping anyone from making music. She was trying to come up with a good-enough filter.

The songs Mrs. Gore objected to seem innocent compared with today’s raunchy, shall we say pornified, playlist. As the pornography industry explores the darkest reaches of the human psyche in search of profits, liberals may want to rethink the assumption that only archconservatives would try to stop children from going there, too.