In the article, Mr. Posner supported urging companies like Facebook and YouTube to crack down on propaganda by the Islamic State, which is also known as ISIS or ISIL, but said that could never be fully effective. He proposed, in addition, passing a law to deter potential consumers from viewing dangerous sites. While the law would apply to all Internet users, his goal, admittedly limited, is to head off the radicalization of those he described as “naïve people” who research the Islamic State out of curiosity, “rather than sophisticated terrorists.”

His law would make it illegal to go onto websites that glorify the Islamic State or support recruitment of new followers, or to distribute links to such sites. He would impose graduated penalties, starting with a warning letter, then fines or prison for repeat offenders, to send the message that “looking at ISIS-related websites, like looking at websites that display child pornography, is strictly forbidden.”

David G. Post, a former professor of constitutional law who is a senior fellow at the Open Technology Institute of the New America Foundation in Washington, was one of many legal experts to condemn Mr. Posner’s idea.

“I think it is a slippery slope,” Mr. Post said in an interview. In a popular legal blog, The Volokh Conspiracy, he wrote that efforts to suppress radical views “can be far too easily twisted into a prohibition against dissenting viewpoints.”