These latest messages came came on the heels of a bizarre barrage of tweets—odd even by the president’s standards—that set off a new round of scrutiny of his use of social media. Beginning on June 29, Trump began tweeting repeated insults at Joe Scarborough and Mika Brzezinski, the hosts of the MSNBC talk show, Morning Joe. Trump’s treatment of Brzezinski was particularly strange. In addition to calling her “dumb,” “crazy,” and “low I.Q.” in three separate tweets, he claimed that she and Scarborough traveled to Mar-a-Lago for New Year’s Eve and insisted on seeing Trump while Brzezinski was “bleeding badly from a face-lift.” (Brzezinski and Scarborough published a rebuke in The Washington Post, calling the president’s claim “a lie.”)

In true Trump fashion, the president doubled down, calling Scarborough “crazy” and Brzezinski “dumb as a rock.”

Does that constitute targeted harassment? And given Trump’s huge following—more than 33.1 million Twitter followers on his primary account—does a string of attacks against the same two individuals constitute inciting harassment? “We don’t comment on individual accounts, for privacy and security reasons,” a Twitter spokesperson told me on Saturday. Twitter also declined to tell me whether, when considering the question of a user inciting harassment, it takes into consideration that person’s number of followers or public status—a movie star or politician, for example.

Twitter’s website does offer some clarification on how it assesses abusive behavior. The company says it assesses whether the primary purpose of an account is to harass or send abusive messages; and it looks at whether the reported behavior is “one-sided.”Setting aside Twitter’s notoriously bad track record for actually enforcing its own standards on harassment, the question of one-sidedness poses an interesting problem here.

When one of the people involved in a Twitter fight isn’t just a public official but also the president of the United States, is it fair to consider anyone he’s attacking an equal player in a fight?

We know what Trump would say. This is a man whose 2007 book Never Give Up has multiple chapters dedicated to the subject of fighting with people. There’s Chapter 5 (“I Love a Good Fight”) and Chapter 29 (“You Will Be Attacked For Trying to Change Anything”) and Chapter 38 (“When You’re Attacked, Bite Back”). If Trump doesn’t like what a person says about him, he attacks them. Period.

But Trump’s Twitter conduct also raises a question about what Twitter is, and what it should be. Often, the service is treated as a new kind of public square, a place for the unfiltered exchange of ideas (and, clearly, hurling of insults). Silicon Valley has rarely stepped in to correct the persistent cultural conflation between the actual right to free speech—that is, the constitutionally protected right that says the government cannot make a law that inhibits people’s freedom of expression—and the idea that people should get to say whatever they want wherever they want to without consequence. (Complicating things further, Twitter must answer to its shareholders, and having the president use its service so routinely—and so bombastically—certainly keeps the service relevant.)