President Trump. (Alex Brandon/Associated Press)

Journalists make inquiries for a living, but they are keenly aware that the shortlist of taboo questions includes this one: Is the president of the United States crazy?

The Fix's Aaron Blake wrote in August about why the media tread lightly on the subject of a president's sanity. He noted that the American Psychological Association considers it unethical for members to speculate about the mental health of people they have not evaluated firsthand, and “if professionals aren't supposed to go there, how in the world can amateurs without mental-health expertise offer informed opinions about this topic?”

Yet journalists and commentators stretched typical boundaries this week, as multiple news outlets reported President Trump has privately suggested that the infamous “Access Hollywood” tape for which he apologized last year might be fake.

“Is there some chance that the president actually now believes that his voice is not on the ‘Access Hollywood’ tape?” NBC's John Heilemann wondered on “Morning Joe” on Wednesday. “Those would be signals of someone who has become, in a fundamental way — I don't want to sound too much like Mika Brzezinski here — but fundamentally unhinged.”

The next day, Joe Scarborough added: “When are we supposed to say this? After the first nuclear missile goes? Is that when it’s proper to bring this up in polite society? Tell me, General Mattis, when is it polite to bring this up in polite society? Rex Tillerson, when is this the right time to talk about a mentally unstable president in the White House and a nuclear showdown with another unstable madman in North Korea? Is it after the first nuclear missiles fly?”

Part of the thinking among some in the press is that Trump’s behind-the-scenes remarks to aides and lawmakers could be more indicative of his mental state than anything he says publicly because private comments might reveal his true thinking.

“It's one thing if he’s saying it to you, or to me, or to the base, or from the podium to just kind of excite his base and play with people’s uglier suspicions about life,” CNN's Chris Cuomo said Wednesday, when interviewing New York Times reporter Jonathan Martin. “But if he's saying it in private, like he means it, what does the reporting reveal?”

Washington Post columnist Eugene Robinson wrote on Thursday that “it is one thing to create a fantasyland for political ends — appealing to some voting group’s prejudices or giving supporters a reason to excuse bad behavior. It is another thing altogether, however, for Trump to fall into his own rabbit hole and actually believe what he once knew to be untrue.”

Recall what Trump said in October 2016, when The Post published the hot-mic recording on which Trump boasted that he can grope women and get away with it because he is famous: “I said it, I was wrong, and I apologize.”

Trump won't commit to a physical, never mind a psychiatric evaluation. Here's an exchange between CBS News Radio's Steven Portnoy and White House press secretary Sarah Huckabee Sanders at Thursday's media briefing:

PORTNOY: I have a question about the president’s health. Mr. Trump’s predecessors, going back — I checked as far as Ronald Reagan — every year would go up to Bethesda to be looked at by the best doctors in the military, and they would report on their health and their vital statistics to the American public. We have a month left in the year. Does President Trump intend to get a physical at Walter Reed?

SANDERS: I’d have to ask. That’s not something I’ve checked on, but I would be happy to check on it.

PORTNOY: Do you know if the president intends to share any details about his health the way his predecessors have?

SANDERS: Like I said, I haven’t asked him that, but I’d be happy to check.

Sanders was asked a similar question during a briefing in August. “I’ll let you know if that’s going to happen,” she said then.

An official medical report on the president’s health, in general, and his mental capacity, in particular, does not appear to be forthcoming. That leaves the media to wonder, and they are increasingly doing so aloud.