Mr. Trump has asserted that the Islamic State is gaining strength, questioned the need for NATO, praised President Vladimir V. Putin of Russia and extolled the benefits of Brexit. Yet I can picture that he’ll soon receive a briefing that would include phrases like recent successes against the Islamic State, or threats to NATO unity, or Mr. Putin’s ambitions in Ukraine, or the crippling consequences of Brexit.

Might a briefing change his mind? Probably not. After meetings with Henry A. Kissinger and James A. Baker III, prominent Republican secretaries of state, Mr. Trump said he came away with “a lot of knowledge.” But asked if those meetings had altered his views, Mr. Trump simply replied, “No.” Yet such openness to conflicting views is critical for a president who must constantly assess a complicated and ever-changing world.

Mrs. Clinton, whose candidacy I am not supporting, presents different challenges. Absent the email kerfuffle, the briefing for Mrs. Clinton could well begin with her saying, “Now, where were we?” But it was the director of national intelligence’s inspector general, I. Charles McCullough III, who held his ground in saying that some of the emails on her server were indeed highly classified. Will hard feelings — or lingering concerns about protecting data — strain her relationship with the intelligence services?