Many people find reassurance in the sober, capable military men who surround him.
His chief of staff, his defence secretary and his national security adviser all understand the horrors of war and will stop him from doing anything rash, the argument goes.
Optimists even speculate that he might emulate Ronald Reagan, by shaking up the diplomatic establishment, restoring America's military muscle and projecting such strength abroad that a frightened, over-stretched North Korea will crumble like the Soviet Union.
Others confidently predict that even if he causes short-term damage to America's standing in the world, Mr Trump will be voted out in 2020 and things will return to normal.
All this is wishful thinking.
On security, Mr Trump has avoided some terrible mistakes.
He has not started a needless row with China over Taiwan's ambiguous status, as he once threatened to do.
Congress and the election-hacking scandal prevented him from pursuing a grand bargain with Vladimir Putin that might have left Russia's neighbours at the Kremlin's mercy.
And he has apparently coaxed China to exert a little more pressure on North Korea to stop expanding its nuclear arsenal.
However, he has made some serious errors, too, such as undermining the deal with Iran that curbs its ability to make nuclear bombs.
And his instincts are atrocious.
He imagines he has nothing to learn from history.
He warms to strongmen, such as Mr Putin and Xi Jinping.
His love of generals is matched by a disdain for diplomats—he has gutted the State Department, losing busloads of experienced ambassadors.
His tweeting is no joke: he undermines and contradicts his officials without warning, and makes reckless threats against Kim Jong Un, whose paranoia needs no stoking.