Hugh Akston stated that, when he first met John Galt, John asked a question on Plato's metaphysics that he would've been proud to get from someone who had studied philosophy for six years, a question that Plato didn't have the sense to ask himself. What was the question (or what might it have been)?
1 Answer
I don't think the book ever answers what the question was, so I'd like to take a shot at your more subjective question:
what might it have been?
There's a question that is asked a number of times throughout the book by the heroes:
"By what right?"
A few examples:
What motive moved them?—what was their knowledge?—which one of them, unaided, could bring a chunk of ore out of the earth? . . . Destroyed at the whim of men whom he had never seen and who had never seen those tiers of metal . . . Destroyed, because they so decided. By what right?
"Dagny, by what right?” Eddie Willers had asked her, his voice quiet, but the words sounding like a cry. "By what right are they all doing it?
You, who've kept them all alive, have been called an exploiter. You, the purest and most moral man among them, have been sneered at as a 'vulgar materialist.' Have you stopped to ask them: by what right?—by what code?—by what standard?
So I believe it's plausible that Galt may have asked By what right? when he began to see the world taken over by looters and began to see men of the mind suffocated by pull peddlers.