His statement, “not if he eats while uncertain whether the sun has set,” means that his fast is not valid, because Allah says:
“Then complete the fast until nightfall.”
Thus, it must be completed until nightfall. The Prophet ﷺ said, “When night approaches from this direction”—and he pointed with his hand towards the east—“and day departs from this direction”—and he pointed towards the west—“and the sun has set, then the fasting person has broken his fast.” (1)
The difference between one who eats while uncertain whether dawn has broken and one who eats while uncertain whether the sun has set is that the former relies on an established presumption: that night remains; while the latter likewise relies on an established presumption: that daytime remains. Therefore, he may not eat while uncertain whether the sun has set, and he must make up the fast unless it is known that he ate after sunset. If it is known that he ate after sunset, then he does not have to make it up.
He may eat if he is certain, or if he considers it more likely that the sun has set. Even according to the established position of the school, if he considers it more likely that the sun has set, he may break his fast and does not have to make it up, unless it becomes clear that the sun had not set.
Issue: If he eats thinking that the sun has set, and the matter does not subsequently become clear, then his fast is valid. This is understood from the author’s wording, “while uncertain whether the sun has set.” It follows that if he eats while considering it likely that the sun has set, his fast is valid unless it becomes clear that the sun had not set.
If it becomes clear that the sun had not set, then the correct view is that he does not have to make up the fast, whereas the established position of the school is that he must make it up.