The view of the majority of scholars is that making up the fast is obligatory in this case—that is, when the testimony is established during the day. Shaykh al-Islam Ibn Taymiyyah, however, held that they must abstain for the remainder of the day but are not required to make it up. His reasoning is that their eating and drinking before the testimony was established had been permissible: Allah had permitted it for them, so they had not violated the sanctity of the month. Rather, they were unaware and acted upon the presumption that Sha'ban was still ongoing. They therefore fall under the general purport of Allah’s saying:
“Our Lord, do not take us to task if we forget or make a mistake.”
Their case is thus like that of one who eats thinking that the night remains, only to discover that dawn had already broken, or who eats thinking that the sun has set, only to discover that it had not set. It is authentically reported in Sahih al-Bukhari from Asma' bint Abi Bakr, may Allah be pleased with her, that she said: “We broke our fast on a cloudy day during the time of the Prophet, peace and blessings be upon him, and then the sun appeared.” (1) It has not been reported that they were instructed to make up the fast.
He also answered the objection that they had not formed the intention before dawn by saying that intention follows knowledge, and they had no knowledge that the month had begun. What lies beyond their knowledge is beyond their capacity, and Allah does not burden any soul beyond its capacity. This is why, had they delayed forming the intention until after learning that the month had begun, their fast would not have been valid.
His reasoning and response, may Allah have mercy on him, are strong; nevertheless, the soul is not entirely at ease with his view. His analogy with one who eats thinking that the night remains or that the sun has set is open to question, for such a person had intended to fast, but ate thinking that the night was still ongoing or that it had begun. This is why the disagreement in these two cases is more well known than the disagreement in the first case.