If people do not learn of the beginning of the month until daytime, should they then fast, and do they have to make up that day?

If people do not know about the start of Ramadan until daytime, they are obligated to abstain [from food, drink, etc.] for the rest of the day. As for making up the fast (qada'), there is a difference of opinion among scholars:

1. The majority: They hold that making up the fast is obligatory along with abstaining, because the intention (niyyah) was not formed overnight. Thus, the fast was not valid, and the abstention is out of respect for the time.

2. Ibn Taymiyyah: He holds that only abstention is obligatory, without the need for making up the fast. This is because their eating and drinking before they knew was permissible, as they were ignorant and not deliberate [in breaking the fast]. He cites the Hadith of Ashura and argues that whoever ate out of assumption and then realized their mistake does not have to make up the fast, just as intention follows knowledge.