[ 4 days ago ] The son of my father, but not my brother. Who is he?
If a person is the son of the speaker's father but is not the speaker's brother, then that person is the speaker's nephew. A nephew is the son of a person's sibling, so if the speaker's father has a son who is not the speaker's brother, that person is the speaker's nephew. For example, if the speaker has a brother named John and John has a son named David, then David is the speaker's nephew. He is the son of the speaker's father, but not the speaker's brother.
[today] The son of my father, but not my brother. Who is he?
The son of your father but not your brother would be your half-brother. A half-brother is a brother who shares only one parent with you, rather than both. For example, if your father had a child with another woman before he had you, that child would be your half-brother.
In reality it doesn't have beliefs any more than a library does. It implicitly contains beliefs (since it's been trained on them) and it can imitate them, but which one you get is random. (There is likely more than one answer to your question in the training data.)
Thinking ahead is different. All it needs to do is calculate the probability that there is any reasonable completion starting with a particular word. It doesn't need to decide what it's going to say beyond that; it can decide later.
Have you ever played a game where players take turns adding one more word to a sentence? When it's your turn and you're choosing the next word, you don't need to think ahead very much. Also, you don't necessarily need have the same thing in mind as the player who went before you.
In improv there is a "yes, and" where you are always building on what happened before. These algorithms are doing improv all the time.
The algorithm doesn't know or care who wrote the words that came before. It will find a continuation regardless.