My father's grandfather and his brother fought at the battle of Vimy Ridge.
My first question looking at this sentence is, "Whose brother? Your Dad's, or his Grandpa's?"
There's some confusion over whose brother actually went to Vimy. How would you describe what's wrong with the above sentence?
First of all, there is no ‘participle’ and so no dangling participle. Nor is there a dangling preposition (which is the commonly recognised dangler).
If there is a problem, it is in the potentially ambiguous reference of “his”: it could refer to the brother of the father of the subject of the sentence or to the brother of the subject’s father.
It is a common problem with pronouns and with possessive adjectives. Common sense suggests that it is probably the grandfather’s brother (i.e. the the father’s great uncle that fought at Vimy Ridge. It stretches credulity that someone’s uncle and great great uncle both fought in the same battle.
Ambiguity is not a grammatical fault. But if it is to be avoided, it is by finding another way round it. For example:
My great grandfather and his brother ....
This will do fine.
This is called an unclear antecedent or ambiguous antecedent. The default rule when parsing an ambiguous antecedent is to assume it refers to the most recent sensible noun. So in your example, we'd assume it's Grandpa's brother.
One way to fix it would be to avoid having two possible antecedents in the first place:
My great-grandfather and his brother ...
In this version, it's clear that it's your grandfather's brother, because we never mention your father.
You can also avoid the pronoun:
My father's grandfather and brother ...
Now it's clearly Dad's brother.
You can find more discussion of this problem at The case of the ambiguous antecedent and Unclear Pronoun Antecedents.
Nothing wrong with the sentence, actually. First, it is syntactically well-formed. Here is a tree drawing:
It is just one where there are two logically possible bindings for the possessive pronoun his. k=i or k=j. So if you want to say something about the sentence, it's semantically ambiguous. A similar case would be sentences like
Thomas reminded Billy to put his toys away.
Billy asked Thomas for help with his homework.
The two examples aren't a problem because you understand pretty quickly what his binds to. The OP's example, you also understand quickly that people two generations apart don't fight in the same battles. But it's funny to think about someone fighting alongside their grandfather in 100 years ago. Very funny.
The grammar school books will have you believe that there is a problem with ambiguous sentences that have an improbable but amusing reading. Maybe they picked this example because it seemed it would be parsed on the fly as involving a parallelism of possessors, leading to the wrong semantic reading.
The bigger problem for students of English is writing ambiguous sentences that have no clear resolution, rather than an improbable but funny one. Avoiding it takes practice writing and reading rather than learning slogans, because it's silly to avoid all ambiguity when writing (this is not computer programming). Then again, if you diagram out every sentence you write and record all of the bindings (pronoun to antecedent), just to make sure that there is no ambiguity, that is probably good practice!
