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Reading through your story makes me think that, in a way, the narrator has to be a character himself. The story doesn't even have to revolve around the narrator for him to count as a character. I'...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/31517 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Reading through your story makes me think that, in a way, the narrator has to be a character himself. The story doesn't even have to revolve around the narrator for him to count as a character. I'm using the rough and loose definition of a character as anything that shares the person-like quality of having a personality and of thinking. So, the rabbits in the Watership Down are characters because they all behave and think person-like. A story about a rock that wants to see whats on the other side on the hill it's resting on, has the human-like quality of thinking. Any story you would want to tell would need to have a narrator, basically some voice through which to communicate the story with. The fact that you now have someone to observe/speak of the event, means you necessarily would need to have a character, someone or something with the ability to perceive and think and tell the story in a way that is funny, engaging, meaningful, or even boring. Essentially, you can't have a story without a character because, without anyone to see the story unfold, there can't be a story to be told in the first place. It's like that age old adage about the tree that falls in the woods... if there is no one there to hear it (or in our case, see it), does it really fall? Do we really have a story to tell if no one is there to either see or tell of it?