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This question really comes down to the definition of story (and, to a certain extent, of fiction). If we take story in the broad sense of a sequential narrative and fiction in the broad sense of an...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/24837 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
This question really comes down to the definition of story (and, to a certain extent, of fiction). If we take story in the broad sense of a sequential narrative and fiction in the broad sense of any statement that is not true, then clearly there can be stories without characters. If we take story and fiction in the narrower sense of a drama, then there can be no drama without characters, since it is the desire of a character that drives drama. But human beings are interested in other types of stories besides dramas, so there are is certainly scope for stories without characters. But since you posit that the intent of the question is to understand character by removing them from story, then I would suggest that what character is, in terms of a drama, is desire. Characters, dramatically speaking, are expressions of desire and the willingness to act in pursuit of desire.