Write a story without a setting? It's like trying to write a story without a character. I don't think it can be done. A story has to happen to somone or something, even if it's just a grain of sand, and it has to happen sometime and somewhere. The setting can be pinpointed to the second or it can be as vague as long, long ago. It can be as isolated and simple as the inside of a coffin, or it can be as vast as the universe.
I would guess that for most authors, establishing a setting is one of the easiest aspects of creating a story. That doesn't mean it isn't important. In fact, setting is instrumental in defining the parameters for character development and plot movement. In my novel, Return to Bone Tree Hill, the setting is almost another character, and in the novel I'm currently working on, The Sentinel of Mabry Moor, the setting dictates the entire plot. (Notice how the setting is mentioned in both titles.)
Anyway, the topic came up at my critique group last week, and I've thought about it quite a bit since then. One of our members, who is writing a science fiction novel, has been floundering in recent months. Oh, she's been writing, but often just writing exercises, and even when she has submitted a scene from her WIP, it isn't always clear where or how it fits with her storyline. Plot direction and character attributes tend to be in flux. Last session, she told us that instead of writing, she's been world-building. She's been mapping, researching, juggling, rethinking and reforming the setting of her story, because she can't write her novel until she clearly comprehends where and when it's happening.(When you're creating a completely new world, the setting is obviously more intricate.)
By forcing herself to examine her setting and make some concrete decisions about it, it has gone from a blurry idea to a vivid world. Finally she can picture the place her story is set. She can see every part in relation to every other part and she can see her characters moving within it. (I cannot stress enough how crucial it is to be able to do this. You cannot hope to paint a picture for readers, when you can't visualize it yourself.)
Most important of all, clearly defining her setting helped her make decisions about the direction her story must take if it is to fit the setting. She realizes that she needs to change the time element, because by doing so she can reveal the story in a more dramatic way. Understanding her setting has also made her realize that her characters will react to situations based on their backgrounds (personal settings) as well as the present setting in which they find themselves. (It's the old you can take the boy out of the country, but you can't take the country out of the boy adage.) People are in part a result of where and how they grow up. What motivates them is connected to their backgrounds too.
Of course, this spills over into the plot as well. Instead of trying to force the plot into the mold she had originally devised, she is using the aspects of the setting to dictate how scenes play out and how important they are to the story.
Now she finds herself weaving the elements together in a more natural progression and she is anxious to get back to writing. I have a feeling it's going to be a new, improved story.