Mapping mental spaces: An example

Here's my attempt to go map rollick's exchange with Miller. It's a little rough, but it gives you an idea how space-building is hypothesised to work.

The Onion: Who could you take in a fight?

This sentence sets up two spaces: The Base space, which includes the element m (Miller) and a Possibility space, with the element m', corresponding to m in the base space. (The use of could rather than can implies hypotheticalness: I know you don't fight, but if you did, who could you beat? The linguistic term for this special use of past tense is distal.) The P space also hosts a property FIGHT (short for "take in a fight") and a set of elements x, such that the truth value of m' FIGHT x is T.

Frank Miller: [Laughs.] Let's see. Give me a second. I'd say Little Lulu.

Here, Miller supplies the value "Little Lulu" for x. Cultural knowledge tells us that Little Lulu is a fictional figure; to the degree that she is an entity who could participate in a fight, it's in an Imaginary space. The I space doesn't have counterparts for everything in the real world (i.e. roughly speaking, the B space); there's no element corresponding to m. So how do we make sense of such a response?

[stuff about tubby deleted]
O: You say you could take her in a fight, but you're not familiar with her mythos? What if she has powers you're not aware of?

Here, rollick chooses to set up an Imaginary Possibility space that blends the I space ("the Little Lulu mythos") with the P space. As I said before, for our purposes, it doesn't really matter whether this is an imaginary world where Miller is also a cartoon figure or where Little Lulu is a real person. The point is, it has to be such a world where the property FIGHT can apply to both. This space has counterparts for elements in both the I and P spaces (i.e. m'' and l'), but inherits the structure of the P space (i.e. m' FIGHT x) to yield the structure m'' FIGHT l', i.e. "Miller takes Little Lulu in a fight". Using her background knowledge of Little Lulu's characteristics in the I space and Miller's characteristics in the B space (all of which carry over into the IP space unless explicitly negated), she attempts to evaluate the truth value of the proposition.

FM: Well, she doesn’t exist. She’s just lines on paper. If you want to go along those lines, I’ll just say I could take Galactus.

...and then Miller comes along and negates all this space-building! He returns to the B space, where Little Lulu "exists" only as lines drawn on paper, and projects a counterpart of this entity--still only lines on paper--into the P space. By denying the existence of the I space, Miller explicitly blocks the carry-over of Little Lulu's fictonal characteristics into any space where he has a counterpart. But, as rollick later noted, interpreting the statement m' FIGHT l'' in the P space is only possible if one reinterprets the meaning of FIGHT:

O: I suppose you could erase him.
FM: Paper rips.

Erasing a picture of someone or tearing it up is not a typical example of "fighting". As a metaphorical extension, it's not without precedent. (We speak of "fighting" inanimate objects all the time.) This, of course, opens another can o' worms, since "fight" is not a classical category and exhibits prototype effects, etc. And I'd have to bring in Gricean maxims and other types of background assumptions to explain why rollick and flagpolesitta view Miller's switcheroo negatively. For another time...