We are not thereby constructing the world. Today it's fashionable to see intellectual, and even scientific, disputes as merely stories competing against one another, narrative vs. narrative. Turner would like the story part of this story. But nothing he says suggests relativism. We may invent stories about reality, but our stories will answer to reality, not to our whims or will.
Meaning is a complex operation of projecting, blending, and integrating over multiple spaces.
Meaning never settles down into a single residence. Meaning is parabolic and literary. To many of us this seems counterintuitive. In the spirit of Turner's book, let's parabolically imagine concepts as countries. These countries are often distinguished from each other by borders that appear as clear, natural divisions, like rivers or mountain ranges.