So you might have two sentences A and B shown as two circles, then "A and B" is their intersection, "A or B" is their union, etc. But "A implies B" doesn't mean one circle lies inside the other, as you might think! Instead it's a shape too, consisting of all points that lie inside B or outside A (or both).

There's nothing intuitionistic about this. You can do exactly the same thing with classical logic, if you just forget about the topological "other details" that you alluded to.

Can anyone point me to any good arguments for, or at least redeeming qualities of, Integrated Information Theory?