I don't see where the author assumes that there's only one switch. All they need is that there is at least one switch. I also still don't see the difference be

I don't see where the author assumes that there's only one switch. All they need is that there is at least one switch. I also still don't see the difference between my argument and the paper's. You can say that "is a pumpkin" is not Boolean, but as long as you concede that the first object has a property the last one lacks, some object along the way must change. You can say unambiguously a pumpkin is not Boolean, but then you just go one level up, to unambiguously unambiguously not a pumpkin. You don't really need Boolean, you just need the property to be determined for some objects. For any object, either it's determined or not, right? So one level up should be enough.