I'll be perfectly honest, I'm half-serious, half-drunk-posting.
But on simple inspection, the idea that a word can fit into a single category is obviously wrong. So to generalize the idea, you have to assume that a word can fit into multiple categories.
Biology is undergoing a similar transformation from simple "this animal looks kinda like this one" to genomics classification, which is revolutionizing the tree of living things used by biologists to organize living things.
There's not really any reason why words, a biological artifact, have been correctly classified all along. Hell! A copy-editor neighbor and I have minor quarrels over the capitalization of college subject names.
Trees are a specialization of graphs, and they're usually wrong. Just assume graphs to start with and your data will organize much better, even if the properties of the organizational metaphor aren't quite as nice.