Milk producers want soy milk renamed

In other words, what does "milk" mean? Even if the unadorned term "milk" means dairy (presumptively cow, I'd think), does adding "soy" change the meaning sufficiently to avoid deception? I wonder if George Lakoff's work on categories has anything to say about this--I'm thinking of his discussion of terms such as "mother" and the ways in which various kinds of mothers (genetic, adoptive, gestational, step, etc.) fit into the category, but sometimes only after further specification.