 One needs to add the assumption that the function from the determinants of meaning to the meanings themselves is one-to-one (that is, not only does any change to a word’s meaning require some change in the determinants of its meaning, but also that any change to the determinants of a word’s meaning must produce a change to its meaning), and doing that will probably require something more like a “direct” argument, since it is unlikely that one could argue that the function from use to meaning had to be one-to-one without some sort of substantial account of how use determined meaning.