Human languages do not strive to avoid ambiguity. They do not try to align words with meanings one to one. They are not in danger of anarchy when a new word sense evolves. People don't just tolerate languages with multiply polysemous words, they seem to love them; people thrive on multiplicity of meaning. There are thousands of examples that show this. It is only the prescriptivist thickheads who cannot see what it means.
So, he argues, polysemy - multiple meanings of the same word - is not inherently confusing. One major argument used by prescriptivists against semantic change is that it leads to misunderstanding and confusion (How can sick mean good when it also means ill, or wicked mean excellent when it also means evil?) but Pullum's take on this is a strong counterblast to all of this.