To put it in layman terms, the thing is, words with precise meaning are not that useful in discussing lots of things. Perhaps because lots of things are not inherently clear, but fuzzy in itself. What is "freedom"? What it "moral"? What is the best thing to do with my life? Etc. None of these are clear cut -- and the things that are clear cut, well, not all of those are worth discussing or really important. A lot of stuff is better described and argued about with imprecise words. Philosophy is also the body of such discussions.
In essense, this parallels Godel's incompleteness result (Note that I say "parallels" -- Godel only proved it within a very specific mathematical context). Mathematics thrive even if they are not concerned with purely axiomatic systems.
I am sorry for the following comment, but isn't that comment actually extremely arrogant as well? One should present ideas and arguments and not credentials, but I guess this is only the opinion of some one not as intelligent as a PhD holder.