This chapter explores the benefit of those who have little taste for the intricacies of mathematical logic, the general significance of Goedel's important logical discoveries. In Goedel's own exposition the relation between certain linguistic and certain arithmetical issues is extremely intimate: the reader is introduced, from the first, to a difficult and complex 'arithmetized syntax', in which all the symbols of a language are correlated with numbers, and all the logical relations among those symbols are mirrored in a set of corresponding numerical relations. The discoveries of Goedel have their origin in the well-known puzzles connected with reflexive sentences, sentences that refer to themselves and predicate properties of themselves. Such sentences are at times wholly innocuous as when a sentence says of itself that it is long, or written in red ink, or occurs on a certain page of a book but lead us, at other times, into hopeless antinomies.