Godel's theory says that in every formal mathematical system there exist true statements that cannot be proved true within the limits of that particular formal system (Casti 1991, p.381). At a surface level, this has similarities to the semiotic result that there can be no perfect language; no formal language can express, "without ambiguity, the essence of all possible things and concepts" (Eco 1993:1995). It is interesting that a formal mathematical system is one that expresses the syntax of mathematics as a symbolic code (Casti 1991) and that constructionist theories of representation also deal with the syntax of symbolic codes (Hall 1998).
The next question to ask is whether a semiotic translation of Godel's theory is actual possible. As noted above, both deal with the syntactic aspects of symbolic codes. From a mathematical side, Casti (1991) provides different translations of Godel's theory for specific formal systems. Hofstadter identifies four theories as being examples of limitative results in mathematics: Godel's Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting Theorem and Tarski's Truth Theorem (1979, p. 697). As Godel's theory applies to all formal systems, the necessary question is: "can the semiotic representation of language be expressed as a formal mathematical system?" If the answer to this question is yes then there will exist a semiotic version of Godel's theory. The exact form of this version is of most interest, it will be the form that provides the context for mathematical/linguistic translations.