Human ecology
Formalism: a linking theme between mathematics, computation, and cultural theory
Links between formalism in mathematics and linguistics: a semiotic version of Godel's Proof.

A brief examination of the histories of linguistics (Hawkes 1977) and mathematics (Barrow 1992) would suggest that the formalist programmes of the early part of the 20th century could provide a reference point between science and the humanities. Perhaps the most important mathematical result of this time was Godel's theory. This theory is still relevant to the philosophies of mathematics, computing, and information theory (Barrow, Casti, Hodstadter, Penrose)

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.



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Written 3/5/99
Created 30/5/99
Modified 5/7/99