Is it true that a language can't be defined within itself like math?
Dear Gabriel Giordano,
You have certainly broached up an insightful question which addresses a very important issue in modern logic concerning formal theories and their explanatory power. Incompleteness theorems introduced by Kurt Gödel tend to challenge the conditions of adequacy evaluating the theoretical worth of particular outcomes which formal theories tend to predict. Clearly, incompleteness theorems concern the limits of provability in formal theories. Differently stated, if certain statements in language A can neither be proved or disproved, such a language system can not be regarded as a consistent system. consequently, Chomsky's formal theory of language called minimal program is an attempt to produce a formal theory of language that represents a realistic and consistent reflection of how linguistic competence works. Within such perspectivization, which is highly idealized, Chomsky has been able to create a conceptual framework that does not fall within the bounds of incompleteness theorems. However, the functional theories of language tackling a wide range of extralinguistic elements are entrapped within many inconsistencies, and as a result, their logic of explaining the realities of language is often adorned with logical fallacies which diminish their power of provability.
Best regards,
R. Biria
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