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Gödel’s Incompleteness Theorems
Gödel’s incompleteness theorems belong to the so-called limitation theorems. They indicate some inner limitations of the axiomatic method. To this group also belong the Löwenheim-Skolem–Tarski theorem (on the existence of a countable model for any consistent theory), Tarski’s theorem (on the undefinability of the concept of truth), and Church’s theorem (on the undecidability of the predicate calculus). All of them have far-reaching consequences for logic, for the foundations of mathematics, and for the philosophy of mathematics. They are also important for general philosophy, in particular for epistemology and methodology. However, in the latter case, the consequences depend on various additional factors, for example, on interpretations and on whether the precise assumptions of those theorems are really fulfilled.
Historical Background of Gödel’s Theorems
Ever since Plato, Aristotle, and ...
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