undefinability of truth


Tarski's Theorem states that no first-order logical theory has a predicate defining the Godel numbers of statements which are true of the natural numbers. In other words, a first-order theory which includes arithmetic can't define its own truth predicate. This is a fundamental limitation on mathematics, because it implies no formal system is powerful enough to define its own semantics.


This concept has the prerequisites:


  • Know the statement of Tarski's Theorem and why this implies a formal language can't define its own truth predicate
  • Prove Tarski's Theorem

Core resources (read/watch one of the following)


See also

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