Tag Archives: Incompleteness Theorem

IS EVERY MATHEMATICAL THEOREM A TAUTOLOGY?

If one uses a classically rigorous definition of a tautology, the answer is yes. Classically, a tautology is a statement that is necessarily true by the classical laws of logic (identity, non-contradiction, excluded middle). So, statements such as “if the grass is green then the grass is green” and “all bachelors are unmarried men” are […]

WHY DID GÖDEL’S INCOMPLETENESS THEOREM BECOME SO FAMOUS OUTSIDE MATHEMATICS?

This question is actually the reverse of what should be asked about this Theorem: why is it so famous within mathematics? Answers by mathematicians to this question assume their conceptual math problems are at the heart of this Theorem and thus ridicule its application to conceptual problems of formal logical explanations for anything else. This […]