Set Theory and Logic

    

Beyond Gödel

Authors: Jim Rock

In 1930 Gödel wrote a landmark paper showing that in any formal system there will always bestatements that cannot be proven. But the deficiency of formal systems goes much deeper. The same logically valid statement can be used in conjunction with two different sets simultaneously proving a true statement and a false statement. This result is profound. It explains why people can use the same sound argument to prove two contradictory statements. It is no wonder the most lucid arguments still sometimes result in hung juries and earnest people can disagree on the most fundamental issues. Truth is a much deeper concept than logical validity.

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[v1] 2024-05-30 02:48:59
[v2] 2025-05-08 19:52:14
[v3] 2025-08-26 01:36:46

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