Single Idea 15353

[catalogued under 5. Theory of Logic / K. Features of Logics / 5. Incompleteness]

Full Idea

It is a lesson of the first incompleteness theorem that consistency does not entail soundness. If we add the negation of the gödel sentence for PA as an extra axiom to PA, the result is consistent. This negation is false, so the theory is unsound.

Clarification

PA is Peano Arithmetic

Gist of Idea

The first incompleteness theorem means that consistency does not entail soundness

Source

Leon Horsten (The Tarskian Turn [2011], 04.3)

Book Reference

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.52