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Ideas for 'Elements of Mind', 'The Tarskian Turn' and 'Reportatio'

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5. Theory of Logic / K. Features of Logics / 5. Incompleteness

15353	The first incompleteness theorem means that consistency does not entail soundness [Horsten]
	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.
	From: Leon Horsten (The Tarskian Turn [2011], 04.3)