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5. Theory of Logic / K. Features of Logics / 3. Soundness

[whether all formal deductions always lead to truth]

12 ideas
A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]
Soundness would seem to be an essential requirement of a proof procedure [Tharp]
If everything that a theory proves is true, then it is 'sound' [Smith,P]
Soundness is true axioms and a truth-preserving proof system [Smith,P]
A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P]
'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro]
Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach]
Normally we only endorse a theory if we believe it to be sound [Halbach]
Soundness must involve truth; the soundness of PA certainly needs it [Halbach]
If soundness cannot be proved internally, 'reflection principles' be added which assert soundness [Halbach/Leigh]