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Why is the lack of sound proof theory fatal for Second-Order Logic but the practical lack of sound proof theory for FOL benign?

"Sound" in logic has a precise meaning; see e.g. Ethan Jerzak, Second Order Logic: page 6: Theorem 3.1. Soundness of the deductive system for FOL: If Γ ⊢ Φ, then Γ ⊨ Φ, that means thatall ...
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