The Soundness Paradox

An inference is standardly said to be sound just in case it is deductively valid and it has only true assumptions. The importance of a coherent concept of soundness to proof theory is obvious, in that it is only sound derivations, and not merely deductively valid arguments, that advance knowledge by providing proofs of theorems in logic and mathematics. The soundness paradox is informally albeit impredicatively formulated as argument (S): Argument (S) is unsound, therefore, argument (S) is unsound. This paper introduces and explains the importance of the soundness paradox, formally demonstrates how to avoid superficial impredication via Gödelization, and compares it with the similar but significantly different liar and validity or Pseudo-Scotus paradoxes. Although there are similarities in this family of semantic diagonalizations, the soundness paradox is not just a hybrid of the liar and validity paradoxes, but is more fundamental, belonging to a special category that resists the most powerful received solutions to the liar and validity paradoxes.