Abstract
The family of diagonalization techniques in logic and mathematics supports important mathematical theorems and rigorously demonstrates philosophically interesting formal and metatheoretical results. Diagonalization methods underwrite Cantor’s proof of transfinite mathematics, the generalizability of the power set theorem to the infinite and transfinite case, and give rise at the same time to unsolved and in some instances unsolvable problems of transfinite set theory. Diagonalization is also frequently construed as the logical basis of the liar, Richard’s, Grelling’s, the Russell and Curry paradoxes, Godel’s theorems, Church’s and Rosser’s incompleteness results, and every logically or semantically self-limiting metatheorem and self-referential logical puzzle and formal semantic paradox.
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