The Tarski T-Schema is a Tautology (Literally)


Edward N. Zalta


Analysis, 74/1 (2014): 5–11.


The Tarski T-Schema has a propositional version. If we use φ as a metavariable for formulas and use terms of the form that-φ to denote propositions, then the propositional version of the T-Schema is: that-φ is true if and only if φ. For example, that Cameron is Prime Minister is true if and only if Cameron is Prime Minister. If that-φ is represented formally as [λ φ], then the T-Schema can be represented as the 0-place case of λ-Conversion. If we interpret [λ …] as a truth-functional context, then using traditional logical techniques, one can prove that the propositional version of the T-Schema is a tautology, literally. Given how well-accepted these logical techniques are, we conclude that the T-Schema, in at least one of its forms, is a not just a logical truth but a tautology at that.

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