## The Tarski T-Schema is a Tautology (Literally)

### Author

Edward N. Zalta
### Reference

*Analysis*, 74/1 (2014): 5–11.
### Abstract

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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