The Tarski T-Schema is a tautology (literally) | Zendy

Edward N. Zalta | Zendy

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The Tarski T-Schema is a tautology (literally)

Author(s) -

Edward N. Zalta

Publication year - 2013

Publication title -

analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.452

H-Index - 45

eISSN - 1467-8284

pISSN - 0003-2638

DOI - 10.1093/analys/ant099

Subject(s) - tautology (logic) , schema (genetic algorithms) , propositional calculus , truth table , mathematics , computer science , philosophy , epistemology , propositional variable , discrete mathematics , algorithm , theoretical computer science , information retrieval , intermediate logic , description logic

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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