Logic & Set Theory seminar: The Simple Truth
Graham Leigh, Technical University of Vienna
Howard House 4th floor seminar room
Note unusal day and time!
The 'truth bi-conditionals' are the statements of the form ‘A ↔ T[A]’ where A is a sentence, T is a predicate symbol and [A] denotes a name for A (e.g. Gödel code of A). Theories defined in terms of truth bi-conditionals are typically deductively and conceptually simple. As observed already by Tarski, compositional truth principles, such as ‘for all sentences A, B: T[A & B] ↔ T[A] & T[B]’, are not derivable from the basic bi-conditionals except in trivial cases. Nevertheless, Quine, Horwich and others have proposed that the truth bi-conditionals are all there is to truth. In this talk I present proof-theoretic support for this extreme view and show how remarkably strong systems (both truth- and proof-theoretically) are implicit in very weak truth-theoretic assumptions.