By Adam Schaff; Version al espanol de Mireia Bofill

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Additional resources for Lenguaje y Conocimiento

Example text

Then the lemma follows from these definitions. 0 t ϑ h. t definition of g definition of h. Since the translation function h is primitive recursive it is provably total in Peano arithmetic. I will also invoke a variant of the lemma where the translation function replaces indexed truth predicates depending on an additional argument for the translation function. Adding a parameter in the above lemma requires only minimal modifications of the proof. 6 Comparing axiomatic theories of truth The main technical results of this book compare axiomatic theories of truth but also compare such theories of truth with other theories like the base theory or, in some cases, second-order theories of arithmetic.

First I will introduce a very general and widely used notion of reducibility between theories: relative interpretability. This notion can be applied even in cases where the theories do not share any non-logical vocabulary. I will 39 40 comparing axiomatic theories of truth begin with this very general notion of reducibility before passing on to more specific notions with a more limited range of applicability. For the following definitions I assume that S and T are deductive systems formulated in the languages LS and LT , respectively.

By the above conventions, the symbol T. 1 stands for the function that yields, applied to a term t, the formula T1 t; T. 2 is to be understood in an analogous way. It might be tempting to say that the truth predicate T1 can be easily defined in the second theory by defining T1 as T2 (assuming that this translation works also for other axioms for T1 ). This definition of T1 as T2 does not yield a truth-definition, however, as the translation of the axiom for T1 is the following sentence: ∀t T2 T.

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