Guest Editors’ Introduction

Abstract

by Hans Herzberger, revision theory appears as a proposal to deal with a type-free concept of formal truth that preserves the classical scheme [7,20,28,29]. Though the story is well-known, we think it would be useful to recapitulate here, in a brief and obviously incomplete summary, some of the main events by means of which the original proposals developed into the current, broader field of investigation, to give the uninitiated reader a rough idea of the context for the contributions in this volume. 1 In his seminal work from the 1930's, Alfred Tarski proved the existence of a fundamental inconsistency emerging in a situation where: (i) there is a formal language L respecting some modest assumptions on its strength in expressive capabilities; (ii) the language contains a unary, unrestricted predicate T for (codes of) formulas working as a truth predicate, verifying natural principles that require that the formula T ( ϕ ) be equivalent to ϕ, for every sentence ϕ of L; (iii) a classical relation of satisfaction for formulas of L in any interpretation, or model M, is retained, therefore each sentence ϕ of L is assumed to take either semantic value 1 or 0. Tarski's contradiction took the form of a theorem about the (arithmetical) undefinability of such predicate T for any L, granted (i)-(iii). Tarski's theorem shows that no sufficiently expressive, classical formal language can consistently contain its own truth predicate. As a solution, he proposed a typed theory of formal truth, asserting that every language L for 1 The interested reader should consult [38] for a more detailed introduction to revision theory.