Truth and the Unprovability of Consistency
By Hartry Field
It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible.
Professor Field is one of the leading advocates of the Deflationary Theory of Truth and his views are among the most challenging ones at the turn of the century. This papers tries to tackle one of the most difficult and most important Philosophical issues of the XXth century.