Journal of Philosophical Logic

, Volume 28, Issue 1, pp 1-28

First online:

Tarski on “essentially richer” metalanguages

  • David DeVidiAffiliated withDepartment of Philosophy, University of Waterloo
  • , Graham SolomonAffiliated withDepartment of Philosophy, Wilfrid Laurier University

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It is well known that Tarski proved a result which can be stated roughly as: no sufficiently rich, consistent, classical language can contain its own truth definition. Tarski's way around this problem is to deal with two languages at a time, an object language for which we are defining truth and a metalanguage in which the definition occurs. An obvious question then is: under what conditions can we construct a definition of truth for a given object language. Tarski claims that it is necessary and sufficient that the metalanguage be “essentially richer”. Our contention, put bluntly, is that this claim deserves more scrutiny from philosophers than it usually gets and in fact is false unless “essentially richer” means nothing else than “sufficient to contain a truth definition for the object language.”

truth definitions T-scheme material adequacy hierarchies consistency