19-20 May 2016, International Workshop "Language and metalanguage, logic and meta-logic.
Revisiting Tarski's hierarchy", Louvain-la-Neuve, Belgium

The goal of this workshop is to bring together researchers in logic, philosophy of logic, philosophy of language and philosophy of mathematics to investigate the problem of the separation between object-language and metalanguage.

Ever since the work of Alfred Tarski we have known that trivializing paradoxes arise when one designs a precise language that is able to express at the same time the object theory and the metatheory of a certain domain. As a solution, Tarski suggested a strict hierarchy of languages in which every language can only talk about the language immediately below it in the hierarchy. Although this works as a technical solution, it is rather artificial and remote from our intuitions about natural language.

Since Tarski's results, logic, philosophy of language and mathematics have changed quite a bit. Nowadays we have a multitude of non-classical logical systems that can prevent the paradoxes from popping up or from destroying all meaning. There are well-established mathematical tools to carefully deal with the possibility of reasoning about the metatheory of a foundational theory ('forcing' in set theory, category theory, consistency strength). Ways of dealing sensibly with non-stratified full comprehension in mathematics have been proposed. Sophisticated grounding and revision techniques for self-referential truth have been developed. Formal tools have been devised to better understand natural language. People are trying to emancipate themselves from the norm that urges us to use a classical metatheory. Given all these new developments, we think now is a good time to reopen the philosophical debate on the distinction between object-language and metalanguage.

For more information, see http://perso.uclouvain.be/peter.verdee/metalang2016