Workshop (en)

Language and metalanguage, logic and meta-logic. Revisiting Tarski’s hierarchy.


May 19-20, 2016


Université catholique de Louvain, Louvain-la-Neuve, Belgium

SOCR 43, Bâtiment Socrate
12, Place Cardinal Mercier
1348 Louvain-la-Neuve


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. Specialists in the relevant fields are invited to present their own current research (on any related topic) and, from that perspective, reflect upon the implications of their work for at least one of the following issues:

    • Is the distinction necessary, desirable, natural?
    • Importance of a clear meta/object-language distinction for truth theory
    • Importance of a clear meta/object-language distinction for metamathematics
    • Importance of a clear meta/object-language distinction for the famous foundational theorems: Gödel (incompleteness), Löwenheim-Skolem (for each cardinality a model), Cohen (forcing)
    • How can one formalize metalanguage?
    • How to avoid infinite regress (object, meta, meta-meta, meta-meta-meta...) when trying to make a language precise?
    • Should the same logic be used at the object level as at the metalevel?
    • Is it reasonable to assume a shared natural metalanguage?
    • Is it possible/useful to unify (meta-)languages and to reduce one to another language?
    • Category/type/set theory as unifying metalanguage of mathematics and computer science
    • Universality of languages
    • Logical pluralism

Invited speakers

ACHOURIOTI Dora, Universiteit van Amsterdam (ILLC), Amsterdam, Netherlands

RUSSELL Gillian, University of North Carolina, Chapel Hill, NC, USA 

VENTURI Giorgio, State University of Campinas (UNICAMP); Campinas, SP, Brazil

WEBER Zach, University of Otago, Dunedin, Otago, New-Zealand 

DE BRABANTER Philippe, Université Libre de Bruxelles, Brussels, Belgium

DEGAUQUIER Vincent, Université Namur, Namur, Belgium 

RICHARD Sébastien, Université Libre de Bruxelles, Brussels, Belgium

URBANIAK Rafal, Ghent University, Ghent, Belgium and University of Gdansk, Gdansk, Poland