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

## Dates

May 19-20, 2016

## Location

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

SOCR 43, Bâtiment Socrate

12, Place Cardinal Mercier

1348 Louvain-la-Neuve

## Description

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

## Sponsors

**CNRL-NCNL**

**CEFISES**

**ISP**