Projects in Previous Years

2nd Semester 2016/17: Truth theories and their strength

Cezary Cieslinski (University of Warsaw)
If you are interested in this project, please contact the instructor by email.
The goal of the project is to give an overview of formal results that provide the basis of contemporary discussions about truth. The focus will be on axiomatic theories of truth built over first-order arithmetic, treated as a theory of syntax. Given an arithmetical theory S, we enrich its language with a new one-place predicate "T"; then we supplement S with additional axioms or rules for the new predicate. The idea is that these new axioms or rules will play the role of "meaning postulates" - basic principles characterising the content of the notion of truth.

The strength of such theories will be analysed from two angles. Firstly, we will ask about the truth-theoretic strength of axiomatic theories of truth. Here we would like to know how efficient these theories are in proving useful general facts about truth (e.g. the compositionality principles). Secondly, we will be interested in the arithmetical strength of axiomatic theories of truth. In this context we will analyse the conservativity properties of these theories, employing two non-equivalent notions of conservativity: syntactic and semantic (or model-theoretic). A theory T is syntactically conservative over a theory S if T does not prove any theorems in the language of S which would be unprovable already in S. On the other hand, T is model-theoretically conservative over S iff every model of S can be expanded to a model of T. Various examples of axiomatic truth theories will be analysed from this point of view, with their semantic and syntactic conservativity properties investigated.

The overall aim of the project is that of providing the formal background necessary for following the current debates about truth in logic and philosophy. In addition, we will also discuss a selection of open problems in this area of research.

There will be 4 meetings of two hours in the week of 19-23 June, with the whole project being planned as a mixture of lectures and discussion sessions.

1st meeting: Tuesday 20 June: 13-15

2nd and 3rd meetings: Wednesday 21 June: 9-11 and 11-13

4th meeting: Thursday 22 June: 13-15

All meetings will be in the ILLC seminar room, F1.15.
Basic knowledge of logic, set theory and model theory.
Homework assignments.