The underlying motivation for the research in the field of axiomatic theories of truth is to determine the logical relations between various properties of the notion of truth.
The underlying motivation for the research in the field of axiomatic theories of truth is to determine the logical relations between various properties of the notion of truth. The examples of such properties include: compositionality with respect to a given set of connectives (for example: a disjunction is true if and only if one of its disjuncts is true), self–applicability (i.e. the truth can be meaningfully ascribed to sentences with the truth predicate) and providing (new) justifications for accepting sentences without the truth predicate (for example various consistency assertions). Such properties can naturally be modeled as certain set of axioms for the truth predicate or metalogical properties of certain theories.
In the talk we focus on axiomatic theories of truth over Peano Arithmetic (PA), thought of as the base theory. Such theories result by extending the latter theory with some axioms for the newly added unary predicate, thought of as a truth predicate for the language of arithmetic. Any such theory can be thought of as an axiomatization of a certain aspect of the notion of truth. We start by introducing all the relevant definitions and explaining the naturalness of this model. Next, we show how such an approach can give us new insights into some interesting philosophical problems. In particular we show various approaches to understand the deflationary claim that the notion of truth is epistemically light.
We end our talk by presenting the most recent developments concerning the Tarski Boundary, i.e. the „line” demarcating axiomatic theories of truth which prove arithmetical sentences unprovable in PA from the ones which are its conservative extensions. In particular we provide results showing how much about the notion of truth one should know in order to prove the consistency of the base theory.
Sekcja LogikiPrzewodnicząca Sekcji: dr hab. Joanna Golińska-Pilarek (UW)
Sekretarz Sekcji: dr Michał Zawidzki (UW)
prof. dr hab. Jerzy Pogonowski
Uniwersytet im. Adama Mickiewicza w Poznaniu