Cool Logic

Bartosz WcisŁo (University of Warsaw)

Measuring the Content of Truth

January 29th at 17:30, in Seminar Room (F1.15)

My talk will concern certain results and directions of research in formal theories of truth. Formal theories of truth try to investigate this central concept of logic in both axiomatic and semantic way. On the axiomatic side, the basic methodology may roughly be outlined as follows:

1. Take your favourite metamathematical theory B. Call it a base theory.
2. Add a fresh predicate T(x) with the intended reading "x is a (code of a) true sentence". Add some axioms governing the predicate.
3. Compare the resulting theory with the base theory you started with.

Now, there are many possible concrete realisations of the above programme, depending on what we mean by "compare". we may compare theories for example by asking:

1. Which theories prove more theorems?
2. Which theories put more restrictions on how models look like?
3. Which theories interpret the other ones?
4. Which theories prove theorems more efficiently?

In my talk I will focus on the first two points. I will specifically concentrate on the question: when does a theory of truth start to nontrivially extend the base theory? So, in other words which aspects of the notion of truth endow it with a nontrivial content? I will mostly speak of the extensions of pure compositional theory of truth CT􀀀 whose axioms state that the truth predicate satisfies usual Tarskian inductive clauses.

If time allows, I will additionally tell something about the dual question: how much can be assumed about the notion of truth until we reach a paradox? In particular, I would like to discuss a possible approach in which the axioms for the truth predicate are kept fixed and we allow the underlying logic to vary, asking which logics admit a fully naïve truth predicate.