Metaworlds: A Possible Worlds Semantics of Truth

H. Leitgeb

I focus on the notion of a metaworld relation between worlds: w2 is a metaworld of w1 iff

for every A: A is true in w1 iff Tr(‘A’) is true in w2.

I.e. w2 is a model for a language with truth predicate Tr, and the extension of the truth predicate in w2 is the set of sentences true in w1.

In the first part of my talk I will suggest some plausible structural constraints on the metaworld relation. Secondly, I will give some philosophical motivation for such a possible worlds semantics of truth, in which I relate the issues of truth to those of translation between languages. In the third part I will investigate what the metaworld relation may look like, when we concentrate our efforts on semantically closed languages (s.t. w1 and w2 are members of the same set of worlds). I will present some existence theorems for this case, and I will show what the corresponding necessary laws of truth are. The fourth part is devoted to a comparison between the metaworld semantics and the possible worlds semantics of temporal logic, where temporal modalities are reconstructed as predicates.

Partial Truth: History, Applications and Problems

A. Cantini

We deal with logical results, which should be useful to answer the following general questions: how do problems arising in formal semantics relate to the mainstream of logic ? Which relevant tools emerge from investigation of self-reference in semantics ? Are logical investigations about truth of any import to philosophical theories of truth ?

To this aim, after trying a (rough and quick) classification of research on semantical paradoxes, we concentrate upon axiomatic theories of self-referential partial truth since 1975, when work in the area started producing highly sophisticated “semantical machines”.

In this talk we stress the relative proof-theoretic weakness of the theories of partial truth that have been proposed, and their privileged link with predicative/inductive views (on the foundational side).

We plan to consider a weak theory of partial positive truth and its (possible) application to feasibility, and to discuss the sensitivity of the Kripke-Feferman axioms for partial truth with respect to logic (since the notion of KF-truth is given via a process of potential approximation, isn't some form of constructive logic more adequate for KF ?).

Modalized Disquotationalism

V. Halbach

The instances of the disquation scheme

“A” is true if and only if A

are necessary at least on one reading. The consequences of combining this position with a suitable axiomatic theory of necessity are studied in a formal setting and it is shown how the resulting theory overcomes some deficiencies of traditional disquotationalist theories of truth.

Modalized Disquotationalism sheds some light on the interaction of truth and necessity. It is shown that there are disquotational theories of truth equivalent to a system embracing the Tarski's inductive clauses for truth. Another disquotational theory is equivalent to the Kripke-Feferman theory KF.