Disquotation and Infinite Conjunctions (joint work with Thomas Schindler)

The truth predicate has expressive powers akin to those of logical connectives, for it allows to express infinitely many sentences at once via generalizations or, as it is usually said, infinite conjunctions, that cannot be expressed otherwise neither in natural language nor in most formal languages. For instance, it allows us to express the infinitely many theorems of arithmetic by uttering "All theorems of arithmetic are true". This capacity prompts the search for 'logics' or, better, formal theories of truth that give the truth predicate the necessary features to perform its task. Authors working on the topic believe such theories should consist (partly) of transparency principles, the most famous of which is the T-schema. Since these principles are inconsistent in classical logic plus some required syntactic assumptions, most opt either to weaken classical logic or to resign part of the expressive power of truth. We show that transparency is neither necessary nor sufficient to grant this expressive power. In classical logic a weaker subprinciple that is ceteris paribus consistent over the syntax theory suffices, while in other logical systems none of the transparency principles does the job. Thus, there is no need (and it is not generally well-advised) to abandon classical logic in order to guarantee the logical role of truth or to sacrifice part of it to remain classical.