Advancing research on theories of truth
The project 'The set theory of semantic theories of truth' (STSTT) worked to link set theory and formal theories of truth, and advance simple techniques facilitating contemporary research into logics of truth. Using set theoretic tools, STSTT met its original objectives. It produced a tableau proof system for various semantic theories of truth, permitting a better understanding of fixed point theories of truth. The tableau provides a clearer presentation for the mathematical analysis of these theories. The approach led to development of a consistency proof for a strong validity predicate, satisfying principles previously thought impossible to satisfy. Use of descriptive set theory also supported establishing the groundwork for analysing revision theoretic truth, dispelling claims that revision theory is ungrounded. Other accomplishments include employing tools from formal theories of truth to show how they can be analogously applied to problems in set theory. Finally, STSTT paved the way for use of a common framework to understand logical paradoxes in both set theory and formal theories of truth. STSTT work has been disseminated in journal publications and presented at leading centres for philosophical and mathematical logic. Opening up a new avenue of research into truth and set theory, project outcomes should enable proper mathematical understanding of logical paradox and diagonal argument. The tools offer appropriate means for classifying these problems and understanding what is involved in solving them.
Keywords
Theories of truth, set theory, semantic theories, logical paradox, diagonal argument
