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The Set Theory of Semantic Theories of Truth

Final Report Summary - STSTT (The Set Theory of Semantic Theories of Truth)

Final Publishable summary:
The Set Theory of Semantic Theories of Truth (STSTT) project was to use tools from set theory and formal theories of truth in concert with the aim of cross pollination. More particularly, STSTT aimed to:
• Map out the mathematical landscape of semantic theories of truth.
• Develop methodologies for bringing the lessons learned with regard to semantic theories
• of truth to bear upon axiomatic theories of truth and logics of truth.
• Develop tools for a perspicuous analysis of revision theoretic definitions.
• Provide a general theory for the provision of consistency proofs using semantic truth theories.

The STSTT project has successfully used set theoretic tools to meet these goals and in so doing opened up new avenue of research into truth and set theory. In particular, the STSTT project has:
• Produced a tableau proof system for a variety of semantic theories of truth. This allows a more transparent understanding of fixed point theories of truth and provides a clearer presentation for their mathematical analysis.
• Developed a consistency proof for a strong validity predicate that satisfies principles that were previously thought impossible to satisfy.
• Developed the groundwork for analysis of revision theoretic truth using descriptive set theory which shows that claims of revision theory being ungrounded are misguided.
• Taken tools from formal theories of truth and showed how they may be analogously applied to problems in set theory.
• Developed the groundwork for a common framework for understanding logical paradoxes in both set theory and formal theories of truth.

This work has been disseminated through journal publications and presentations at leading centres for philosophical and mathematical logic.

It is anticipated that the results of this research will culminate in proper mathematical understanding of logical paradox and diagonal argument. These tools will provide philosophers and mathematicians with the appropriate means to classify these problems and properly understand what is involved in solving them.