Paradoxicality and Semantic Notions: Philosophical and Axiomatic Foundations.

Semantic notions such as truth, validity, and paradoxicality are central to both philosophical and logical inquiries, shaping our understanding of language, meaning, and rationality. An approach studying semantic concepts individually, rather than globally, has proven insufficient. Developing unified systems describing multiple semantic notions simultaneously is a key and outstanding challenge in contemporary philosophical logic. This challenge is made particularly complex by concepts which are reluctant to formal treatment, like 'paradoxicality'. At present, it is unknown whether formal theories of paradoxicality can even be developed.AXIOMS aims to address this challenge by providing formal and philosophical foundations for unified theories of semantic notions and paradoxicality. Specifically, the project seeks to pioneer the development of axiomatic systems modeling their behaviour. It will determine which formal principles for paradoxicality are consistent with various rules of reasoning, and it will investigate how paradoxicality interacts with other key notions, such as truth. Moreover, AXIOMS will explore the potential duality between paradoxicality and 'determinateness', a concept currently at the forefront of logical and philosophical research. This part of the project will be carried out under the supervision of Prof. Volker Halbach during a secondment at the University of Oxford.The impact of AXIOMS extends beyond its immediate scope. It promises to (i) influence ongoing philosophical debates on topics such as classical recapture and (ii) serve as a critical step toward constructing formal and artificial systems capable of reasoning globally with diverse semantic information. For the researcher, the project offers an opportunity to deepen cross-disciplinary expertise, expand his publication record, and acquire a wide range of transferable skills, significantly enhancing his prospects for securing an ERC Starting Grant or a tenure-track position.