Paradoxicality and Semantic Notions: Philosophical and Axiomatic Foundations.

Description du projet

Établir les fondements de théories unifiées des notions sémantiques et de la paradoxalité

Les concepts sémantiques tels que la vérité, la validité et la paradoxalité sont des éléments essentiels des enquêtes philosophiques et logiques. Les approches qui analysent les concepts sémantiques individuellement, plutôt que globalement, se sont révélées inadéquates. Toutefois, l’établissement d’approches unifiées décrivant simultanément différentes notions sémantiques est un défi majeur, qui est encore compliqué par des concepts qui défient le traitement formel, tels que la paradoxalité. Soutenu par le programme Actions Marie Skłodowska-Curie, le projet AXIOMS vise à relever ce défi en établissant les fondements formels et philosophiques de théories unifiées des notions sémantiques et de la paradoxalité. Dans le but de développer des systèmes axiomatiques modélisant leur comportement, il identifiera les principes formels de paradoxalité compatibles avec les règles de raisonnement classiques ou non classiques et analysera la relation entre la paradoxalité et d’autres concepts fondamentaux, tels que la vérité.

Objectif

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.