Reflection Principles and their Epistemic Warrant

• Applicant: Professor Dr. Leon Horsten
• Subject Area: Theoretical Philosophy
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563760604

This interdisciplinary project focuses on a comprehensive study of reflection principles - key theoretical constructs that play a foundational role across various disciplines, including mathematical logic, epistemology, and formal sciences. Reflection principles enable systems, whether mathematical or epistemic, to reason about their own properties, fostering a deeper understanding of concepts like self-awareness, consistency, and trust in formal frameworks. In mathematical logic, these principles are crucial for exploring foundational questions about consistency and self-referential reasoning, with notable connections to Gödel’s incompleteness results. Within set theory, reflection principles are essential for analyzing the structure of large cardinals and hierarchical systems. In the domains of probability and formal epistemology, they help model rational belief updates, providing a framework for understanding how agents refine their credences. Moreover, in the context of truth theories, reflection principles contribute to the development of robust and mathematically strong axiomatic systems. Philosophically, reflection principles are tied to debates about their rational justification, their relationship to self-trust, and their boundaries of applicability. Despite their significance, current investigations into these principles remain fragmented, with little interaction among disciplines such as proof theory, set theory, and formal epistemology. This lack of integration leaves critical connections between these areas unexplored. The primary aim of this project is to create a unified framework that bridges these fields, offering a systematic analysis of reflection principles and their interrelations. It seeks to clarify the epistemic foundations of these principles, examine their justification within different theoretical domains, and explore their implications for understanding reasoning, knowledge, and truth. By synthesizing mathematical rigor with philosophical inquiry, this research aspires to advance our understanding of reflection principles and their applications in both theoretical and practical contexts. This is an interdisciplinary research project, engaging both philosophy and formal disciplines. Accordingly, apart from the methods of philosophical analysis, the techniques of modern logic will be extensively employed. In particular, the tools and techniques of arithmetic, model theory, set theory, probability theory, and proof theory will be of crucial importance.

• DFG Programme: Research Grants
• International Connection: Poland
• Cooperation Partner: Professor Dr. Cezary Cieslinski, Ph.D.