From November 2025, I am the Principal Investigator in the project Mathematical justification and entitlement in the foundations of mathematics funded by NCN (National Science Center OPUS grant, grant number 2024/53/B/HS1/03927). The grant is hosted by the University of Warsaw. Below you can find a(n incredibly) short description of the research project.

Mathematical justification and entitlement in the foundations of mathematics

The notion of proof is integral to the concept of justification in mathematics, and is at the core of Philosophy of Mathematics and Epistemology. However, the concept of proof provides only an incomplete picture of mathematical justification: Epistemic practices such as mathematics have cornerstones, preconditions or presuppositions, which are essential for the practice's epistemic integrity. That proofs in our best theories can only provide a partial Epistemology is not only a philosophical, but also a mathematical fact: Since the discovery of the Incompleteness Theorems due to Kurt Gödel, philosophers, logicians and mathematicians must face not only a logical and mathematical, but also an epistemic incompletability of mathematics: No consistent mathematical theory can justify all of mathematics. The incompletability of mathematics poses the issue of justifying mathematical cornerstones. Examples of mathematical cornerstones are principles expressing fundamental properties of the most basic mathematical concepts or principles expressing the reliability of our best mathematical theories.

There has been a shift in epistemology towards the idea that mathematical cornerstones, or basic mathematical axioms and concepts, can only be entitled. Crucially, entitlement behaves quite differently in contrast to more traditional mathematical justifications: Entitlement is a default type of justification, which is never the result of some cognitive, evidential work. Importantly, entitlements can be defeated or undercut. Entitlement drastically changes the traditional epistemological landscape and, if successfully integrated into our epistemology of mathematics, it has the potential to provide a more complete picture of mathematical practices and to provide a more fine-grained conceptual framework for the epistemology of mathematics. Yet, the notion of mathematical entitlement must still be fully developed. Moreover, no attempt has been made towards a systematic integration of entitlement into the standard proof-based epistemology. Little is known about the normative force and epistemic role of entitlement. Moreover, we know little about the impact of entitlement for the question of the objectivity of mathematics.

The projects main goal is to make substantial progress towards a better understanding of entitlement and its integration in our proof-based epistemology. The project thrives towards its aim by pursuing three objectives:

(1) Determine the normative force of entitlement as justification

(2) Evaluate the epistemic role of entitlement for mathematical justification

(3) Analyse the impact of entitlement for the objectivity of mathematics