Research
I am a philosopher working in formal philosophy, where I investigate philosophical notions such as acceptance, truth, and rationality through the lens of logic and metamathematics.
The central question of my PhD project concerns what we implicitly commit ourselves to when we accept a scientific or mathematical theory. Gödel's incompleteness theorem shows that no sufficiently rich theory can prove its own consistency — yet anyone who reasonably relies on such a theory must assume it will not lead to contradiction. Acceptance, therefore, carries hidden commitments that extend beyond what the theory itself can prove. Using tools of proof theory, I analyze these implicit commitments across different ways of accepting a theory, from full to instrumental acceptance.
This work continues in my current NCN OPUS project on metatheoretic and intertheoretic reductions in the foundations of mathematics, which asks when two theories, though framed in different vocabularies, should be treated by agents as expressing the same content.
Projects
Metatheoretic and Intertheoretic Reductions in the Foundations of Mathematics
In my current project, Metatheoretic and intertheoretic reductions in the foundations of mathematics, I study reductions — the many ways one theory or concept in mathematics can be captured by, or translated into, another. Formal theories in the foundations of mathematics are typically taken to be about something: arithmetic is about the natural numbers, set theory about sets, axiomatic theories of truth about the notion of truth. The project asks two connected questions. First, when does a formal theory succeed in capturing an informal concept or philosophical standpoint — what makes such a formalization adequate? Second, when two theories are framed in different vocabularies, how tightly must they be related before we can say they express the same content, rather than merely proving the same results? Drawing on proof theory and the model theory of formal theories, I aim to clarify the epistemic significance of reductions and to develop a precise measure of the conceptual distance between theories. More details and project outputs are on the MIRFoM project page.
Grant no. 2024/53/B/HS1/02173
Epistemic and Semantic Commitments of Foundational Theories
As a PhD researcher on this NCN MAESTRO project (PI: Prof. Cezary Cieśliński), I contributed to a formal analysis of the commitments of foundational theories — theories in which a significant portion of mathematics can be carried out. The project examined two kinds of commitment: epistemic commitments (sentences one should accept once one accepts a theory's axioms and rules, such as its consistency or the claim that everything it proves is true) and semantic commitments (the restrictions a theory's axioms place on its possible interpretations). Much of my work on implicit commitments and axiomatic truth was carried out here. See the project website.
Grant no. 2019/34/A/HS1/00399
Seminar
I am a co-organizer of the Formal Philosophy of Mathematics (ForMat) seminar at the University of Warsaw — a common meeting place for several research projects that study the philosophy of mathematics with formal tools.