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Philosophy and Hermeneutics of Mathematics Unit


We conduct interdisciplinary research in the field of philosophy of mathematics (ontology of mathematics, epistemology of mathematics, issues of development of mathematical knowledge, foundations of mathematics), combining historical and hermeneutical approaches with formal ones. Hermeneutics of mathematics reconstructs and analyzes hidden assumptions, background knowledge, tacit knowledge, showing their role in the creation of even the most formalized theories of modern mathematics. Such hidden determinants of the creation of mathematics include – broadly defined – Platonic methods, e.g. related to the use of classical logic, non-predicative concepts, etc.

Among other things, the research is concerned with the mechanisms of development and creation of mathematical knowledge. Analyses of ancient historical forms of mathematics, mainly ancient Greek mathematics, modern mathematics and the beginnings of modern mathematics, allow us to determine the historical specifics of formalized modern mathematics. As a result, we get, on the one hand, a number of new and relevant pieces of information on classical philosophical problems related to mathematics, and on the other hand, the necessity and possibility emerges  of analyzing some open and hitherto unanalyzed mathematical problems in the foundations of mathematics, the theory of mathematical truth, set theory and category theory.

The unit’s long-standing research topics include: Intuitive Foundations of Mathematics. Intuition versus truth in mathematics.

Research objectives:

Reconstructing the intuitive basis for the creation of mathematics in different historical eras and in the present,  together with showing the role of the intuitive basis of mathematics in science and classical philosophical problems (ontology, epistemology, philosophy and methodology of science, philosophical hermeneutics and phenomenology).

Research activities on the development and history of mathematics are only part of the research carried out within the Team. Another strand of research is the development of new systems of mathematical foundations, including formalized ones, and the study of their properties. 

The problems mentioned so far have not been described in more detail because they have not been noticed (or have been analyzed from a different point of view). The detected mechanisms have significance for modern science and can stimulate the emergence of new directions in the foundations of mathematics.

Dr. hab. Zbigniew Król, prof. IFiS PAN – Head
(willing to act a supervisor for doctoral students)