The Krakow Methodological Conferences have a long tradition – one that dates back to the early 1990s. Their aim is to engage researchers in an interdisciplinary discussion concerning fundamental problems in science and philosophy.
The 23rd edition will be devoted to the role of logic in the natural sciences, considered from the perspective of category theory.
Topics of interest include, but are not limited to, the following:
– the categorification of mathematics and physics;
– the internal logic of physical theories (topoi, the logic of quantum mechanics);
– universal logic and its relevance for the methodology of science;
– ontology (category theory as a network ontology, substantivalism, relationism);
– structuralism in the philosophy of mathematics and physics;
– traditional philosophical issues viewed from the perspective of category theory (the existence of mathematical objects, access to mathematical objects, intuition, the everyday practice(s) of mathematics);
– the foundations of mathematics (category theory and the foundations of mathematics, homotopy type theory, univalent foundations);
– the history of category theory.
Professor, Department of Philosophy at Carnegie Mellon University. Research Areas: Category Theory, Logic, Philosophy of Mathematics, Early Analytic Philosophy.
More generally, I am interested in the Foundations of Physics, in particular the structures involved, with a strong structural bias towards Logic, Order and Category Theory, and their applications.
Main research interests: in physics: Quantum information theory, QFTs and nonequilibrium quantum stat. mech., Space-time emergence, Multi-agent information relativity; in mathematics: Quantum information geometry, Operator algebras and functional, analysis, 1/n/∞-category/topos theory, Foundations of smoothness and integration; in philosophy (out of office): Structural epistemology and inference, Intersubjectivity and semiotics, Cross-cultural anthropology, Yoga.
Zbigniew Król is a philosopher who works at the Department of the Philosophy of Science, Sociology and Foundations of Technology, Faculty of Administration and Social Sciences, Warsaw University of Technology, and at the two departments of the Institute of Philosophy and Sociology, Polish Academy of Sciences: the Department of Philosophy and Hermeneutics of Mathematics and the Department of Inquiries on Ancient Philosophy and the History of Ontology. His research concerns hermeneutics, the hermeneutical philosophy of mathematics and science, the history of mathematics and science, logic, mathematics, ontology and epistemology. He is an author of many papers and two monographs: Plato and the Foundations of Modern Mathematics: the Concept of Number by Plato (2005) and Mathematical Platonism and Hermeneutics (2006). He is also a climber: speleologist and Himalayan mountaineer.
Area of interest: mathematical physics, quantum chaos, quantum information theory.
My research mainly concerns questions of logic, the foundations of mathematics and the philosophy of mathematics. It can be divided roughly into 3 overlapping fields: the philosophical scope and applications of categorical logic, the foundations of mathematics deriving from category theory and, lastly, the epistemology and ontology of contemporary mathematics.
Research: Logic, Philosophy of Logic, Philosophy of Mathematics, Philosophy of Science, Contemporary French Philosophy.