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Category Theory in Physics, Mathematics, and Philosophy

  • Conference proceedings
  • © 2019

Overview

Editors:
  1. Marek Kuś

    1. Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

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  2. Bartłomiej Skowron

    1. Faculty of Administration and Social Sciences, International Center for Formal Ontology, Warsaw University of Technology, Warsaw, Poland

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  • Shows that the categorical ontology could serve as a basis for bonding mathematics, physics, and philosophy

Part of the book series: Springer Proceedings in Physics (SPPHY, volume 235)

Included in the following conference series:

Conference proceedings info: CTPMP 2017.

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Table of contents (10 papers)

  1. Front Matter

    Pages i-xii
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  2. Why Categories?

    • Marek Kuś, Bartłomiej Skowron, Krzysztof Wójtowicz
    Pages 1-19

  3. Category Theory and Philosophy

    • Zbigniew Król
    Pages 21-32

  4. Are There Category-Theoretical Explanations of Physical Phenomena?

    • Krzysztof Wójtowicz
    Pages 33-43

  5. The Application of Category Theory to Epistemic and Poietic Processes

    • Józef Lubacz
    Pages 45-53

  6. Asymmetry of Cantorian Mathematics from a Categorial Standpoint: Is It Related to the Direction of Time?

    • Zbigniew Semadeni
    Pages 55-62

  7. Extending List’s Levels

    • Neil Dewar, Samuel C. Fletcher, Laurenz Hudetz
    Pages 63-81

  8. From Quantum-Mechanical Lattice of Projections to Smooth Structure of \(\mathbb {R}^4\)

    • Krzysztof Bielas, Jerzy Król
    Pages 83-93

  9. Beyond the Space-Time Boundary

    • Michael Heller, Jerzy Król
    Pages 95-103

  10. Aspects of Perturbative Quantum Gravity on Synthetic Spacetimes

    • Jerzy Król
    Pages 105-117

  11. Category Theory as a Foundation for the Concept Analysis of Complex Systems and Time Series

    • G. N. Nop, A. B. Romanowska, J. D. H. Smith
    Pages 119-134
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  1. Category Theory in Physics, Mathematics, and Philosophy

Keywords

About this book

The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes.


The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations.


Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science. 

Editors and Affiliations

  • Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

    Marek Kuś

  • Faculty of Administration and Social Sciences, International Center for Formal Ontology, Warsaw University of Technology, Warsaw, Poland

    Bartłomiej Skowron

About the editors

Dr. Bartłomiej Skowron is a Platonic philosopher. He wrote his Ph.D. thesis on Mereotopological aspects of philosophical part-whole theory at the University of Wroclaw, and defended his thesis in 2012. He received also BA in Mathematics from the University of Wroclaw, Faculty of Mathematics and Computer Science, in 2011. From October2015, he is an assistant professor at the Faculty of Administration and Social Sciences at the Warsaw University of Technology. He is a member of the International Center for Formal Ontology and the Academyof Young Scholars and Artists. He served as a President of the
Academy from 2013 to 2017. His main research interest is in Mathematical (especially Topological) Philosophy. He is laso interested in formal ontology (part-whole theory, mereotopology), phenomenology, philosophy of morality, axiology, philosophical anthropology, the basis and philosophy of mathematics, applied logic and appliedtopology.
He has edited or is currently editing 7 books. He is the author of over 30 original articles.
Prof. Dr. Marek Kus is a theoretical physicis, professor at the Centre of Theoretical Physics of the Polish Academy of Sciences in Warsaw, Director of the International Center for Formal Ontology at the Faculty of Administration and Social Sciences of the Warsaw University of Technology, member of Academia Europea. His scientific interests include:
mathematical physics, in particular the application of geometric and group-theoretic methods (simplectic geometry, algebraic geometry, Lie group theory) in quantum computer science, quantum chaos and the basics of quantum mechanics. He is also interested in formal methods in philosophy and the application of methods of exact sciences in social sciences. He is the author of over 150 original articles.

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