This book is a collection of articles authored by renowed Polish ontologists living and working in the early part of the 21st century. Harking back to the well-known Polish Lvov-Warsaw School, founded by Kazimierz Twardowski, we try to make our ontological considerations as systematically rigorous and clear as possible - i.e. to the greatest extent feasible, but also no more than the subject under consideration itself allows for. Hence, the papers presented here do not seek to steer clear of methods of inquiry typical of either the formal or the natural sciences: on the contrary, they use such methods wherever possible. At the same time, despite their adherence to rigorous methods, the Polish ontologists included here do not avoid traditional ontological issues, being inspired as they most certainly are by the great masters of Western philosophy - from Plato and Aristotle, through St. Thomas and Leibniz, to Husserl, to name arguably just the most important.

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.

This book is a collection of articles authored by renowed Polish ontologists living and working in the early part of the 21st century. Harking back to the well-known Polish Lvov-Warsaw School, founded by Kazimierz Twardowski, we try to make our ontological considerations as systematically rigorous and clear as possible - i.e. to the greatest extent feasible, but also no more than the subject under consideration itself allows for. Hence, the papers presented here do not seek to steer clear of methods of inquiry typical of either the formal or the natural sciences: on the contrary, they use such methods wherever possible. At the same time, despite their adherence to rigorous methods, the Polish ontologists included here do not avoid traditional ontological issues, being inspired as they most certainly are by the great masters of Western philosophy - from Plato and Aristotle, through St. Thomas and Leibniz, to Husserl, to name arguably just the most important.

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.