A critical analysis of the philosophical motivations and development of the concept of the field of rationality as a representation of the fundamental ontology of the physical reality - Grygiel, Wojciech (Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce), 2022)
The unusual applicability of mathematics to the description of the physical reality still remains a major investigative task for philosophers, physicists, mathematicians and cognitive scientists. The presented article offers a critical analysis of the philosophical motivations and development of a major attempt to resolve this task put forward by two prominent Polish philosophers: Józef Życiński and Michał Heller. In order to explain this particular property of mathematics Życiński has first introduced the concept of the field of rationality together with the field of potentiality to be followed by Heller’s formal field and the field of categories. It turns out that these concepts are fully intelligible once located within philosophical stances on the relations between mathematics and physical reality. It will be argued that in order to achieve more extended conceptual clarification of the precise meaning of the field of rationality, further advancements in the understanding of the nature of the human mind are required.
Keywords: ontology; mathematics; platonism; category theory; Roger Penrose; Alfred North Whitehead