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Wyszukujesz frazę "field of rationality" wg kryterium: Wszystkie pola


Wyświetlanie 1-2 z 2
Tytuł:
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
Autorzy:
Grygiel, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/2140673.pdf
Data publikacji:
2022-11-08
Wydawca:
Copernicus Center Press
Tematy:
ontology
mathematics
platonism
category theory
Roger Penrose
Alfred North Whitehead
Opis:
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.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2022, 72; 87-108
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Logika racjonalności. W stronę modalnego platonizmu matematycznego
The Logic of Rationality. Towards Modal Mathematical Platonism
Autorzy:
Wilczek, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/691018.pdf
Data publikacji:
2011
Wydawca:
Copernicus Center Press
Tematy:
Alfred N. Whitehead
Alfred Tarski
logical consequence
ZFC
second-order set theory
forcing
modal logics
field of rationality
structuralism
platonism
Opis:
In this article Whitehead’s philosophy of mathematics is characterized as a Structural Second-Order Platonism and it is demonstrated that the Whiteheadian ontology is consistent with modern formal approaches to the foundation of mathematics. We follow the pathway taken by model-theoretically and semantically oriented philosophers. Consequently, it is supposed that all mathematical theories (understood as deductively closed set of sentences) determine their own models. These models exist mind-independently in the realm of eternal objects. From the metatheoretical point of view the hypothesis (posed by Józef Życiński) of the Rationality Field is explored. It is indicated that relationships between different models can be described in the language of modal logics and can further be axiomatized in the framework of the Second Order Set Theory. In conclusion, it is asserted that if any model (of a mathematical theory) is understood, in agreement with Whitehead’s philosophy, as a collection of eternal objects, which can be simultaneously realized in a single actual occasion, then our external world is governed by the hidden pattern encoded in the field of pure potentialities which constitute the above mentioned Field of Rationality. Therefore, this work can be regarded as the first step towards building a Logic of Rationality.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2011, 49; 98-122
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-2 z 2

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