Temat: modal structuralism - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Antyrealistyczna ucieczka w sferę możliwości
Antirealist escape to the realm of possibilities
Autorzy:: Wójtowicz, Krzysztof
Powiązania:: https://bibliotekanauki.pl/articles/690612.pdf
Data publikacji:: 2008
Wydawca:: Copernicus Center Press
Tematy:: Charles S. Chihara
constructivism
Geoffrey Hellman
structuralism
linguistic constructivism
modal structuralism
Opis:: The article is devoted to a popular presentation of two important styles of thinking concerning the problem of existence of mathematical objects: Chihara's linguistic constructivism, and Hellman's modal structuralism. According to Chihara, mathematical statements should be interpreted as referring to certain linguistic construction; according to Hellman, mathematics is the science of possible structures. The motivations and main ideas are examined (without going into technical details), and the similarities and differences between these two viewpoints are highlighted.
Źródło:: Zagadnienia Filozoficzne w Nauce; 2008, 42; 15-27
0867-8286
2451-0602
Pojawia się w:: Zagadnienia Filozoficzne w Nauce
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

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

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