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One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. / Rodin, A.

Handbook of the History and Philosophy of Mathematical Practice. Vol. 3 Springer Nature, 2024. p. 2339-2364.

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Harvard

Rodin, A 2024, One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. in Handbook of the History and Philosophy of Mathematical Practice. vol. 3, Springer Nature, pp. 2339-2364. https://doi.org/10.1007/978-3-031-40846-5_28

APA

Rodin, A. (2024). One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. In Handbook of the History and Philosophy of Mathematical Practice (Vol. 3, pp. 2339-2364). Springer Nature. https://doi.org/10.1007/978-3-031-40846-5_28

Vancouver

Rodin A. One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. In Handbook of the History and Philosophy of Mathematical Practice. Vol. 3. Springer Nature. 2024. p. 2339-2364 https://doi.org/10.1007/978-3-031-40846-5_28

Author

Rodin, A. / One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. Handbook of the History and Philosophy of Mathematical Practice. Vol. 3 Springer Nature, 2024. pp. 2339-2364

BibTeX

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title = "One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice",
abstract = "The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for metatheoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more practically oriented functions of theoretical foundations such as verification of mathematical constructions and proofs. Using alternative foundations of mathematics such as the univalent foundations is compatible with using the received set-theoretic foundations for metamathematical purposes provided the two foundations are mutually interpretable. Changes in foundations of mathematics do not, generally, disqualify mathematical theories based on older foundations but allow for reconstruction of these theories on new foundations. Mathematics is one but its foundations are many. {\textcopyright} Springer Nature Switzerland AG 2024.",
keywords = "Foundations of mathematics, Metamathematics, Univalent foundations",
author = "A. Rodin",
note = "Export Date: 27 October 2024",
year = "2024",
doi = "10.1007/978-3-031-40846-5_28",
language = "Английский",
isbn = "9783031408465 (ISBN); 9783031408458 (ISBN)",
volume = "3",
pages = "2339--2364",
booktitle = "Handbook of the History and Philosophy of Mathematical Practice",
publisher = "Springer Nature",
address = "Германия",

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RIS

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AU - Rodin, A.

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Y1 - 2024

N2 - The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for metatheoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more practically oriented functions of theoretical foundations such as verification of mathematical constructions and proofs. Using alternative foundations of mathematics such as the univalent foundations is compatible with using the received set-theoretic foundations for metamathematical purposes provided the two foundations are mutually interpretable. Changes in foundations of mathematics do not, generally, disqualify mathematical theories based on older foundations but allow for reconstruction of these theories on new foundations. Mathematics is one but its foundations are many. © Springer Nature Switzerland AG 2024.

AB - The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for metatheoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more practically oriented functions of theoretical foundations such as verification of mathematical constructions and proofs. Using alternative foundations of mathematics such as the univalent foundations is compatible with using the received set-theoretic foundations for metamathematical purposes provided the two foundations are mutually interpretable. Changes in foundations of mathematics do not, generally, disqualify mathematical theories based on older foundations but allow for reconstruction of these theories on new foundations. Mathematics is one but its foundations are many. © Springer Nature Switzerland AG 2024.

KW - Foundations of mathematics

KW - Metamathematics

KW - Univalent foundations

UR - https://www.mendeley.com/catalogue/b1874aee-0fc1-3412-ab6d-8adee37553f2/

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DO - 10.1007/978-3-031-40846-5_28

M3 - глава/раздел

SN - 9783031408465 (ISBN); 9783031408458 (ISBN)

VL - 3

SP - 2339

EP - 2364

BT - Handbook of the History and Philosophy of Mathematical Practice

PB - Springer Nature

ER -

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