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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. Том 3 Springer Nature, 2024. стр. 2339-2364.

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Harvard

Rodin, A 2024, One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice. в Handbook of the History and Philosophy of Mathematical Practice. Том. 3, Springer Nature, стр. 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. в Handbook of the History and Philosophy of Mathematical Practice (Том 3, стр. 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. в Handbook of the History and Philosophy of Mathematical Practice. Том 3. Springer Nature. 2024. стр. 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. Том 3 Springer Nature, 2024. стр. 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",
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language = "Английский",
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pages = "2339--2364",
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RIS

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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.

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KW - Metamathematics

KW - Univalent foundations

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BT - Handbook of the History and Philosophy of Mathematical Practice

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