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AN00150430-00000146-0083.pdf
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Download
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:318.2 KB
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| Last updated |
:Aug 31, 2023 |
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Total downloads since Aug 31, 2023 : 595
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| Title |
| Title |
竹内の整礎性証明再訪
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| Kana |
タケウチ ノ セイソセイ ショウメイ サイホウ
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| Romanization |
Takeuchi no seisosei shōmei saihō
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| Other Title |
| Title |
Takeuti's well-ordering proofs revisited
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| Title |
Takeuti's well-foundedness arguments revisited
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| Creator |
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秋吉, 亮太
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アキヨシ, リョウタ
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| Romanization |
Akiyoshi, Ryōta
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| Affiliation |
早稲田大学高等研究所・招聘研究員
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| Name |
Arana, Andrew
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| Kana |
アラナ, アンドリュー
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Université de Lorraine, département de philosophie, Professeur
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三田哲學會
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| Kana |
ミタ テツガクカイ
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| Romanization |
Mita tetsugakukai
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2021
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| Name |
哲學
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| Name (Translated) |
Philosophy
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| Issue |
146
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| Year |
2021
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| Month |
3
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| Start page |
83
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| End page |
110
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| Abstract |
Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's school.
For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them.
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| History |
| Apr 16, 2021 | | インデックス を変更 |
| Aug 31, 2023 | | Other Title Title,Other Title Kana,Other Title Romanization,Creator 著者ID,Creator Name,Creator Kana,Creator Romanization,Creator Affiliation,Creator Affiliation (Translated),Creator Role,Creator Link,Abstract 内容,Note 注記 を変更 |
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