A Philosophical Significance of Gentzen’s 1935 Consistency Proof for First-Order Arithmetic:

• Takahashi Yuta

Bibliographic Information

Other Title

• 1階算術に対するゲンツェンの1935年版無矛盾性証明がもつ哲学的意義
• 第8回石本基金若手研究助成･成果報告書 1階算術に対するゲンツェンの1935年版無矛盾性証明がもつ哲学的意義 : 含意を巡る循環との関わりにおいて
• ダイ8カイ イシモト キキン ワカテ ケンキュウ ジョセイ ・ セイカ ホウコクショ 1カイ サンジュツ ニ タイスル ゲンツェン ノ 1935ネンバン ムムジュンセイ ショウメイ ガ モツ テツガクテキ イギ : ガン イ オ メグル ジュンカン ト ノ カカワリ ニ オイテ
• ―含意を巡る循環との関わりにおいて―
• on a Circularity of Implication

Abstract

    Gentzen remarked that one of the aims of his 1935/36 consistency proofs for first-order arithmetic was to give a “finitist” interpretation for the implication-formulas in first-order arithmetic. He imposed the following requirement on such an interpretation: a “finitist” interpretation for the implication-formulas must be able to avoid the circularity of implication that was urged by himself. However, Gentzen did not present his “finitist” interpretation explicitly. Moreover, he gave no argument for its non-circularity. In this paper, first we formulate an interpretation for the implication-formulas in first-order arithmetic by using Gentzen’s 1935 consistency proof. Next, we argue that this interpretation avoids the circularity urged by Gentzen.

Journal

• Kagaku tetsugaku

  Kagaku tetsugaku 49 (1), 49-66, 2016

  The Philosophy of Science Society, Japan

Details

• CRID: 1390282680061980544
• NII Article ID: 130005279438
• NII Book ID: AN00037482
• DOI: 10.4216/jpssj.49.1-49
• ISSN: 18836461
• ISSN: 02893428
• NDL BIB ID: 027635292
• Web Site: http://id.ndl.go.jp/bib/027635292
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I027635292
• Web Site: https://www.jstage.jst.go.jp/article/jpssj/49/1/49_49/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed