<一般論文> 大きな数としての超準数 : 超準数と厳格有限主義

• 矢田部 俊介

書誌事項

タイトル別名

• <Regular Articles> Non-standard natural numbers as large numbers : Non-standard numbers and strict finitism

抄録

In his 2003 paper, Peacocke insisted that our implicit conception of natural numbers essentially uses a primitive recursion which consists of three clauses, and claimed that this excludes the non-standard models of natural numbers. In this article, we construct a counter “model” to his argument, which contains a non-standard natural number though the set ω of natural numbers is defined as an analogy to his primitive recursion, in a set theory with the comprehension principle within many-valued logic. This result suggests that we should interpret non-standard natural numbers from a philosophical viewpoint. We discuss this by reviewing Strict Finitism, and we conclude that non-standard natural numbers can be interpreted as “large numbers” in a Strict Finitist sense: It expresses new numbers which are introduced by expanding the notation system of natural numbers.

収録刊行物

• 科学哲学科学史研究

  科学哲学科学史研究 6 1-15, 2012-02-28

  京都大学文学部科学哲学科学史研究室

キーワード

• 401

詳細情報

• CRID: 1390009224839274240
• NII論文ID: 120003891659
• NII書誌ID: AA12164361
• DOI: 10.14989/153499
• HANDLE: 2433/153499
• ISSN: 18839177
• 本文言語コード: ja
• データソース種別:
  • JaLC
  • IRDB
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用可