The concept of given in Greek mathematics

Nathan Sidoli*

*この研究の対応する著者

研究成果: Article査読

2 被引用数 (Scopus)

抄録

This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work.

本文言語English
ページ(範囲)353-402
ページ数50
ジャーナルArchive for History of Exact Sciences
72
4
DOI
出版ステータスPublished - 2018 7 1

ASJC Scopus subject areas

  • 数学(その他)
  • 科学史および科学哲学

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