TY - JOUR

T1 - The concept of given in Greek mathematics

AU - Sidoli, Nathan Camillo

PY - 2018/6/14

Y1 - 2018/6/14

N2 - 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.

AB - 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.

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U2 - 10.1007/s00407-018-0211-5

DO - 10.1007/s00407-018-0211-5

M3 - Article

AN - SCOPUS:85048551461

SP - 1

EP - 50

JO - Archive for History of Exact Sciences

JF - Archive for History of Exact Sciences

SN - 0003-9519

ER -