TY - JOUR

T1 - The concept of given in Greek mathematics

AU - Sidoli, Nathan

N1 - Funding Information:
Acknowledgements The core ideas of this paper go back some years now to my dissertation, and I thank Alexander Jones and Jan Hogendijk for their comments on that work. I presented an overview of this argument at a conference of the SAW Project, under the direction of Karine Chemla. The discussion following this presentation helped me to clarify some of my thinking. During the time that I was a guest of the SAW Project in Paris, 2015, some of the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007– 2013) / ERC Grant Agreement No. 269804. Ken Saito read an earlier draft of this paper and made a number of valuable suggestions. This paper has benefited considerably from the extensive notes made by Karine Chemla and Matthieu Husson.

PY - 2018/7/1

Y1 - 2018/7/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85048551461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048551461&partnerID=8YFLogxK

U2 - 10.1007/s00407-018-0211-5

DO - 10.1007/s00407-018-0211-5

M3 - Article

AN - SCOPUS:85048551461

VL - 72

SP - 353

EP - 402

JO - Archive for History of Exact Sciences

JF - Archive for History of Exact Sciences

SN - 0003-9519

IS - 4

ER -