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Epistemic justification and operational symbolism

(2014) FOUNDATIONS OF SCIENCE. 19(1). p.89-113
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Abstract
By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280–1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of mathematical practices necessary for the development towards symbolic reasoning. It is shown how justification schemes compensated for the lack of symbolism in abbaco treatises and at the same time facilitated a process of abstraction.
Keywords
MATHEMATICS. Abbaco, 3RD-CENTURY CHINA, Symbolism, Justification, Fractions

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Citation

Please use this url to cite or link to this publication:

Chicago
Heeffer, Albrecht. 2014. “Epistemic Justification and Operational Symbolism.” Foundations of Science 19 (1): 89–113.
APA
Heeffer, A. (2014). Epistemic justification and operational symbolism. FOUNDATIONS OF SCIENCE, 19(1), 89–113.
Vancouver
1.
Heeffer A. Epistemic justification and operational symbolism. FOUNDATIONS OF SCIENCE. 2014;19(1):89–113.
MLA
Heeffer, Albrecht. “Epistemic Justification and Operational Symbolism.” FOUNDATIONS OF SCIENCE 19.1 (2014): 89–113. Print.
@article{3144548,
  abstract     = {By the end of the twelfth century in the south of Europe, new methods of calculating with Hindu-Arabic numerals developed. This tradition of sub-scientific mathematical practices is known as the abbaco period and flourished during 1280--1500. This paper investigates the methods of justification for the new calculating procedures and algorithms. It addresses in particular graphical schemes for the justification of operations on fractions and the multiplication of binomial structures. It is argued that these schemes provided the validation of mathematical practices necessary for the development towards symbolic reasoning. It is shown how justification schemes compensated for the lack of symbolism in abbaco treatises and at the same time facilitated a process of abstraction.},
  author       = {Heeffer, Albrecht},
  issn         = {1233-1821},
  journal      = {FOUNDATIONS OF SCIENCE},
  keyword      = {MATHEMATICS. Abbaco,3RD-CENTURY CHINA,Symbolism,Justification,Fractions},
  language     = {eng},
  number       = {1},
  pages        = {89--113},
  title        = {Epistemic justification and operational symbolism},
  url          = {http://dx.doi.org/10.1007/s10699-012-9311-x},
  volume       = {19},
  year         = {2014},
}

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