Ghent University Academic Bibliography

Advanced

Epistemic justification and operational symbolism

Albrecht Heeffer UGent (2014) FOUNDATIONS OF SCIENCE. 19(1). p.89-113
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MATHEMATICS. Abbaco, 3RD-CENTURY CHINA, Symbolism, Justification, Fractions
journal title
FOUNDATIONS OF SCIENCE
volume
19
issue
1
pages
89 - 113
Web of Science type
Article
Web of Science id
000331006500006
JCR category
HISTORY & PHILOSOPHY OF SCIENCE
JCR impact factor
0.653 (2014)
JCR rank
17/60 (2014)
JCR quartile
2 (2014)
ISSN
1233-1821
DOI
10.1007/s10699-012-9311-x
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
3144548
handle
http://hdl.handle.net/1854/LU-3144548
date created
2013-02-26 14:22:46
date last changed
2016-12-19 15:43:45
@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},
}

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.