Article ID: CBB001201186

Epistemic Justification and Operational Symbolism (2014)


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.


Description On the methods of calculating with Hindu-Arabic numerals in what is known as the Abbaco period, which flourished during 1280--1500.

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Authors & Contributors
Weill-Parot, Nicolas
Iqbal, Muzaffar
Pfeiffer, Judith
Hauko Wakabayashi
Rider, Javier López
Kenneth R. Robinson
Nazariyat: İslam Felsefe ve Bilim Tarihi Araştırmaları Dergisi (Journal for the History of Islamic Philosophy and Sciences)
Tarikh-e Elm (The Iranian Journal for the History of Science)
Han'guk Kwahak-sa Hakhoe-ji (Journal of the Korean History of Science Society)
Dynamis: Acta Hispanica ad Medicinae Scientiarumque Historiam Illustrandam
Bollettino di Storia delle Scienze Matematiche
Edizioni Cadmo
Presses universitaires de la Méditerranée
Les Belles Lettres
Franz Steiner Verlag
Cambridge Scholars Publishing
Arab/Islamic world, civilization and culture
Transmission of ideas
Cross-cultural interaction; cultural influence
Transmission of texts
Alcuin of York
Qūshjī, ʿAlī ibn Muḥammad
Sadr al-Shari'a
al-Ṭūsī, Abū Jaʿfar Muḥammad Naṣīr al-Dīn
Time Periods
14th century
13th century
15th century
12th century
Mediterranean region
Tabrīz (Iran)
Middle and Near East

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