# Epistemic Justification and Operational Symbolism

@article{Heeffer2014EpistemicJA, title={Epistemic Justification and Operational Symbolism}, author={Albrecht Heeffer}, journal={Foundations of Science}, year={2014}, volume={19}, pages={89-113} }

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…

## 3 Citations

Surmounting obstacles: circulation and adoption of algebraic symbolism

- Mathematics
- 2012

This introductory paper provides an overview of four contributions on the epistemological functions of mathematical symbolism as it emerged in Arabic and European treatises on algebra. The evolution…

Algebraic symbolism as a conceptual barrier in learning mathematics

- Psychology
- 2013

The use of symbolism in mathematics is probably the mostly quoted reason people use for explaining their lack of understanding and difficulties in learning mathematics. We will consider symbolism as…

## References

SHOWING 1-10 OF 53 REFERENCES

Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

- MathematicsScience in Context
- 2003

Argument Abstraction is commonly valued as being essential to mathematics or even consubstantial with it. In relation to this belief, mathematical texts from Antiquity – be they from Babylon, Egypt,…

ON THE NATURE AND ORIGIN OF ALGEBRAIC SYMBOLISM

- Mathematics
- 2008

Ever since Nesselmann’s study on “Greek algebra” (1842), historical accounts on algebra draw a distinction in rhetorical, syncopated and symbolic algebra. This tripartite distinction has become such…

Hesitating progress - the slow development toward algebraic symbolization in abbacus- and related manuscripts, c.1300 to c.1550 : Contribution to the conference "Philosophical Aspects of Symbolic Reasoning in Early Modern Science and Mathematics",Ghent, 27-29 August 2009

- Computer Science, Mathematics
- 2009

The algebraic abbreviations and symbolic operations the authors find in German Rechenmeister writings can be seen to have antecedents in Italian manuscripts, which might suggest a continuous trend or perhaps even an inherent logic in the process.

The Symbolic Model for Algebra: Functions and Mechanisms

- Computer Science
- 2010

It is argued that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition and facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers.

On the curious historical coincidence of algebra and double-entry bookkeeping

- Computer Science, MathematicsFotFS
- 2008

It is argued that the answers to the most important methodological innovation in mathematics since the Euclidean axiomatic method in geometry will involve multiple disciplines and will go beyond the boundaries of the history of mathematics.

The Semantics of Indian Numerals in Arabic, Greek and Latin

- 2006

This paper investigates the impact of Indian numerals on the mentality of Western scholars. What did they make of these strange shapes which apparently had such power in arithmetic? Never before had…

Text production reproduction and appropriation within the abbaco tradition: a case study

- Computer Science
- 2008

This paper presents a chapter on algebra from an abbaco treatise on arithmetic, providing a critical edition in line with the Latin scholarly tradition and an English translation.

Logic, Epistemology, and the Unity of Science

- Philosophy, Computer ScienceLogic, Epistemology, and the Unity of Science
- 2004

This chapter discusses Logic, Epistemology and the Unity of Science: An Encyclopedic Project in the Spirit of Neurath and Diderot Shahid Rahman and John Symons, and some of the contributions from Non-Classical Logics.

Visualization, Explanation and Reasoning Styles in Mathematics

- Computer Science, Mathematics
- 2005

This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of…

Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation

- History
- 2003

First published in 1202, Fibonacci's "Liber abaci" was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.Its author,…