Epistemic Justification and Operational Symbolism

  title={Epistemic Justification and Operational Symbolism},
  author={Albrecht Heeffer},
  journal={Foundations of Science},
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… 
Surmounting obstacles: circulation and adoption of algebraic symbolism
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
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


Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China
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,
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
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
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
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
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
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
  • Shahid Rahman
  • Philosophy, Computer Science
    Logic, 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
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
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,