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The symbolic model for algebra: Functions and mechanisms

In W. Carnielli L. Magnani (ed.), Model-Based Reasoning in Science and Technology. Springer. pp. 519--532 (2010)

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  1. Logic, Reasoning, and Rationality.Erik Weber, Joke Meheus & Dietlinde Wouters (eds.) - 2014 - Dordrecht, Netherland: Springer.
    This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far (...)
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  • Historical Objections Against the Number Line.Albrecht Heeffer - 2011 - Science & Education 20 (9):863-880.
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  • Epistemic Justification and Operational Symbolism.Albrecht Heeffer - 2014 - Foundations of Science 19 (1):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 that these schemes provided the validation of mathematical practices (...)
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