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The emergence of symbolic algebra as a shift in predominant models

Albrecht Heeffer

Foundations of Science 13 (2):149--161 (2008)

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Conceptual Modelling, Combinatorial Heuristics and Ars Inveniendi: An Epistemological History (Ch 1 & 2).Tom Ritchey - manuscriptdetails (1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and combinatoric (...) Download Export citation Bookmark
The natures of numbers in and around Bombelli’s L’algebra.Roy Wagner - 2010 - Archive for History of Exact Sciences 64 (5):485-523.details The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra. Download Export citation Bookmark 4 citations
Logic, Reasoning, and Rationality.Erik Weber, Joke Meheus & Dietlinde Wouters (eds.) - 2014 - Dordrecht, Netherland: Springer.details 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 (...) Download Export citation Bookmark
François Viète’s revolution in algebra.Jeffrey A. Oaks - 2018 - Archive for History of Exact Sciences 72 (3):245-302.details Françios Viète was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized magnitudes in which the “calculations” must respect dimension. Along with this foundational shift Viète adopted a radically new notation based in Greek geometric equalities. (...) Download Export citation Bookmark 1 citation
How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining.Jurgen Naets - 2010 - Topoi 29 (1):77-86.details This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the (...) Download Export citation Bookmark 4 citations
Historical Objections Against the Number Line.Albrecht Heeffer - 2011 - Science & Education 20 (9):863-880.details Download Export citation Bookmark 3 citations

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