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Medieval Arabic Algebra as an Artificial Language

Jeffrey A. Oaks

Journal of Indian Philosophy 35 (5-6):543-575 (2007)

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Mathematical symbols as epistemic actions.Johan De Smedt & Helen De Cruz - 2013 - Synthese 190 (1):3-19.details Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...) Download Export citation Bookmark 22 citations
Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra.Michalis Sialaros & Jean Christianidis - 2016 - Science in Context 29 (2):129-150.details ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 as (...) Download Export citation Bookmark 2 citations
Irrational “Coefficients” in Renaissance Algebra.Jeffrey A. Oaks - 2017 - Science in Context 30 (2):141-172.details ArgumentFrom the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply$\sqrt {18} $byx, for instance, the result was expressed as the rhetorical equivalent of$\sqrt {18{x^2}} $. The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the scalar (...) Download Export citation Bookmark 1 citation
Cognitive stories and the image of mathematics.Wagner Roy - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):305-323.details Download Export citation Bookmark

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