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(Article II.3.) Tertium Non Datur, or, on Reasoning Styles in Early Mathematics

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Selected Essays on Pre- and Early Modern Mathematical Practice

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Abstract

In much general historiography of mathematics, also of the fairly serious kind, Greek mathematics is presented not only as the beginning of systematic deduction and axiomatic presentation but also as the point where mathematics changed from a purely empirical activity to a practice based on reasoning and proof. In a number of recent writings defending the honour of “non-Western” mathematics, seen more or less as an undifferentiated lump, it is on the contrary claimed that there was nothing particular in the ancient Greek proofs, even though (it is paradoxically claimed) for instance the Indians had a different understanding of what constitutes a proof.

Basing itself in the main on the relation between Babylonian and Euclidean mathematics, the following tries to clarify the issue, making use of the notions of “naive” versus “critical” reasoning.

Originally published in Paolo Mancosu et al (eds), Visualization, Explanation and Reasoning Styles in Mathematics, pp. 91–121. Dordrecht: Springer, 2005

Small corrections of style made tacitly A few additions touching the substance in 〚…〛

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  1. Section for Philosophy and Science Studies, Roskilde University, Roskilde, Denmark

    Jens Høyrup

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Høyrup, J. (2019). (Article II.3.) Tertium Non Datur, or, on Reasoning Styles in Early Mathematics. In: Selected Essays on Pre- and Early Modern Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19258-7_20

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