From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

Abstract

The following discusses the practice of mathematical argument or demonstration—
at first based on what I shall speak of as “the locally obvious”, that is,
presuppositions which the interlocutor—or, in case of writing, the imagined or
“model” reader—will accept as obvious; next in its interaction with critique, investigation
of the conditions for the validity of the seemingly obvious as well as the limits
of this validity. This is done, in part through analysis of material produced within late
medieval Italian abbacus culture, in part from a perspective offered by the Old
Babylonian mathematical corpus—both sufficiently distant from what we are familiar
with to make phenomena visible which in our daily life go as unnoticed as the air
we breathe; that is, they allow Verfremdung. These tools are then applied to the development
from argued procedure toward axiomatics in ancient Greece, from the midfifth
to the mid-third century bce. Finally is discussed the further development of
ancient demonstrative mathematics, when axiomatization, at first a practice, then a
norm, in the end became an ideology. The whole is rounded off by a few polemical
remarks about present-day beliefs concerning the character of mathematics.
Original languageEnglish
Title of host publicationInterfaces between Mathematical Practices and Mathematical Education
EditorsGert Schubring
Place of PublicationCham
PublisherSpringer VS
Publication date2019
Pages27-46
ISBN (Print)978-3-030-01616-6
ISBN (Electronic)978-3-030-01617-3
Publication statusPublished - 2019
SeriesInternational Studies in the History of Mathematics and its Teaching
ISSN2524-8022

Cite this

Høyrup, J. (2019). From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay. In G. Schubring (Ed.), Interfaces between Mathematical Practices and Mathematical Education (pp. 27-46). Cham: Springer VS. International Studies in the History of Mathematics and its Teaching
Høyrup, Jens. / From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay. Interfaces between Mathematical Practices and Mathematical Education. editor / Gert Schubring. Cham : Springer VS, 2019. pp. 27-46 (International Studies in the History of Mathematics and its Teaching).
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Høyrup, J 2019, From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay. in G Schubring (ed.), Interfaces between Mathematical Practices and Mathematical Education. Springer VS, Cham, International Studies in the History of Mathematics and its Teaching, pp. 27-46.

From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay. / Høyrup, Jens.

Interfaces between Mathematical Practices and Mathematical Education. ed. / Gert Schubring. Cham : Springer VS, 2019. p. 27-46.

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

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Høyrup J. From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay. In Schubring G, editor, Interfaces between Mathematical Practices and Mathematical Education. Cham: Springer VS. 2019. p. 27-46. (International Studies in the History of Mathematics and its Teaching).