# Visualization, Explanation and Reasoning Styles in MathematicsTertium Non Datur: On Reasoning Styles in Early Mathematics

Visualization, Explanation and Reasoning Styles in Mathematics: Tertium Non Datur: On Reasoning... JENS HØYRUP TERTIUMNONDATUR: ON REASONINGSTYLES IN EARLY MATHEMATICS Arpad ´ ´ Szabo ´ ´ in memoriam 1.TWOCONVENIENT SCAPEGOATS Some philosophers of mathematics hold that real proof is quite recent and that, for instance, Euclid’s arguments for the correctness of his theorems and constructions do not count as “proofs” (those contributing to the present vol- ume are less dogmatic!). The rest of the world (in as far as it knows at all about the topic) sees things differently. Contemporary mathematicians may ﬁnd Euclid’s proofs insufﬁcient or shaky,but they agree with their prede- cessors that Euclid’s strings of arguments from the properties of theobjects involveddo constitute proofs. According to thisview, Greek theoretical ge- ometry isthus based on proofs. Does that mean that mathematical proof was inventedbythe ancient Greeks(and, by tacit but rampant corollary, that it is thus yet another “proof”of “Western” superiority)? Some writers on mathematics andits history have indeed claimed proof to beaGreekinvention (without necessarily deducing from that the corol- lary that “our” saturation of selected spots of the world with napalm, cluster bombsanddepleted uranium ismorally justiﬁed). In (1972, 3, 14), Morris Kline wrote the following lines: Mathematics as an organized, independent, and reasoned dis- cipline did not exist before http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Visualization, Explanation and Reasoning Styles in MathematicsTertium Non Datur: On Reasoning Styles in Early Mathematics

Part of the Synthese Library Book Series (volume 327)
Editors: Mancosu, Paolo; Jørgensen, Klaus Frovin; Pedersen, Stig Andur
30 pages

/lp/springer-journals/visualization-explanation-and-reasoning-styles-in-mathematics-tertium-LO13wRAXM8

# References (48)

Publisher
Springer Netherlands
ISBN
978-1-4020-3334-6
Pages
91 –121
DOI
10.1007/1-4020-3335-4_6
Publisher site
See Chapter on Publisher Site

### Abstract

JENS HØYRUP TERTIUMNONDATUR: ON REASONINGSTYLES IN EARLY MATHEMATICS Arpad ´ ´ Szabo ´ ´ in memoriam 1.TWOCONVENIENT SCAPEGOATS Some philosophers of mathematics hold that real proof is quite recent and that, for instance, Euclid’s arguments for the correctness of his theorems and constructions do not count as “proofs” (those contributing to the present vol- ume are less dogmatic!). The rest of the world (in as far as it knows at all about the topic) sees things differently. Contemporary mathematicians may ﬁnd Euclid’s proofs insufﬁcient or shaky,but they agree with their prede- cessors that Euclid’s strings of arguments from the properties of theobjects involveddo constitute proofs. According to thisview, Greek theoretical ge- ometry isthus based on proofs. Does that mean that mathematical proof was inventedbythe ancient Greeks(and, by tacit but rampant corollary, that it is thus yet another “proof”of “Western” superiority)? Some writers on mathematics andits history have indeed claimed proof to beaGreekinvention (without necessarily deducing from that the corol- lary that “our” saturation of selected spots of the world with napalm, cluster bombsanddepleted uranium ismorally justiﬁed). In (1972, 3, 14), Morris Kline wrote the following lines: Mathematics as an organized, independent, and reasoned dis- cipline did not exist before

Published: Jan 1, 2005

Keywords: Double False Position