欧几里得第四公设:其真实性及其对希腊数学基础的意义。

IF 0.3 4区 哲学 Q2 Arts and Humanities Science in Context Pub Date : 2022-03-01 Epub Date: 2023-12-07 DOI:10.1017/S0269889723000145
Vincenzo De Risi
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引用次数: 0

摘要

欧几里得的第四个公设说所有的直角都是相等的。在论著的演绎经济中,这个原则一直被认为是有问题的,甚至古代的诠释者也对它的数学作用和认识论地位感到困惑。本文重新考虑了古代关于第四假设的证词,表明没有一定的证据证明它的真实性,也没有证据证明它的虚假。本文还考虑了对这一假设的现代数学解释,指出了各种时代错误。它进一步讨论了第四公设叠加的古代证明的有效性。最后,本文对欧几里得和阿波罗尼乌斯之间希腊几何中角度概念的历史进行了解释,并对希腊化时代第四公设的插值提出了一个猜想。这篇文章有助于对古代数学的公理基础进行普遍的重新评估。
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Euclid's Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics.

The Fourth Postulate of Euclid's Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek geometry between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age. The essay contributes to a general reassessment of the axiomatic foundations of ancient mathematics.

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来源期刊
Science in Context
Science in Context 综合性期刊-科学史与科学哲学
CiteScore
0.80
自引率
0.00%
发文量
1
审稿时长
>12 weeks
期刊介绍: Science in Context is an international journal edited at The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, with the support of the Van Leer Jerusalem Institute. It is devoted to the study of the sciences from the points of view of comparative epistemology and historical sociology of scientific knowledge. The journal is committed to an interdisciplinary approach to the study of science and its cultural development - it does not segregate considerations drawn from history, philosophy and sociology. Controversies within scientific knowledge and debates about methodology are presented in their contexts.
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