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朱塞佩·皮亚诺

1858–1932

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皮亚诺认为，算术可以建立在自然数的几条公理之上，数学和逻辑可以用一种精确的符号记法来书写，后来罗素和怀特海采用了这种记法。

定位

分析哲学 · 南欧 · 逻辑学, 科学

意大利数学家，他给自然数以简短的公理形式，并设计了一套为罗素和怀特海所采用的逻辑符号记法；弗雷格1897年针对它为自己的概念文字作了辩护。

核心思想

  • 自然数公理
  • 逻辑与数学的符号记法

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影响

影响了 1

  • 伯特兰·罗素

    影响了 ✓

    Russell met Peano at the Paris congress of 1900, and Principia Mathematica adopts Peano’s logical notation. SEP “Bertrand Russell” (A. D. Irvine), chronology; SEP “The Algebra of Logic Tradition” (S. Burris, J. Legris)

    依据: 亦见于 Wikidata · Wikidata

    伯特兰·罗素 › 1872–1970

批评

相互批评 1

  • 戈特洛布·弗雷格 ⇄ 相互

    批评了 存在争议

    Peano’s 1895 review of Frege’s Grundgesetze I in the Rivista di matematica prompted Frege’s replies of 1896–97; what exactly Peano objected to was not checked. Bibliographic data from the Frege–Peano literature (G. Besler; Rivista di matematica 5, 1895, 122–128 and 6, 1896–99, 53–61); review text not read

    依据: AI 草稿

    受其批评

    In 1897 Frege compared Peano’s logical notation with his own and defended the superiority of his concept-script. Frege, “Über die Begriffsschrift des Herrn Peano und meine eigene” (1897), listed in SEP “Frege’s Logic” (R. Cook, 2023)

    依据: AI 草稿

    戈特洛布·弗雷格 › 1848–1925

作品

  • 1889算术原理：以新方法阐述

    一部拉丁文短篇论著，用符号记法陈述自然数公理，即今天所称的皮亚诺公理。

  • 1895数学公式集

    用皮亚诺的符号记法写成的数学定理汇编，始于1891年；第五版也是最后一版出版于1908年。罗素1900年见到皮亚诺时，被其中的逻辑符号所打动。

立场

Peano is on the map for two things that shaped logic and the foundations of mathematics: a short axiomatisation of the natural numbers, set out in Latin in Arithmetic Principles (1889) and now called the Peano axioms, and a symbolic notation for logic and mathematics, developed in the Rivista and in the Formulario, a collection of mathematical theorems written in it, of which the fifth and last edition appeared in 1908. At the Paris congress of 1900 he met Bertrand Russell, who was struck by his logical symbols and went on to study his work and that of his school; the Principia Mathematica adopts Peano’s notation. Frege compared Peano’s notation with his own concept-script in a paper of 1897 and defended the superiority of his own; Peano’s review of Frege’s Basic Laws of Arithmetic, vol. 1 (1895), which prompted Frege’s replies of 1896–97, has not been checked in the sources, and the line from Frege to Peano is marked as disputed.

生平与背景

Giuseppe Peano was born on 27 August 1858 in Spinetta near Cuneo in Piedmont. He studied at the University of Turin from 1876, graduated in 1880 with high honours and worked first as assistant to Enrico D’Ovidio and then to Angelo Genocchi. From 1886 he also taught at the Royal Military Academy, which dismissed him later because he neglected calculus in favour of his new symbols, and from 1890 he was a professor at Turin. In 1890 he founded the Rivista di matematica, whose first issue appeared in 1891. In 1903 he announced an auxiliary language based on Latin vocabulary with simplified grammar, Latino sine flexione, in which he wrote most of his later work. He died on 20 April 1932 in Turin.

其他主要作品

  • Arithmetic Principles, Presented by a New Method (Arithmetices principia, nova methodo exposita, 1889)
  • Mathematical Formulary (Formulario mathematico, from 1895; fifth edition 1908)
  • Rivista di matematica (journal, founded 1890)

来源: Wikipedia · Wikidata

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