伯纳德·波尔查诺
真理自身存在，不管有没有人想到它们，而逻辑研究它们如何相互推出。
定位
布拉格的神父和数学家：命题和真理“自在地”存在，独立于是否被思考——现代逻辑的先驱。
核心思想
- 自在的命题
- 逻辑后承
- 无限的悖论
影响
受影响于 2
亚里士多德
受其影响
Commentators trace Bolzano’s objective relation of ground and consequence (Abfolge) among truths to Aristotle’s demonstrative science; unlike Aristotle, he admitted infinite chains of grounds (Wissenschaftslehre, 1837). B. Bolzano, Wissenschaftslehre (1837); S. Roski, Bolzano’s Conception of Grounding (2017); SEP “Bernard Bolzano”
依据: AI 草稿
亚里士多德 › 公元前384—前322年
戈特弗里德·威廉·莱布尼茨
受其影响
Bolzano, called ‘the Bohemian Leibniz’ in his lifetime, developed a monadology of simple substances which, unlike Leibniz’s monads, have location in space (Athanasia, 1827). B. Bolzano, Athanasia oder Gründe für die Unsterblichkeit der Seele (1827); P. Simons, “Bolzano’s Monadology”; SEP “Bernard Bolzano”
依据: AI 草稿
戈特弗里德·威廉·莱布尼茨 › 1646–1716
影响了 1
埃德蒙德·胡塞尔
影响了 ✓
Husserl took from Bolzano’s Wissenschaftslehre (1837) the propositions and truths in themselves, ideal unities independent of thinking, for his critique of psychologism (Prolegomena, 1900). E. Husserl, Logische Untersuchungen I: Prolegomena zur reinen Logik (1900); B. Bolzano, Wissenschaftslehre (1837); SEP “Bernard Bolzano”
依据: 亦见于 Wikidata · Wikidata
埃德蒙德·胡塞尔 › 1859–1938
批评
批评了 1
伊曼努尔·康德
批评了
Bolzano rejected Kant’s grounding of mathematics in pure intuitions of space and time and sought proofs from concepts alone (Beyträge zu einer begründeteren Darstellung der Mathematik, 1810). B. Bolzano, Beyträge zu einer begründeteren Darstellung der Mathematik (1810), appendix “Über die Kantische Lehre von der Construction der Begriffe durch Anschauungen”; Wissenschaftslehre (1837); SEP “Bernard Bolzano”
依据: AI 草稿
伊曼努尔·康德 › 1724–1804
作品
- 1837科学论
自在的命题、真理与逻辑后承——一种独立于心理学的逻辑。
立场
Bolzano separated logic from psychology. A proposition in itself is what is said or thought, not the act of thinking: it is true or false whether or not anyone ever grasps it, and truths in themselves form the objective content of all science. On this basis he defined logical consequence by systematically varying the parts of propositions, anticipating ideas later made precise by Tarski. As a mathematician he gave rigorous definitions of continuity and proved central theorems of analysis, and his Paradoxes of the Infinite prepared the way for Cantor’s set theory. Largely overlooked in his lifetime, he later influenced Husserl and the Polish school of logic.
生平与背景
Bernard Bolzano was born in Prague in 1781, son of an Italian art dealer and a German-speaking mother. He studied mathematics and theology, was ordained in 1805 and appointed to the new chair of religious science in Prague. Suspected of rationalism by the authorities in Vienna, he was dismissed in 1819 and forbidden to publish. He lived largely with friends in the countryside and died in Prague in 1848.
其他主要作品
- Purely Analytic Proof (1817)
- Athanasia, or Grounds for the Immortality of the Soul (1827)
- Textbook of the Science of Religion (1834)
- Theory of Science (1837)
- Paradoxes of the Infinite (1851)
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