Bernard Bolzano
Prawdy istnieją same w sobie, niezależnie od tego, czy ktokolwiek je myśli, a logika bada, jak wynikają one jedna z drugiej.
Umiejscowienie
Praski kapłan i matematyk: zdania i prawdy istnieją „same w sobie”, niezależnie od tego, czy są myślane – prekursor nowoczesnej logiki.
Kluczowe idee
- Zdania same w sobie
- Wynikanie logiczne
- Paradoksy nieskończoności
Wpływ
Pod wpływem 2
Arystoteles
pod wpływem
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”
Źródło: szkic AI
Arystoteles › 384–322 p.n.e.
Gottfried Wilhelm Leibniz
pod wpływem
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”
Źródło: szkic AI
Gottfried Wilhelm Leibniz › 1646–1716
Wpływ na 1
Edmund Husserl
wpływ na ✓
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”
Źródło: także w Wikidanych · Wikidata
Edmund Husserl › 1859–1938
Krytyka
Krytykuje 1
Immanuel Kant
krytykuje
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”
Źródło: szkic AI
Immanuel Kant › 1724–1804
Dzieła
Zdania same w sobie, prawda i wynikanie logiczne – logika niezależna od psychologii.
Stanowisko
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.
Życie i kontekst
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.
Dalsze główne dzieła
- 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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