Bernard Bolzano
Truths exist in themselves whether or not anyone thinks them, and logic studies how they follow from one another.
Placement
Prague priest and mathematician: propositions and truths exist “in themselves”, independently of being thought – a forerunner of modern logic.
Key ideas
- Propositions in themselves
- Logical consequence
- Paradoxes of the infinite
Influence
Influenced by 2
Aristotle
influenced by
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”
Evidence: AI draft
Aristotle › 384–322 BCE
Gottfried Wilhelm Leibniz
influenced by
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”
Evidence: AI draft
Gottfried Wilhelm Leibniz › 1646–1716
Influenced 1
Edmund Husserl
influenced ✓
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”
Evidence: also in Wikidata · Wikidata
Edmund Husserl › 1859–1938
Criticism
Criticizes 1
Immanuel Kant
criticised
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”
Evidence: AI draft
Immanuel Kant › 1724–1804
Works
Propositions in themselves, truth and logical consequence – a logic independent of psychology.
Position
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.
Life & context
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.
Further main works
- Purely Analytic Proof (1817)
- Athanasia, or Grounds for the Immortality of the Soul (1827)
- Textbook of the Science of Religion (1834)
- Paradoxes of the Infinite (1851)
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