Bernard Bolzano
modernEarly Analytic Philosophy / Philosophy of Mathematics1781 – 1848
Bernard Bolzano (1781-1848) was a Bohemian mathematician, logician, philosopher, and Catholic priest whose rigorous work on the foundations of analysis anticipated developments in mathematics by decades. He is best known for providing purely analytic proofs of theorems previously justified by geometric intuition, and for his posthumously influential work on logic and the theory of science.
Notable Achievements
1
Proved the intermediate value theorem using a purely analytic method (1817)
2
Authored the Wissenschaftslehre (Theory of Science), a foundational work in logic and semantics
3
Developed an early rigorous definition of continuity, predating Cauchy and Weierstrass
4
Introduced the concept of 'propositions in themselves' (Sätze an sich) as mind-independent logical objects
5
Pioneered set-theoretic reasoning about infinity in Paradoxes of the Infinite