Background
Becker, Oskar was born on September 5, 1889 in Leipzig.
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Oskar Becker
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Education
Studied at Leipzig; habilitated at Freiburg, where he was Husserl’s assistant.
Career
1923-1930, edited Husserl’s Jahrbuch with Heidegger. 1928-1931, Associate Professor, Freiburg. 1931 to retirement Professor Ordinarius of the History of Mathematics, Bonn.
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Husserl hoped that Heidegger and Becker would complete his massive research plan—Heidegger the human sciences part and Becker the natural sciences part. Philosophically and politically Heidegger was a great disappointment to Husserl. Initially Becker worked on Husserl’s project. Later he was influenced by Heidegger’s hermeneutics and finally he developed his own ‘mantic phenomenology’. In his later life Becker made only passing references to his phenomenological past. In his ‘Contributions’ (1923) he employed Husserl’s concept of ‘definite multiplicities’ in investigating the various fundamental concepts of mathematical continua. Following Hermann Weyl. he opted for L. E. J. Brouwer's intuitionism. which guarantees mathematical entities by a stepby-step construction and avoids the paradoxes of formalism. Investigating the phenomenal constitution of spatiality, he demonstrated the rationality of the intuitive foundation of the continuum and Euclidean geometry, idealized the vague morphology of space into an exact metric by a process of ‘going to the limit’ and demonstrated the transcendental necessity of physical systems and of Euclidean axioms. Following Heidegger, his ‘Mathematical Existence. Investigations on Logic and the Ontology of Mathematical Phenomena' (1927) incorporates mathematical existence within a ‘hermeneutic of facticity’. Attempting a synthesis of mathematical-constructivism and hermeneutics, he also investigated lifeworld philosophy and the anthropological foundation of mathematical science. He later redressed the ‘one-sided’ hermeneutical imbalance and introduced Dawesen as a counterconcept to Dasein. As the ahistorical realms of nature, aesthetic existence and the unconscious lie ‘before, under and outside’ historical factuality, they cannot be hermeneutically interpreted but only ‘mantically deciphered’. Like his mathematical works, his aesthetic studies again treat of the ahistorical as a ‘parontological’ or ‘hyperontological’ phenomenon. In his ‘On the Logic of Modalities' (1930) he demonstrated that C. I. Lewis’s S3 System of ‘strict implication’ involved—besides Lewis’ six modalities—numerous irreducible complex modalities. To achieve intuitive understanding, he added a postulate reducing iterated modalities, such that ‘improper’ modalities, resulting from iterated negation (~), reduce to two: ‘p’ and ‘~p and ‘proper’ modalities, resulting from iterated necessity (□) and possibility (0) reduce to 12. Adding a further postulate, he defined a system of six modalities. By translating A. Heyting’s connectives into Lewis’s connectives, he gave a modal interpretation of intuitionistic logic and enabled others to find a modal meaning forall of Heyting’s theorems. In his Investigations on the Modal Calculus (1952) he also created a deontic logical system parallel to modal logic. Following his influential ‘Eudoxos Studies', his succession of mathematicalhistorical investigations led to his standard work. The Foundation of Mathematics in its Historical Development (1954), which covers the history of mathematics from its Egyptian and Babylonian origins to the modern schools of logicism, intuitionism and formalism. He died shortly after editing On the History of Greek Mathematics (1965).
