Work in Phenomenology and Mathematical Philosophy
He published Mathematical Existence his magnum opus, in the Yearbook in 1927. A famous work that also appeared in the Yearbook that year was Martin Heidegger's Being and Time. Becker frequently attended Heidegger's seminars during those years.
Becker utilized not only Husserlian phenomenology but, much more controversially, Heideggerian hermeneutics, discussing arithmetical counting as "being toward death". His work was criticized both by neo-Kantians and by more mainstream, rationalist logicians, to whom Becker feistily replied. This work has not had great influence on later debates in the foundations of mathematics, despite its many interesting analyses of the topic of its title.
Becker debated with David Hilbert and Paul Bernays over the role of the potential infinite in Hilbert's formalist metamathematics. Becker argued that Hilbert could not stick with finitism, but had to assume the potential infinite. Clearly enough, Hilbert and Bernays do implicitly accept the potential infinite, but they claim that each induction in their proofs is finite. Becker was correct that complete induction was needed for assertions of consistency in the form of universally quantified sentences, as opposed to claiming that a predicate holds for each individual natural number.
Read more about this topic: Oskar Becker
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