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
Famous quotes containing the words work, mathematical and/or philosophy:
“Again and again, faith in a possible satisfaction of the human race breaks through at the very moments of most zealous discord because humankind will never be able to live and work without this consoling delusion of its ascent into morality, without this dream of final and ultimate accord.”
—Stefan Zweig (18811942)
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“We are tainted by modern philosophy which has taught us that all is good, whereas evil has polluted everything and in a very real sense all is evil, since nothing is in its proper place.”
—Joseph De Maistre (1753–1821)