jairo onorio da Silva

As part of a sequel to his Philosophie der Arithmetik (1891) Husserl, around 1900, considered “relative” and “absolute” completeness. The latter coincides with Hilbert’s “deductive” or “syntactic” completeness. The author gives a modern interpretation of Husserl’s justification of the extension of the natural numbers. A previous interpretation (Claire Ortiz Hill and U. Majer are cited) is deemed fallacious. Much hinges on the author’s appreciation that for Husserl “it is not quite right to say that a system B extends another system A, even if B contains what may look like the same axioms of A plus some extra axioms” (430). Rather the effect of such an addition is to change the meaning of those axioms that A apparently shares with B and even to change the meaning of the symbols used in A.

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in Das Kontinuum. I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular Logische Untersuchungen}