The phenomenological roots of nonstandard mathematics

In this paper we intend to interpret the axiomatical and formal structure of nonstandard mathematics in terms of a phenomenological analysis by means of two approaches: On the formal-deductive level by means of conservative enlargements of relatively definite axiomatical systems to which Husserl made reference in his 1901 Göttingen lectures ([9], Abhand. VI, VII) and on a formal ontological level by means of the reduction of principles of analytical logic to subjective evidences of experience. In the latter approach we attempt a phenomenological interpretation to the notion of urelements and that of pro- longation principles in nonstandard structures. Further, we demonstrate the relevance of the shift of the horizon approach in Husserlian sense in the construction of alternative models of nonstandard mathematics in the intensional part of nonstandard analysis.

Keywords: Horizon of life-world, nonstandard theories, non-Cantorian theories, relatively definite system, urelement, Continuum.