Stathis LIVADAS
The phenomenological roots of nonstandard mathematics
Abstract.
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. |