Abstract
Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis.
Highlights
Philosophical phenomenology (Husserl’s doctrine, first of all) establishes an inherent link between: (a) logic and mathematics; (b) philosophy; (c) psychology: The link relates the three by means a kind of transcendental idealism in the German philosophical tradition
A bridge for transfer and reinterpretation between notions of psychology, logic and mathematics is created under the necessary condition for those concepts to be considered as philosophical as referred to that kind of transcendental subject
Mach’s and Husserl’s doctrines share descriptivism, but they are radically different to phenomenality distinguishing the phenomenalism of the former from the phenomenology of the latter
Summary
Philosophical phenomenology (Husserl’s doctrine, first of all) establishes an inherent link between: (a) logic and mathematics; (b) philosophy; (c) psychology: The link relates the three by means a kind of transcendental idealism in the German philosophical tradition. If one applies Mach’s economy of thought to his “elements” reducing them to the necessary properties and “razoring” any metaphysical hypotheses about their metaphysical nature including the sensual one, they might be identified as the successive stages of Husserl’s reduction. The unification of Mach’s phenomenalism and Husserl’s phenomenology leads to a kind of Pythagoreanism reducing all being to the natural numbers just as in Leopold Kroneker famous sentence. The last, 5th Section summarizes and generalizes the paper to a few conclusions and directions for future work
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