Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental

Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24 (2021)
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Abstract

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself.

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Vasil Penchev
Bulgarian Academy of Sciences

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References found in this work

Logical Investigations.Edmund Husserl - 1970 - London, England: Routledge. Edited by Dermot Moran.
Logical Investigations.Edmund Husserl & J. N. Findlay - 1972 - Journal of Philosophy 69 (13):384-398.
Cybernetics or Control and Communication in the Animal and the Machine.N. Wiener - 1948 - Revue Philosophique de la France Et de l'Etranger 141:578-580.
Sein und Zeit.Martin Heidegger - 1929 - Mind 38 (151):355-370.

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