Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental

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

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.

Author's Profile

Vasil Penchev
Bulgarian Academy of Sciences

Analytics

Added to PP
2021-08-31

Downloads
184 (#68,171)

6 months
56 (#66,269)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?