Hilbert Mathematics Versus (or Rather “Without”) Gödel Mathematics: V. Ontomathematics!

EasyChair Preprint no. 13069

Abstract

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”.

Keyphrases: Aletheia, Arithmetics, Boolean algebra, epoché to reality, foundations of mathematics, Fundamental Ontology, Heidegger, Hilbert arithmetic, Hilbert mathematics, Husserl, information and quantum information, language, locality and nonlocality, ontomathematics, Phenomenology, propositional logic, Pythagoreanism, set theory

@Booklet{EasyChair:13069,
  author = {Vasil Penchev},
  title = {Hilbert Mathematics Versus (or Rather “Without”) Gödel Mathematics: V. Ontomathematics!},
  howpublished = {EasyChair Preprint no. 13069},

  year = {EasyChair, 2024}}