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”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

From its Presocratic beginnings, Western philosophy concerned itself with a quest for unity both in terms of the systematization of knowledge and as a metaphysical search for a unity of being—two trends that can be regarded as converging and culminating in Hegel’s system of absolute idealism. Since Hegel, however, the philosophical quest for unity has become increasingly problematic. Jussi Backman returns to that question in this book, examining the place of the unity of being in the work of Heidegger. Backman (...) sketches a consistent picture of Heidegger as a thinker of unity who throughout his career in different ways attempted to come to terms with both Parmenides’s and Aristotle’s fundamental questions concerning the singularity or multiplicity of being—attempting to do so, however, in a “postmetaphysical” manner rooted in rather than above and beyond particular, situated beings. Through his analysis, Backman offers a new way of understanding the basic continuity of Heidegger’s philosophical project and the interconnectedness of such key Heideggerian concepts as ecstatic temporality, the ontological difference, the turn (Kehre), the event (Ereignis), the fourfold (Geviert), and the analysis of modern technology. (shrink)

Phenomenology, broadly construed, is the study of the meaningful structure of human experience. It is a philosophical tradition that begins with Edmund Husserl, develops with thinkers like Martin H...

Heidegger’s reading of Plato is variable and multifaceted, giving way to different and, at times, opposing interpretations of Plato’s work. To give an example that is relevant to the following pape...