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)

Hubert Dreyfus's commentary on Being and Time has been a long time in preparation but it has also been worth the wait. Dreyfus limits his account to the first division of Part I of Being and Time with some passages from Division II brought into the discussion. For Dreyfus, the first 230 pages of Being and Time comprise Heidegger's most important metaphysical innovations, while Division II, the “existentialist” side of Heidegger, contains discussions of death, guilt, resoluteness and Angst rarely, if (...) ever, mentioned in any other works. (shrink)

This dissertation shows how Martin Heidegger and Michel Foucault, by questioning the very understanding of the subject-object relationship on which all epistemology is grounded, challenge two of its most cherished beliefs: 1. Thought and knowledge are essentially activities on the part of the subject understood anthropologically or transcendentally. 2. The history of knowledge exhibits teleological progress towards a better and more comprehensive account of its objects. In contrast to traditional epistemology, both Heidegger and Foucault show how thought and knowledge are (...) not just acts, which can be attributed to the subject but also events which elude any such subjective characterization. They also show us how the history of knowledge exhibits ruptures when the very character of knowledge undergoes drastic transformation in the course of history. The dissertation concludes by hinting at how these new accounts of thought and knowledge have the potential to shake the very foundations of epistemology and lead us to a new framework for discussing the most basic questions of epistemology, towards an epistemology of ruptures. (shrink)