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)

The Heidegger–Deleuze relationship has attracted significant attention of late. This paper contributes to this line of research by examining Deleuze’s claim, recently reiterated and developed by Philip Tonner, that Heidegger offers a univocal conception of Being where there is one sense of Being that is said throughout all entities. Although these authors maintain that this claim holds across Heidegger’s oeuvre, I purposefully adopt a conservative hermeneutical strategy that focuses on two writings from the 1927–1928 period—Being and Time and the following (...) year’s lecture course translated as The Metaphysical Foundations of Logic—and emphasize the lesson of the ontological difference that Being is always the Being of an entity, to argue that with regards to these texts, at least, an alternative equivocal interpretation is possible in which Being is always said differently. The conclusion draws out the implications of this for the relationship between Heidegger’s fundamental ontology and Deleuze’s differential ontology. (shrink)

Heidegger accuses ontotheologies of reducing God to a mere object of intelligibility, and thereby falsifying them, and in doing so distracting attention from or forgetting the ground of Being as unconcealment in the Lichtung. Conventional theistic responses to Heidegger’s ontotheological challenges proceed by offering analogy, speech-act theorising or negative theology as solutions. Yet these conventional solutions, however suitable as responses to Heidegger’s Die ontotheologische Verfassung der Metaphysik version of the ontotheological problem, still fall foul of Heidegger’s more profound characterisation of (...) ontotheology in his treatise Seinsgeschichtliche Bestimmung des Nihilismus. Therein Heidegger characterises ontotheology as a metaphysics that posits a first-causal ground of Being combining together an essentia and an existentia. This article presents an alternative family of metaphysical schemes that instead develop their metaphysical ‘theology’ in a non-naive epistemological context, and indeed maintain that God cannot be cognised by us because we cannot reconcile the whatness and the that-ness of God in one coherent thought. God is thus unintelligible, and though able to be signified, cannot be reduced thereby to an object of cognition, and is not posited at the expense of considering the ground of Being as the encounter in Lichtung with Being. The two examples of such disrupted cognition accounts of a non-ontheological metaphysics are from the medieval Franciscan John Duns Scotus and the British Idealist Francis Herbert Bradley. The paper ends with a discussion of the characteristic ‘disrupted cognition’ as a movement between two concepts that are unreconcilable within thought, without being contradictories or contraries, and explores the differences between theological and philosophical employments of ‘disrupted cognition’. (shrink)