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)

Heidegger claimed that Western philosophy ended, failed even, in the German Idealist tradition. In The Culmination, Robert B. Pippin explores the ramifications of this charge through a masterful survey of Western philosophy, especially Heidegger's critiques of Hegel and Kant. Pippin argues that Heidegger's basic concern was to determine sources of meaning for human life, particularly those that had been obscured by Western philosophy's attention to reason. The Culmination offers a new interpretation of Heidegger, German Idealism, and the fate of Western (...) rationalism. (shrink)

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different categories, (...) on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

Both Heidegger and Wittgenstein consider the possibility of a philosophical inquiry of an absolutely universal scope—an inquiry into the being of all beings, in Heidegger’s case, and into the logical form of everything that can be meaningfully said, in Wittgenstein’s. Moreover, they both raise the worry that the theoretical language by means of which we speak of particular beings and assert particular facts is not suited to this task. And yet their own philosophical work seems to include many assertions of (...) ordinary, theoretical language. Are they being inconsistent? Or are they hoping to use theoretical language in a way that conveys what cannot be said in that language? Much of the scholarship on each of these thinkers takes the form of one of the two horns of this dilemma. In the context of Wittgenstein scholarship, however, a third alternative has been proposed: the Resolute Reading of the Tractatus. My aim is to establish the availability of a similar solution to Heidegger’s predicament. It will emerge that Heidegger rejects the possibility of a theoretical account of being and pursues a project of a radically different sort, whose goal is to bring about a transformation of our fundamental relation to being. (shrink)

Martin Heidegger's philosophy is famous for being unusually rich. It ranges over technology, poetry, theology, history, and many other subjects. In this paper, I focus my attention on two topics which are particularly close to the hearts of analytic philosophers: logic and language. I show that Heidegger faces two different kinds of paradoxes: an ontic paradox and an ontological paradox. Moreover, for each one of these paradoxes, I give an overview of how both Heidegger and the philosophers who engage with (...) his thought have tried to overcome them by challenging either a certain account of language or the authority of logic in philosophical discourse. (shrink)

In this article, I distinguish Wittgenstein's conception of the dissolution of philosophical problems from that of Carnap. I argue that the conception of dissolution assumed by the therapeutic interpretations of the Tractatus is more similar to Carnap's than to Wittgenstein's for whom dissolution involves spelling out an alternative in the context of which relevant problems do not arise. To clarify this I outline a non‐therapeutic resolute reading of the Tractatus that explains how Wittgenstein thought to be able to make a (...) positive contribution to logic and the philosophy thereof without putting forward any (ineffable) theses. This explains why there is no paradox in the Tractatus. (shrink)

While all of the great philosophers are difficult to read, Heidegger and Wittgenstein seem to be so in striking ways. Their writings are oddly reluctant to yield up to us what we might think of as ‘their philosophical claims’; and both seem to manifest an attitude towards argument unlike that of most contemporary philosophers. This paper will re-consider these features of Heidegger’s and Wittgenstein’s work in the light of some common themes in their understanding of philosophical confusion. Given that understanding, (...) writings that would combat such confusion must meet rather distinctive objectives and, as a result, may be required to take on rather distinctive forms. The paper will explore these possibilities, drawing, in particular, on the motif of ‘recollection’ upon which both Heidegger and Wittgenstein draw, Heidegger's scattered remarks on 'formal indication', and The Sophist lectures’ discussion of Platonic dialectic. (shrink)

This paper intends to offer a new assessment of the “Ontological Difference”, one of Martin Heidegger’s mainstays, in the light of the metaphysical view called “dialetheism”. In the first paragraph I briefly summarize the main argument of Heidegger’s contradiction of Being, where OD is present as a premise. In the second paragraph I introduce dialetheism, indicate two kinds of dialetheic solutions to the paradox and explain why they face comeback troubles from OD. The third paragraph is devoted to a review (...) of Heidegger’s uses of OD and underlines the crucial role of negation in it. In the fourth paragraph I investigate the philosopher’s account of negation and show similarities with the account provided by the paraconsistent logic called “Logic of Paradox”. The fifth paragraph puts forward two possible readings of OD, the first based on the classical notion of negation and the second on the notion of negation pointed out in the previous paragraph. The second reading is proved suitable for dialetheists and in accordance with the exegesis of some textual passages from Heidegger’s late works. (shrink)

ABSTRACTIt is well known that, from the beginning to the end of his philosophical trajectory, Martin Heidegger tries to develop a fundamental ontology which aims at answering the so-called question...