Mathematics and positive sciences: a reflection following Heidegger

Bagni, Giorgio T.

doi:10.1007/s10649-009-9214-0

Cited by 13 publications

(3 citation statements)

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“…Michel Foucault ended his famous work "Les Mots et les Choses: Une archéologie des sciences humaines" (1966) with the picturesque and frequently cited metaphor elucidating 22 Harries 2010. Nonetheless, there exist papers about Heidegger's viewpoint to mathematics or to natural sciences (e.g., Kochan 2017;Ma, Brakel 2014;Bagni 2010;Dea 2009;McManus 2007;Glazebrook 2000a: Roubach 1997Kovacs 1990;Kockelmans 1985;Rouse 1985;Kolb 1983;Kisiel 1977) ; also in comparison with Husserl (e.g., Carson 2010;Videla 1994;Kockelmans 1989;Cahoone 1986;Kisiel 1973; quite clearly Heidegger's own position on "humanism" especially briefly and visually as a vanishing figure drawn on the ocean beach sand, which the next tide will obliterate.…”

Section: The Vanishing "Figure Drawn On the Ocean Beach Sand" Or Huma...mentioning

confidence: 99%

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

Penchev

2024

Preprint

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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 theproper philosophical sense of both, including philosophy of mathematics and philosophy of physics notless than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization ofontology 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’sphenomenology 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 thenewly 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” andthe foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as arelation of locality and nonlocality, respectively as a motion from nonlocality to locality if both arephysically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from thepre-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 contemporaryphysics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’sopposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowingfor 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 thefoundations of mathematics, where the latter two ones are both identified with Boolean algebra, and theformer is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it afterdoubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of thefoundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where thelatter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newlyintroduced substance of quantum information being physically dimensionless and generalizing classicalinformation measured in bits. The substance of information, whether classical or quantum, visualizes theway of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic andHilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics tothe Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity,is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectlesschoice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by MichelFoucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as thephilosophy of locality ends the study.

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Section: The Vanishing "Figure Drawn On the Ocean Beach Sand" Or Huma...mentioning

confidence: 99%

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

Penchev

2024

Preprint

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“…Há, portanto, uma cooriginariedade Dasein-mundo. Para Bagni 27 , essa postura coloca-se contra a concepção cartesiana de mundo e de subjetividade, por essa assumir um ego independentemente de seu entorno.…”

Section: A Questão Do Corpo Apresenta Alguma Importância Teórica No Punclassified

As Insuficiências Na Analítica Existencial E Os Posicionamentos Heideggerianos Sobre a Questão Do Corpo

Albuquerque¹

2014

Problemata: Rev. int. filos.

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The first is to provide criteria from which the horizon of the body is evaluated as a phenomenological aspect of clear relevance to the apprehension of the phenomenon of existence as intentionality. The second is to show at what times the existential analytic "demands" phenomenology of corporeality and, finally, determine whether there is a possibility, despite the silence existent in Being and Time on the theme of the body in Dasein's manner of being-and even the lack of a work to take this question in the foreground-to find elements in Heideggerian thought to sustain a consistent position on the body.

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“…Harries 2010. Nonetheless, there exist papers about Heidegger's viewpoint to mathematics or to natural sciences (e.g.,Kochan 2017;Ma, Brakel 2014;Bagni 2010; Dea 2009;McManus 2007;Glazebrook 2000a: Roubach 1997Kovacs 1990;Kockelmans 1985;Rouse 1985;Kolb 1983;Kisiel 1977) ; also in comparison withHusserl (e.g., Carson 2010;Videla 1994; Kockelmans 1989;Cahoone 1986;Kisiel 1973; Electronic copy available at: https://ssrn.com/abstract=4793916…”

mentioning

confidence: 99%

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

Penchev

2024

SSRN Journal

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Mathematics and positive sciences: a reflection following Heidegger

Cited by 13 publications

References 14 publications

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

As Insuficiências Na Analítica Existencial E Os Posicionamentos Heideggerianos Sobre a Questão Do Corpo

Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!

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