Bourbaki: Mathematics and Truth

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„Mathematicians have always been convinced that what they prove is ‚true‘. It is clear that such a conviction can be only of a sentimental or metaphysical order, and cannot be justified, or even ascribed a meaning which is not tautological, within the domain of mathematics. The history of the concept of truth in mathematics therefore belongs to the history of philosophy and not of mathematics; but the evolution of this concept has had an undeniable influence on the development of mathematics, and for this reason we cannot pass over it in silence.“ (p. 306f.) #Bourbaki #mathematics #truth

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Bourbaki, Nicolas, Elements of Mathematics: Theory of Sets. Berlin, Heidelberg, New York: Springer 2004.

Serres: Parasit und Evolution

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„Der Parasit ist der aktive Operator und die logische Operation der Evolution, der irreversiblen Zeit des Lebens.“ (p. 288) #Serres #Parasit #Evolution #Zeit #Leben

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Serres, Michel, Der Parasit; übersetzt von Michael Bischoff. Frankfurt/M.: Suhrkamp 1981. 391 S., ISBN 978-3-518-07581-4.

Heidegger: Chaos

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„Chaos ist der Name für einen eigentümlichen Vorentwurf der Welt im Ganzen und ihres Waltens. Wieder scheint es, und hier am stärksten, daß ein schrankenloses »biologisches« Den­ken am Werk sei, das die Welt gleichsam einen ins Riesenhafte hinaufgesteigerten »Leib« vorstellt, dessen Leiben und Le­ben das Seiende im Ganzen ausmacht und somit das Sein als ein »Werden« erscheinen läßt. Nietzsche spricht es in seiner späteren Zeit oft genug aus, daß der Leib zum Leitfaden nicht nur der Menschen-, sondern der Weltbetrachtung gemacht werden müsse: der Weltentwurf aus dem Standort des Tieres und der Tierheit. Hier ist die Grunderfahrung der Welt als »Chaos« verwurzelt. Sofern aber der Leib für Nietzsche ein Herrschaftsgebilde ist, kann »Chaos« nicht das wüste Durch­einander meinen, sondern die Verborgenheit des unbewältig­ten Reichtums des Werdens und Strömens der Welt im Gan­zen. Der überall naheliegende Verdacht auf einen Biologismus scheint dadurch seine eindeutige und volle Bestätigung zu fin­den.“ (I, p. 510) #Heidegger #Nietzsche #Chaos #Leib

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Heidegger, Martin, Nietzsche, 2 Bde.. Stuttgart: Neske 61998.

Günther: Reality

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„Reality must have a poly-contextural structure“. (II, p. 288) #Günther #reality

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Günther, Gotthard, Beiträge zur Grundlegung einer operationsfähigen Dialektik. Hamburg: Meiner 1976.

Brunschvicq: Temps et espace

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„De là on ne peut pas conclure que l’arithmétique soit la science du temps comme la géométrie est la science de l’espace. Le temps n’est pas un objet; il est une condition de l’arithmétique, ou plus exactement de la mathématique en général.“ (p. 269) #Brunschvicq #mathématique #arithmétique #temps #géométrie #espace

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Brunschvicg, Léon, Les étapes de la philosophie mathématique. Paris: Alcan 1912. 658 S.