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May 20, 2020·HAL (Le Centre pour la Communication Scientifique Directe)
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Mathematical physics vs Philosophy: Hegel, Pythagorean triples, Spinors and Clifford Algebras

Daniel Parrochia

The german philosopher G.W.F. Hegel (1770-1831) in his Phenomenology of Spirit developed a negative conception of mathematics (for him, the pursuit of equality transforms objects into corpses and leaves them in an inert or dismembered state). This conception is however essentially based on a study of the Euclidean demonstration of the Pythagorean theorem which remains superficial. Not only are there many other proofs, but what is at stake in Pythagoras' theorem refers to complex structures unnoticed by Hegel and which he could not know: relationship between quadratic form and square of a linear form, geometric algebra, spinors and rotations in the space, all concepts of great importance in modern physics. But these are also very close, in fact, to what Hegel privileged: dialectical synthesis and movement. Thus, it is mathematics, and especially mathematical physics, which has now something hegelian, and maybe more than (contemporary) philosophy.

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History and Theory of Mathematics
Philosophy and Historical Thought
Kantian Philosophy and Modern Interpretations
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Jan 1, 2011·Goethe yearbook
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Die Gretchenfrage : Goethe and Philosophies of Religion around 1800

John H. Smith

Die Gretchenfrage: Goethe and Philosophies of Religion around 1800 John H. Smith Already in the Urfaust version, Gretchen poses her eponymous question to Faust, raising the issue of belief in God: Margarete: Wie hast du’s mit der Religion? Du bist ein herzlich guter Mann, Allein ich glaub, du hĂ€ltst nicht viel davon. Faust: Laß das, mein Kind! Du fĂŒhlst, ich bin dir gut; FĂŒr meine Lieben ließ’ ich Leib und Blut, Will niemand sein GefĂŒhl und seine Kirche rauben. Margarete: Das ist nicht recht, man muß dran glauben! Faust: Muß man? (3415–22) He continues with his well-known tirade, or cunning seduction, or philosophical panegyric to Sturm und Drang anti-linguistic feeling, culminating with the exclamations: Nenn es dann, wie du willst, Nenn’s GlĂŒck! Herz ! Liebe! Gott! Ich habe keinen Namen DafĂŒr! GefĂŒhl ist alles; Name ist Schall und Rauch, Umnebelnd Himmelsglut. (3453–58) A very different view of the divine is expressed the opening Prologue in Heaven when the Lord himself speaks about the nature of things: Der Herr: Des Menschen TĂ€tigkeit kann allzuleicht erschlaffen, Er liebt sich bald die unbedingte Ruh; Drum geb’ ich gern ihm den Gesellen zu, Der reizt und wirkt und muß als Teufel schaffen.— Doch ihr, die echten Göttersöhne, Erfreut euch der lebendig reichen Schöne! [End Page 183] Das Werdende, das ewig wirkt und lebt, Umfass’ euch mit der Liebe holden Schranken, Und was in schwankender Erscheinung schwebt, Befestiget mit dauernden Gedanken. (340–49) In the time these lines were written and published, the 1770s, 1790, around 1800, and 1808, major revolutions—a Kantian and a post-Kantian—took place in conceptions of nature, God, and religion. These two passages capture some of the rethinking that occurred during this period. In the first, especially in Faust’s “muß man?” we hear the question that motivates key debates, namely: is there a necessity behind faith? And in the second, we hear a new emphasis on human activity and a confidence in the ability to grasp in thought a God defined as “das Werdende.” One can highlight the relevant issues by varying Gretchen’s question slightly and having her ask more academically: “Was ist der Grund deines Glaubens?” or “Bist du atheistisch?” These were burning questions in the turn from Kant-Reinhold to Fichte to Schelling-Hegel between 1790 and 1815. One can think of the lasting echo of the debate about Spinoza and pantheism, the impact that Kant’s Critical Philosophy had on traditional proofs of the existence of God (as Reinhold stressed in his Briefe ĂŒber die Kantische Philosophie), the Atheismusstreit around Fichte and Foberg in Jena in 1799, Schleiermacher’s lectures Über die Religion, and the exchange between Schelling and Jacobi in 1811–12.1 Although these incidents show that the Gretchenfrage was a dicey one, and that matters of religion and belief were central to the debates raging in those extraordinary decades from 1790–1815, they became less central in the literature dealing with the turn to idealism.2 This essay will argue that the intersection of Goethe and idealism needs to be considered in light of theological and religionsphilosophische motivations.3 Once we take them into account, it makes more sense that Goethe would have been in the thick of this philosophical transition. He had a stake—political, philosophical, and literary—in a conception of God, religion, and life that was different from both that of traditional Christianity and the one that emerged out of Kant’s critiques. That the answer Faust gave in the 1770s was insufficient by 1800 helps explain how his thought, including the reworking of Faust I, and that of his philosophical contemporaries developed in tandem as they sought to provide a fuller answer to this question. The reason for focusing on Faust is that it has a special relationship to idealism. As RĂŒdiger Scholz says of Schelling’s and Hegel’s interpretations: “Das Drama erscheint vom philosophischen System her gedeutet, und umgekehrt wird das philosophische GebĂ€ude durch den Faust verstĂ€ndlich” (Scholz 11).4 The ideas that were being explored—What and why must...

German Literature and Culture Studies
Nietzsche, Schopenhauer, and Hegel
Philosophy and Historical Thought
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