Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Continuity and Irrational Numbers'

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11 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Irony is consciousness of abundant chaos [Schlegel,F]
     Full Idea: Irony is the clear conscousness of eternal agility, of an infinitely abundant chaos.
     From: Friedrich Schlegel (works [1798], Vol 2 p.263), quoted by Ernst Behler - Early German Romanticism p.81
     A reaction: [1800, in Athenaum] The interest here is irony as a reaction to chaos, which has made systematic thought impossible. Do romantics necessarily see reality as beyond our grasp, even if not chaotic? This must be situational, not verbal irony.
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Plato has no system. Philosophy is the progression of a mind and development of thoughts [Schlegel,F]
     Full Idea: Plato had no system, but only a philosophy. The philosophy of a human being is the history, the becoming, the progression of his mind, the gradual formation and development of his thoughts.
     From: Friedrich Schlegel (works [1798], Vol.11 p.118), quoted by Ernst Behler - Early German Romanticism
     A reaction: [1804] Looks like the first sign of rebellion against the idea of having a 'system' in philosophy, making it a key idea of romanticism. Systems are classical? This looks like an early opposition of a historical dimension to static systems. Big idea.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
     Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro)
     A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut'].
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
     Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4)
     A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
     Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1)
     A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
     Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value.
     From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7
     A reaction: [Kitcher says he 'showed' this, rather than just stating it]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Poetry is transcendental when it connects the ideal to the real [Schlegel,F]
     Full Idea: There is a kind of poetry whose essence lies in the relation between the ideal and the real, and which therefore, by analogy with philosophical jargon, should be called transcendental poetry.
     From: Friedrich Schlegel (works [1798], Vol 2 p.204), quoted by Ernst Behler - Early German Romanticism p.78
     A reaction: I think the basic idea is that the imaginative creation of poetry has the power to bridge the gap between the transcendental (presupposed) ideal in Fichte, and nature (which Fichte seems to have excluded from his system).
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
For poets free choice is supreme [Schlegel,F]
     Full Idea: Romantic poetry recognises as its first commandment that the free choice [Wilkür] of the poet can tolerate no law above itself.
     From: Friedrich Schlegel (works [1798], Frag 116 p.32), quoted by Terry Pinkard - German Philosophy 1760-1860 06
     A reaction: This leads to Shelley's 'poets are the unacknowledged legislators of the race'. We should also take it as a response to Kant's categorical imperative, which leads to the Gauguin Problem (wickedness justified by the art it leads to).
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
22. Metaethics / B. Value / 2. Values / g. Love
True love is ironic, in the contrast between finite limitations and the infinity of love [Schlegel,F]
     Full Idea: True irony is the irony of love. It arises from the feeling of finitude and one's own limitation, and the apparent contradiction of these feelings with the concept of infinity inherent in all true love.
     From: Friedrich Schlegel (works [1798], Vol.10 p.357), quoted by Ernst Behler - Early German Romanticism
     A reaction: [c.1827] This is more about idealist philosophy and its yearning for the Absolute than it is about the actual nature of love. Love is the door to the Absolute. The irony is our inability to pass through it.
23. Ethics / F. Existentialism / 3. Angst
Irony is the response to conflicts of involvement and attachment [Schlegel,F, by Pinkard]
     Full Idea: Irony is thus the appropriate stance to feeling that is both inescapably committed and inescapably detached at the same time.
     From: report of Friedrich Schlegel (works [1798]) by Terry Pinkard - German Philosophy 1760-1860 06
     A reaction: This is the epitome of romanticism, which carries over into the dilemmas of existentialism. Striking the right balance between caring and not caring seems to me to be the main focus of modern British people.