Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'On the Infinite' and 'The Nature of Musical Expression'

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13 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
I aim to establish certainty for mathematical methods [Hilbert]
We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton]