Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'On the Infinite' and 'Dialectic of Enlightenment'

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14 ideas

1. Philosophy / H. Continental Philosophy / 5. Critical Theory
Adorno and Horkheimer subjected the Enlightenment to 'critical theory' analysis [Adorno/Horkheimer, by Finlayson]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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 / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
De Sade said it was impossible to rationally argue against murder [Adorno/Horkheimer]