Combining Texts

All the ideas for 'fragments/reports', 'On the Infinite' and 'Ontology and the Vicious Circle Principle'

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13 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Could we replace sets by the open sentences that define them? [Chihara, by Bostock]
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 / E. Objects over Time / 8. Continuity of Rivers
Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]