Combining Texts

All the ideas for 'On the Infinite', 'works' and 'Mathematical Thought from Ancient to Modern Times'

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13 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17606 Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
3534 To be is to have causal powers [Alexander,S]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
3398 Epiphenomenalism makes the mind totally pointless [Alexander,S]