Ideas from 'On the Infinite' by David Hilbert [1925], by Theme Structure
[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,0-521-29648-x]].
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expand these ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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12456
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I aim to establish certainty for mathematical methods
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12461
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We believe all mathematical problems are solvable
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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12462
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Only the finite can bring certainty to the infinite
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9633
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No one shall drive us out of the paradise the Cantor has created for us
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12460
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We extend finite statements with ideal ones, in order to preserve our logic
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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12455
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The idea of an infinite totality is an illusion
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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12457
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There is no continuum in reality to realise the infinitely small
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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12459
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The subject matter of mathematics is immediate and clear concrete symbols
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6. Mathematics / C. Sources of Mathematics / 8. Finitism
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18112
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Mathematics divides in two: meaningful finitary statements, and empty idealised statements
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11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
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9636
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My theory aims at the certitude of mathematical methods
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