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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6. Mathematics / A. Nature of Mathematics / 1. Mathematics
I aim to establish certainty for mathematical methods
We believe all mathematical problems are solvable
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / a. The Infinite
Only the finite can bring certainty to the infinite
No one shall drive us out of the paradise the Cantor has created for us
We extend finite statements with ideal ones, in order to preserve our logic
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion
6. Mathematics / A. Nature of Mathematics / 4. The Infinite / k. Infinite divisibility
There is no continuum in reality to realise the infinitely small
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Kant taught that mathematics is independent of logic, and cannot be grounded in it
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The subject matter of mathematics is immediate and clear concrete symbols
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods