Ideas from 'On the Infinite' by David Hilbert [1925], by Theme Structure
[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,052129648x]].
Click on the Idea Number for the full details 
back to texts

expand these ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456

I aim to establish certainty for mathematical methods

12461

We believe all mathematical problems are solvable

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / a. The Infinite
9633

No one shall drive us out of the paradise the Cantor has created for us

12462

Only the finite can bring certainty to the infinite

12460

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
12455

The idea of an infinite totality is an illusion

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / k. Infinite divisibility
12457

There is no continuum in reality to realise the infinitely small

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12458

Kant taught that mathematics is independent of logic, and cannot be grounded in it

6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459

The subject matter of mathematics is immediate and clear concrete symbols

6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112

Mathematics divides in two: meaningful finitary statements, and empty idealised statements

11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636

My theory aims at the certitude of mathematical methods
