Combining Texts

All the ideas for 'Science and Method', 'On the Infinite' and 'Natural Theology'

expand these ideas     |    start again     |     specify just one area for these texts


16 ideas

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 / 2. Geometry
One geometry cannot be more true than another [Poincaré]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Only the finite can bring certainty to the infinite [Hilbert]
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]
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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
All the signs of design found in a watch are also found in nature [Paley]
Even an imperfect machine can exhibit obvious design [Paley]
Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley]
From the obvious purpose and structure of a watch we must infer that it was designed [Paley]
No organ shows purpose more obviously than the eyelid [Paley]