Combining Texts

All the ideas for 'In Metaphysics', 'On the Infinite' and 'Commentary on Sentences'

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14 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 / 5. The Infinite / a. The Infinite
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]
Only the finite can bring certainty to the infinite [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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Accidents always remain suited to a subject [Bonaventura]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substance is only grasped under the general heading of 'being' [Duns Scotus]
9. Objects / E. Objects over Time / 6. Successive Things
Successive things reduce to permanent things [Bonaventura]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]