Combining Texts

All the ideas for 'Quodlibeta', 'The Actual and the Possible' and 'On the Infinite'

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


15 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]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Whiteness does not exist, but by it something can exist-as-white [Aquinas]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
A state of affairs is only possible if there has been an actual substance to initiate it [Pruss]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas]
12. Knowledge Sources / B. Perception / 3. Representation
Minds take in a likeness of things, which activates an awaiting potential [Aquinas]