Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'On the Infinite' and 'There is No A Priori (and reply)'

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15 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
We believe all mathematical problems are solvable [Hilbert]
I aim to establish certainty for mathematical methods [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 / 5. Reason for Existence
Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
The actual universe is the richest composite of what is possible [Leibniz]
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 / 4. A Priori as Necessities
How could the mind have a link to the necessary character of reality? [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt]