Combining Texts

All the ideas for 'fragments/reports', 'On the Infinite' and 'There Are No Abstract Objects'

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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
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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
10. Modality / A. Necessity / 11. Denial of Necessity
Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]