Combining Texts

All the ideas for 'Reflections on my Critics', 'On the Infinite' and 'Summa'

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15 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
'Truth' may only apply within a theory [Kuhn]
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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Prime matter is free of all forms, but has the potential for all forms [Eustachius]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
14. Science / B. Scientific Theories / 1. Scientific Theory
Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird]
14. Science / B. Scientific Theories / 5. Commensurability
In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn]