Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'On the Nature of Truth and Falsehood' and 'On the Infinite'

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13 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth
For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on Russell]
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]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
19. Language / D. Propositions / 6. Propositions Critique
In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk]