Combining Texts

All the ideas for 'Review of Bob Hale's 'Abstract Objects'', 'A Combinatorial Theory of Possibility' and 'On the Infinite'

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14 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
We can't presume that all interesting concepts can be analysed [Williamson]
3. Truth / B. Truthmakers / 6. Making Negative Truths
Negative existentials have 'totality facts' as truthmakers [Armstrong, by Lewis]
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 / 1. Mathematical Platonism / a. For mathematical platonism
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
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]
10. Modality / B. Possibility / 1. Possibility
All possibilities are recombinations of properties in the actual world [Armstrong, by Lewis]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]