Combining Texts

All the ideas for 'Natural Kinds and Biological Realism', 'On the Infinite' and 'Particulars in Particular Clothing'

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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 / B. Properties / 13. Tropes / a. Nature of tropes
Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
Some kinds are very explanatory, but others less so, and some not at all [Devitt]
27. Natural Reality / G. Biology / 5. Species
Species pluralism says there are several good accounts of what a species is [Devitt]
The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt]