Combining Philosophers

All the ideas for Paul Bernays, Philolaus and J.O. Urmson

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12 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
13750 Analysis aims at the structure of facts, which are needed to give a rationale to analysis [Urmson, by Schaffer,J]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10304 Very few things in set theory remain valid in intuitionist mathematics [Bernays]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10303 Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10306 Mathematical abstraction just goes in a different direction from logic [Bernays]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
472 No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
473 There is no falsehood in harmony and number, only in irrational things [Philolaus]
1519 Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus]
1518 Everything must involve numbers, or it couldn't be thought about or known [Philolaus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
469 Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
476 Self-created numbers make the universe stable [Philolaus]
27. Natural Reality / E. Cosmology / 1. Cosmology
1787 Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius]