Combining Texts

All the ideas for 'On the Heavens', 'On the Infinite' and 'Liberalism and the Limits of Justice'

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24 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
19740 A very hungry man cannot choose between equidistant piles of food [Aristotle]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12456 I aim to establish certainty for mathematical methods [Hilbert]
12461 We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
9633 No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
12460 We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
12462 Only the finite can bring certainty to the infinite [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
12455 The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457 There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459 The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
18112 Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
9636 My theory aims at the certitude of mathematical methods [Hilbert]
22. Metaethics / B. Value / 2. Values / b. Successful function
398 Each thing that has a function is for the sake of that function [Aristotle]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
20594 Choosers in the 'original position' have been stripped of most human characteristics [Sandel, by Tuckness/Wolf]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
21120 The self is 'unencumbered' if it can abandon its roles and commitments without losing identity [Sandel, by Shorten]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
394 An unworn sandal is in vain, but nothing in nature is in vain [Aristotle]
396 There has to be some goal, and not just movement to infinity [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
16102 Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML]
17463 An element is what bodies are analysed into, and won't itself divide into something else [Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
399 If the more you raise some earth the faster it moves, why does the whole earth not move? [Aristotle]
27. Natural Reality / C. Space / 1. Void
20918 Void is a kind of place, so it can't explain place [Aristotle]
27. Natural Reality / E. Cosmology / 1. Cosmology
403 The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle]
402 The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle]
27. Natural Reality / E. Cosmology / 3. The Beginning
1498 Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle]
27. Natural Reality / E. Cosmology / 10. Multiverse
395 It seems possible that there exists a limited number of other worlds apart from this one [Aristotle]