Combining Texts

All the ideas for 'The Nature of Things', 'Axiomatic Thought' and 'The Mengzi (Mencius)'

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22 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9406 A class is natural when everybody can spot further members of it [Quinton]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17963 The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
17966 Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17967 To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17965 The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
17964 Number theory just needs calculation laws and rules for integers [Hilbert]
7. Existence / E. Categories / 5. Category Anti-Realism
15730 Extreme nominalists say all classification is arbitrary convention [Quinton]
8. Modes of Existence / B. Properties / 5. Natural Properties
15728 The naturalness of a class depends as much on the observers as on the objects [Quinton]
9407 Properties imply natural classes which can be picked out by everybody [Quinton]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
15729 Uninstantiated properties must be defined using the instantiated ones [Quinton]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
8520 An individual is a union of a group of qualities and a position [Quinton, by Campbell,K]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
8239 If the King likes music then there is hope for the state [Mengzi (Mencius)]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23398 Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
23400 Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
23399 Each correct feeling relies on an underlying virtue [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
8235 Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
8240 A true king shares his pleasure with the people [Mengzi (Mencius)]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
8237 Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
8241 Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)]
25. Social Practice / E. Policies / 1. War / e. Peace
8238 Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)]
25. Social Practice / F. Life Issues / 6. Animal Rights
8236 Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
17968 By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]