Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'The Statesman'

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25 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
16123 Whenever you perceive a community of things, you should also hunt out differences in the group [Plato]
2. Reason / D. Definition / 2. Aims of Definition
16125 To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
16124 No one wants to define 'weaving' just for the sake of weaving [Plato]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
5961 The soul gets its goodness from god, and its evil from previous existence. [Plato]
19. Language / F. Communication / 1. Rhetoric
283 The question of whether or not to persuade comes before the science of persuasion [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
282 Non-physical beauty can only be shown clearly by speech [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
281 The arts produce good and beautiful things by preserving the mean [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22559 Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
28. God / A. Divine Nature / 2. Divine Nature
279 Only divine things can always stay the same, and bodies are not like that [Plato]