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

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27 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
7910 Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
2666 Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero]
3. Truth / B. Truthmakers / 10. Making Future Truths
21390 Future events are true if one day we will say 'this event is happening now' [Carneades]
21672 We say future things are true that will possess actuality at some following time [Carneades, by Cicero]
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]
9. Objects / F. Identity among Objects / 6. Identity between Objects
15825 Carneades denied the transitivity of identity [Carneades, by Chisholm]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / A. Necessity / 3. Types of Necessity
21389 Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades]
16. Persons / F. Free Will / 2. Sources of Free Will
21671 Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
21391 Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero]
16. Persons / F. Free Will / 6. Determinism / b. Fate
21674 Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero]
22. Metaethics / B. Value / 2. Values / i. Self-interest
7398 Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck]
25. Social Practice / D. Justice / 1. Basis of justice
21392 People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
7909 The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
7908 At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha]