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

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35 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
19635 Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
8215 Hegel was the last philosopher of the Book [Hegel, by Derrida]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
16011 Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
5433 For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
3301 On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
19661 Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux]
2. Reason / C. Styles of Reason / 1. Dialectic
20952 Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie]
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 / E. Structures of Logic / 2. Logical Connectives / c. not
21777 Negation of negation doubles back into a self-relationship [Hegel, by Houlgate]
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]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
5645 The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton]
7. Existence / A. Nature of Existence / 5. Reason for Existence
5646 Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton]
7. Existence / E. Categories / 4. Category Realism
21755 For Hegel, categories shift their form in the course of history [Hegel, by Houlgate]
21754 Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate]
7. Existence / E. Categories / 5. Category Anti-Realism
22079 Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate]
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 / 5. A Priori Synthetic
9225 Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / F. Existentialism / 1. Existentialism
21758 Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
20414 Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
3909 Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton]
26. Natural Theory / A. Speculations on Nature / 1. Nature
4347 When man wills the natural, it is no longer natural [Hegel]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
4188 Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
6686 Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham]