Combining Texts

All the ideas for 'talk', 'Elements of Set Theory' and 'Ancient Philosophy: very short introduction'

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13 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
12036 Xenophanes began the concern with knowledge [Annas]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
12046 Plato was the first philosopher who was concerned to systematize his ideas [Annas]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1403 A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
12037 Euripides's Medea is a key case of reason versus the passions [Annas]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
12040 Virtue is a kind of understanding of moral value [Annas]