Combining Texts

All the ideas for 'fragments/reports', 'Elements of Set Theory' and 'The Sophist'

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25 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
1642 We must fight fiercely for knowledge, understanding and intelligence [Plato]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
1645 The desire to split everything into its parts is unpleasant and unphilosophical [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
287 Good analysis involves dividing things into appropriate forms without confusion [Plato]
1644 Dialectic should only be taught to those who already philosophise well [Plato]
2. Reason / C. Styles of Reason / 2. Elenchus
20478 In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato]
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]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [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]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
11278 What does 'that which is not' refer to? [Plato]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
1643 If statements about non-existence are logically puzzling, so are statements about existence [Plato]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
7022 To be is to have a capacity, to act on other things, or to receive actions [Plato]
7. Existence / D. Theories of Reality / 6. Physicalism
1641 Some alarming thinkers think that only things which you can touch exist [Plato]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10784 Whenever there's speech it has to be about something [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
16122 Good thinkers spot forms spread through things, or included within some larger form [Plato]
10422 The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
15855 If we see everything as separate, we can then give no account of it [Plato]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
1637 A soul without understanding is ugly [Plato]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / A. Egoism / 1. Ethical Egoism
1636 Wickedness is an illness of the soul [Plato]
25. Social Practice / E. Policies / 5. Education / c. Teaching
1638 Didactic education is hard work and achieves little [Plato]