Combining Texts

All the ideas for 'fragments/reports', 'Elements of Set Theory' and 'Apology for Raymond Sebond'

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15 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Why can't a wise man doubt everything? [Montaigne]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne]
3. Truth / A. Truth Problems / 3. Value of Truth
Virtue is the distinctive mark of truth, and its greatest product [Montaigne]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
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
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
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
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
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
We can only define functions if Choice tells us which items are involved [Enderton]
7. Existence / D. Theories of Reality / 3. Reality
We lack some sense or other, and hence objects may have hidden features [Montaigne]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
The soul is in the brain, as shown by head injuries [Montaigne]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]