Combining Texts

All the ideas for 'Testability and Meaning', 'Elements of Set Theory' and '01: Book of Genesis'

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12 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ 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]
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
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]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
God made man in his own image [Anon (Tor)]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
The names of all the types of creature were given forever by Adam [Anon (Tor)]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
And God saw the light, that it was good [Anon (Tor)]