Combining Texts

All the ideas for 'Things', 'Moral Relativism' and 'Elements of Set Theory'

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12 ideas

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]

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

7783	Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist [Lowe]

12. Knowledge Sources / B. Perception / 5. Interpretation

22449

When we say 'is red' we don't mean 'seems red to most people' [Foot]

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism

22451

All people need affection, cooperation, community and help in trouble [Foot]

22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value

22452

Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot]