Combining Texts

All the ideas for 'Posthumous notes', 'Philosophical Implications of Mathematical logic' and 'Elements of Set Theory'

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11 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]
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]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
22329 Logic is highly general truths abstracted from reality [Russell, by Glock]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
21971 Transcendental philosophy is the subject becoming the originator of unified reality [Kant]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
21569 It is good to generalise truths as much as possible [Russell]